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

Percentage Accurate: 79.8% → 92.8%

Time: 17.8s

Alternatives: 19

Speedup: 0.8×

• 37.3% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 79.8% 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: 92.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \frac{\mathsf{fma}\left(a, t \cdot -4, \mathsf{fma}\left(x, 9 \cdot \frac{y}{z}, \frac{b}{z}\right)\right)}{c}\\ \mathbf{if}\;z \leq -1.6 \cdot 10^{+45}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 5 \cdot 10^{+121}:\\ \;\;\;\;\frac{\mathsf{fma}\left(a \cdot \left(z \cdot -4\right), t, \mathsf{fma}\left(x, 9 \cdot y, b\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (fma a (* t -4.0) (fma x (* 9.0 (/ y z)) (/ b z))) c)))
   (if (<= z -1.6e+45)
     t_1
     (if (<= z 5e+121)
       (/ (fma (* a (* z -4.0)) t (fma x (* 9.0 y) b)) (* z c))
       t_1))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = fma(a, (t * -4.0), fma(x, (9.0 * (y / z)), (b / z))) / c;
	double tmp;
	if (z <= -1.6e+45) {
		tmp = t_1;
	} else if (z <= 5e+121) {
		tmp = fma((a * (z * -4.0)), t, fma(x, (9.0 * y), b)) / (z * c);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(fma(a, Float64(t * -4.0), fma(x, Float64(9.0 * Float64(y / z)), Float64(b / z))) / c)
	tmp = 0.0
	if (z <= -1.6e+45)
		tmp = t_1;
	elseif (z <= 5e+121)
		tmp = Float64(fma(Float64(a * Float64(z * -4.0)), t, fma(x, Float64(9.0 * y), b)) / Float64(z * c));
	else
		tmp = t_1;
	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 * N[(t * -4.0), $MachinePrecision] + N[(x * N[(9.0 * N[(y / z), $MachinePrecision]), $MachinePrecision] + N[(b / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]}, If[LessEqual[z, -1.6e+45], t$95$1, If[LessEqual[z, 5e+121], N[(N[(N[(a * N[(z * -4.0), $MachinePrecision]), $MachinePrecision] * t + N[(x * N[(9.0 * y), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.6000000000000001e45 or 5.00000000000000007e121 < z

   1. Initial program 57.3%

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

   3. Taylor expanded in x 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. *-commutative N/A

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

      5. associate-*l* N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower-*.f64 45.7

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

   5. Applied rewrites 45.7%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/r* N/A

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

      4. lower-/.f64 N/A

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

   7. Applied rewrites 56.9%

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

   8. Taylor expanded in x around 0

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. associate-*r* N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. associate-/l* N/A

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

      12. associate-*r* N/A

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

      13. *-commutative N/A

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

      14. lower-fma.f64 N/A

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

      15. *-commutative N/A

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

      16. lower-*.f64 N/A

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

      17. lower-/.f64 N/A

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

      18. lower-/.f64 93.2

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

   10. Applied rewrites 93.2%

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

   if -1.6000000000000001e45 < z < 5.00000000000000007e121

   1. Initial program 97.3%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. sub-neg N/A

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

      4. +-commutative N/A

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

      5. associate-+l+ N/A

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

      6. lift-*.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. associate-*l* N/A

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

      9. distribute-lft-neg-in N/A

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

      10. *-commutative N/A

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

      11. associate-*r* N/A

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

      12. lower-fma.f64 N/A

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

      13. lower-*.f64 N/A

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

      14. lift-*.f64 N/A

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

      15. distribute-rgt-neg-in N/A

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

      16. lower-*.f64 N/A

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

      17. metadata-eval N/A

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

      18. lift-*.f64 N/A

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

      19. lift-*.f64 N/A

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

      20. associate-*l* N/A

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

   4. Applied rewrites 94.9%

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

4. Final simplification 94.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{+45}:\\ \;\;\;\;\frac{\mathsf{fma}\left(a, t \cdot -4, \mathsf{fma}\left(x, 9 \cdot \frac{y}{z}, \frac{b}{z}\right)\right)}{c}\\ \mathbf{elif}\;z \leq 5 \cdot 10^{+121}:\\ \;\;\;\;\frac{\mathsf{fma}\left(a \cdot \left(z \cdot -4\right), t, \mathsf{fma}\left(x, 9 \cdot y, b\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(a, t \cdot -4, \mathsf{fma}\left(x, 9 \cdot \frac{y}{z}, \frac{b}{z}\right)\right)}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 85.1% accurate, 0.5× speedup

Math

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

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= (/ (+ b (- (* y (* x 9.0)) (* a (* t (* z 4.0))))) (* z c)) INFINITY)
   (/ (fma (* a (* z -4.0)) t (fma x (* 9.0 y) b)) (* z c))
   (* 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 (((b + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (z * c)) <= ((double) INFINITY)) {
		tmp = fma((a * (z * -4.0)), t, fma(x, (9.0 * y), b)) / (z * c);
	} else {
		tmp = 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 (Float64(Float64(b + Float64(Float64(y * Float64(x * 9.0)) - Float64(a * Float64(t * Float64(z * 4.0))))) / Float64(z * c)) <= Inf)
		tmp = Float64(fma(Float64(a * Float64(z * -4.0)), t, fma(x, Float64(9.0 * y), b)) / Float64(z * c));
	else
		tmp = Float64(a * Float64(Float64(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[N[(N[(b + N[(N[(y * N[(x * 9.0), $MachinePrecision]), $MachinePrecision] - N[(a * N[(t * N[(z * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], Infinity], N[(N[(N[(a * N[(z * -4.0), $MachinePrecision]), $MachinePrecision] * t + N[(x * N[(9.0 * y), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(a * N[(N[(t * -4.0), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 88.2%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. sub-neg N/A

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

      4. +-commutative N/A

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

      5. associate-+l+ N/A

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

      6. lift-*.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. associate-*l* N/A

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

      9. distribute-lft-neg-in N/A

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

      10. *-commutative N/A

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

      11. associate-*r* N/A

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

      12. lower-fma.f64 N/A

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

      13. lower-*.f64 N/A

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

      14. lift-*.f64 N/A

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

      15. distribute-rgt-neg-in N/A

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

      16. lower-*.f64 N/A

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

      17. metadata-eval N/A

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

      18. lift-*.f64 N/A

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

      19. lift-*.f64 N/A

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

      20. associate-*l* N/A

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

   4. Applied rewrites 86.9%

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

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

   1. Initial program 0.0%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l/ N/A

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

      4. lower-/.f64 N/A

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

   4. Applied rewrites 3.3%

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

   5. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-*.f64 5.4

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

   7. Applied rewrites 5.4%

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

   8. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. associate-*r* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. associate-*r/ N/A

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

      7. lower-/.f64 N/A

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

      8. lower-*.f64 62.0

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

   10. Applied rewrites 62.0%

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

4. Final simplification 85.2%

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

Alternative 3: 85.4% accurate, 0.5× speedup

Math

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

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= (/ (+ b (- (* y (* x 9.0)) (* a (* t (* z 4.0))))) (* z c)) INFINITY)
   (/ (fma (* z -4.0) (* t a) (fma x (* 9.0 y) b)) (* z c))
   (* 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 (((b + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (z * c)) <= ((double) INFINITY)) {
		tmp = fma((z * -4.0), (t * a), fma(x, (9.0 * y), b)) / (z * c);
	} else {
		tmp = 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 (Float64(Float64(b + Float64(Float64(y * Float64(x * 9.0)) - Float64(a * Float64(t * Float64(z * 4.0))))) / Float64(z * c)) <= Inf)
		tmp = Float64(fma(Float64(z * -4.0), Float64(t * a), fma(x, Float64(9.0 * y), b)) / Float64(z * c));
	else
		tmp = Float64(a * Float64(Float64(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[N[(N[(b + N[(N[(y * N[(x * 9.0), $MachinePrecision]), $MachinePrecision] - N[(a * N[(t * N[(z * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], Infinity], N[(N[(N[(z * -4.0), $MachinePrecision] * N[(t * a), $MachinePrecision] + N[(x * N[(9.0 * y), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(a * N[(N[(t * -4.0), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 88.2%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. sub-neg N/A

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

      4. +-commutative N/A

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

      5. associate-+l+ N/A

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

      6. lift-*.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. associate-*l* N/A

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

      9. distribute-lft-neg-in N/A

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

      10. lower-fma.f64 N/A

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

      11. lift-*.f64 N/A

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

      12. distribute-rgt-neg-in N/A

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

      13. lower-*.f64 N/A

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

      14. metadata-eval N/A

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

      15. lower-*.f64 N/A

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

      16. lift-*.f64 N/A

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

      17. lift-*.f64 N/A

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

      18. associate-*l* N/A

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

      19. lower-fma.f64 N/A

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

      20. lower-*.f64 87.4

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

   4. Applied rewrites 87.4%

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

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

   1. Initial program 0.0%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l/ N/A

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

      4. lower-/.f64 N/A

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

   4. Applied rewrites 3.3%

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

   5. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-*.f64 5.4

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

   7. Applied rewrites 5.4%

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

   8. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. associate-*r* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. associate-*r/ N/A

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

      7. lower-/.f64 N/A

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

      8. lower-*.f64 62.0

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

   10. Applied rewrites 62.0%

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

4. Final simplification 85.6%

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

Alternative 4: 85.1% accurate, 0.5× speedup

Math

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

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= (/ (+ b (- (* y (* x 9.0)) (* a (* t (* z 4.0))))) (* z c)) INFINITY)
   (/ (fma (* x 9.0) y (fma a (* -4.0 (* z t)) b)) (* z c))
   (* 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 (((b + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (z * c)) <= ((double) INFINITY)) {
		tmp = fma((x * 9.0), y, fma(a, (-4.0 * (z * t)), b)) / (z * c);
	} else {
		tmp = 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 (Float64(Float64(b + Float64(Float64(y * Float64(x * 9.0)) - Float64(a * Float64(t * Float64(z * 4.0))))) / Float64(z * c)) <= Inf)
		tmp = Float64(fma(Float64(x * 9.0), y, fma(a, Float64(-4.0 * Float64(z * t)), b)) / Float64(z * c));
	else
		tmp = Float64(a * Float64(Float64(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[N[(N[(b + N[(N[(y * N[(x * 9.0), $MachinePrecision]), $MachinePrecision] - N[(a * N[(t * N[(z * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], Infinity], N[(N[(N[(x * 9.0), $MachinePrecision] * y + N[(a * N[(-4.0 * N[(z * t), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(a * N[(N[(t * -4.0), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 88.2%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. associate-+l- N/A

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

      4. sub-neg N/A

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

      5. lift-*.f64 N/A

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

      6. lower-fma.f64 N/A

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

      7. neg-sub0 N/A

         \[\leadsto \frac{\mathsf{fma}\left(x \cdot 9, y, \color{blue}{0 - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}\right)}{z \cdot c} \]

      8. associate-+l- N/A

         \[\leadsto \frac{\mathsf{fma}\left(x \cdot 9, y, \color{blue}{\left(0 - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}\right)}{z \cdot c} \]

      9. neg-sub0 N/A

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

      10. lift-*.f64 N/A

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

      11. *-commutative N/A

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

      12. distribute-rgt-neg-in N/A

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

      13. lower-fma.f64 N/A

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

      14. lift-*.f64 N/A

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

      15. lift-*.f64 N/A

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

      16. *-commutative N/A

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

      17. associate-*l* N/A

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

      18. distribute-lft-neg-in N/A

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

      19. lower-*.f64 N/A

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

      20. metadata-eval N/A

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

      21. lower-*.f64 88.2

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

   4. Applied rewrites 88.2%

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

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

   1. Initial program 0.0%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l/ N/A

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

      4. lower-/.f64 N/A

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

   4. Applied rewrites 3.3%

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

   5. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-*.f64 5.4

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

   7. Applied rewrites 5.4%

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

   8. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. associate-*r* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. associate-*r/ N/A

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

      7. lower-/.f64 N/A

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

      8. lower-*.f64 62.0

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

   10. Applied rewrites 62.0%

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

4. Final simplification 86.3%

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

Alternative 5: 52.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot 9\right)\\ \mathbf{if}\;t\_1 \leq -4 \cdot 10^{-36}:\\ \;\;\;\;\frac{9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \mathbf{elif}\;t\_1 \leq -1 \cdot 10^{-125}:\\ \;\;\;\;a \cdot \frac{t \cdot -4}{c}\\ \mathbf{elif}\;t\_1 \leq -2 \cdot 10^{-207}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+134}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(9 \cdot \frac{y}{z \cdot c}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* y (* x 9.0))))
   (if (<= t_1 -4e-36)
     (/ (* 9.0 (* x y)) (* z c))
     (if (<= t_1 -1e-125)
       (* a (/ (* t -4.0) c))
       (if (<= t_1 -2e-207)
         (/ b (* z c))
         (if (<= t_1 2e+134)
           (* -4.0 (* t (/ a c)))
           (* x (* 9.0 (/ y (* z c))))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = y * (x * 9.0);
	double tmp;
	if (t_1 <= -4e-36) {
		tmp = (9.0 * (x * y)) / (z * c);
	} else if (t_1 <= -1e-125) {
		tmp = a * ((t * -4.0) / c);
	} else if (t_1 <= -2e-207) {
		tmp = b / (z * c);
	} else if (t_1 <= 2e+134) {
		tmp = -4.0 * (t * (a / c));
	} else {
		tmp = x * (9.0 * (y / (z * c)));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (x * 9.0d0)
    if (t_1 <= (-4d-36)) then
        tmp = (9.0d0 * (x * y)) / (z * c)
    else if (t_1 <= (-1d-125)) then
        tmp = a * ((t * (-4.0d0)) / c)
    else if (t_1 <= (-2d-207)) then
        tmp = b / (z * c)
    else if (t_1 <= 2d+134) then
        tmp = (-4.0d0) * (t * (a / c))
    else
        tmp = x * (9.0d0 * (y / (z * c)))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = y * (x * 9.0);
	double tmp;
	if (t_1 <= -4e-36) {
		tmp = (9.0 * (x * y)) / (z * c);
	} else if (t_1 <= -1e-125) {
		tmp = a * ((t * -4.0) / c);
	} else if (t_1 <= -2e-207) {
		tmp = b / (z * c);
	} else if (t_1 <= 2e+134) {
		tmp = -4.0 * (t * (a / c));
	} else {
		tmp = x * (9.0 * (y / (z * c)));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	t_1 = y * (x * 9.0)
	tmp = 0
	if t_1 <= -4e-36:
		tmp = (9.0 * (x * y)) / (z * c)
	elif t_1 <= -1e-125:
		tmp = a * ((t * -4.0) / c)
	elif t_1 <= -2e-207:
		tmp = b / (z * c)
	elif t_1 <= 2e+134:
		tmp = -4.0 * (t * (a / c))
	else:
		tmp = x * (9.0 * (y / (z * c)))
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(y * Float64(x * 9.0))
	tmp = 0.0
	if (t_1 <= -4e-36)
		tmp = Float64(Float64(9.0 * Float64(x * y)) / Float64(z * c));
	elseif (t_1 <= -1e-125)
		tmp = Float64(a * Float64(Float64(t * -4.0) / c));
	elseif (t_1 <= -2e-207)
		tmp = Float64(b / Float64(z * c));
	elseif (t_1 <= 2e+134)
		tmp = Float64(-4.0 * Float64(t * Float64(a / c)));
	else
		tmp = Float64(x * Float64(9.0 * Float64(y / Float64(z * c))));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = y * (x * 9.0);
	tmp = 0.0;
	if (t_1 <= -4e-36)
		tmp = (9.0 * (x * y)) / (z * c);
	elseif (t_1 <= -1e-125)
		tmp = a * ((t * -4.0) / c);
	elseif (t_1 <= -2e-207)
		tmp = b / (z * c);
	elseif (t_1 <= 2e+134)
		tmp = -4.0 * (t * (a / c));
	else
		tmp = x * (9.0 * (y / (z * c)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(y * N[(x * 9.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -4e-36], N[(N[(9.0 * N[(x * y), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -1e-125], N[(a * N[(N[(t * -4.0), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -2e-207], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+134], N[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(9.0 * N[(y / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -3.9999999999999998e-36

   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 x around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 66.4

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

   5. Applied rewrites 66.4%

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

   if -3.9999999999999998e-36 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -1.00000000000000001e-125

   1. Initial program 83.2%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l/ N/A

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

      4. lower-/.f64 N/A

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

   4. Applied rewrites 83.8%

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

   5. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-*.f64 52.1

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

   7. Applied rewrites 52.1%

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

   8. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. associate-*r* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. associate-*r/ N/A

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

      7. lower-/.f64 N/A

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

      8. lower-*.f64 57.6

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

   10. Applied rewrites 57.6%

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

   if -1.00000000000000001e-125 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -1.99999999999999985e-207

   1. Initial program 89.8%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   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. *-commutative N/A

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

      3. lower-*.f64 81.9

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

   5. Applied rewrites 81.9%

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

   if -1.99999999999999985e-207 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 1.99999999999999984e134

   1. Initial program 84.8%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l/ N/A

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

      4. lower-/.f64 N/A

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

   4. Applied rewrites 83.8%

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

   5. Taylor expanded in a around inf

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   6. 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. lower-*.f64 45.8

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

   7. Applied rewrites 45.8%

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

   9. Applied rewrites 46.9%

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

   if 1.99999999999999984e134 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 72.5%

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

   3. Taylor expanded in x 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. *-commutative N/A

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

      5. associate-*l* N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower-*.f64 28.4

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

   5. Applied rewrites 28.4%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/r* N/A

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

      4. lower-/.f64 N/A

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

   7. Applied rewrites 24.0%

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

   8. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. associate-*r* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 61.5

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

   10. Applied rewrites 61.5%

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

4. Final simplification 56.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \left(x \cdot 9\right) \leq -4 \cdot 10^{-36}:\\ \;\;\;\;\frac{9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \mathbf{elif}\;y \cdot \left(x \cdot 9\right) \leq -1 \cdot 10^{-125}:\\ \;\;\;\;a \cdot \frac{t \cdot -4}{c}\\ \mathbf{elif}\;y \cdot \left(x \cdot 9\right) \leq -2 \cdot 10^{-207}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;y \cdot \left(x \cdot 9\right) \leq 2 \cdot 10^{+134}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(9 \cdot \frac{y}{z \cdot c}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 74.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot 9\right)\\ t_2 := \frac{\mathsf{fma}\left(9, x \cdot y, b\right)}{z \cdot c}\\ \mathbf{if}\;t\_1 \leq -4 \cdot 10^{-47}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{-39}:\\ \;\;\;\;\mathsf{fma}\left(a, t \cdot \frac{-4}{c}, \frac{b}{z \cdot c}\right)\\ \mathbf{elif}\;t\_1 \leq 4 \cdot 10^{+301}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;9 \cdot \left(x \cdot \frac{y}{z \cdot c}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* y (* x 9.0))) (t_2 (/ (fma 9.0 (* x y) b) (* z c))))
   (if (<= t_1 -4e-47)
     t_2
     (if (<= t_1 5e-39)
       (fma a (* t (/ -4.0 c)) (/ b (* z c)))
       (if (<= t_1 4e+301) t_2 (* 9.0 (* x (/ y (* z c)))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = y * (x * 9.0);
	double t_2 = fma(9.0, (x * y), b) / (z * c);
	double tmp;
	if (t_1 <= -4e-47) {
		tmp = t_2;
	} else if (t_1 <= 5e-39) {
		tmp = fma(a, (t * (-4.0 / c)), (b / (z * c)));
	} else if (t_1 <= 4e+301) {
		tmp = t_2;
	} else {
		tmp = 9.0 * (x * (y / (z * c)));
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(y * Float64(x * 9.0))
	t_2 = Float64(fma(9.0, Float64(x * y), b) / Float64(z * c))
	tmp = 0.0
	if (t_1 <= -4e-47)
		tmp = t_2;
	elseif (t_1 <= 5e-39)
		tmp = fma(a, Float64(t * Float64(-4.0 / c)), Float64(b / Float64(z * c)));
	elseif (t_1 <= 4e+301)
		tmp = t_2;
	else
		tmp = Float64(9.0 * Float64(x * Float64(y / Float64(z * c))));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(y * N[(x * 9.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(9.0 * N[(x * y), $MachinePrecision] + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -4e-47], t$95$2, If[LessEqual[t$95$1, 5e-39], N[(a * N[(t * N[(-4.0 / c), $MachinePrecision]), $MachinePrecision] + N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 4e+301], t$95$2, N[(9.0 * N[(x * N[(y / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -3.9999999999999999e-47 or 4.9999999999999998e-39 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 4.00000000000000021e301

   1. Initial program 85.7%

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

   3. Taylor expanded in z 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. lower-fma.f64 N/A

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

      3. lower-*.f64 75.3

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

   5. Applied rewrites 75.3%

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

   if -3.9999999999999999e-47 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 4.9999999999999998e-39

   1. Initial program 81.4%

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

   3. Taylor expanded in x 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. cancel-sign-sub-inv N/A

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. associate-/l* N/A

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

      6. associate-*r* N/A

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

      7. *-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. *-commutative N/A

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

      10. associate-*l/ N/A

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

      11. associate-/l* N/A

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

      12. lower-*.f64 N/A

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

      13. lower-/.f64 N/A

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

      14. *-commutative N/A

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

      15. associate-/l* N/A

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

      16. associate-*l* N/A

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

      17. *-commutative N/A

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

   5. Applied rewrites 85.7%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 86.1%

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

   if 4.00000000000000021e301 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 54.4%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l/ N/A

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

      4. lower-/.f64 N/A

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

   4. Applied rewrites 48.5%

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

   5. Taylor expanded in x around inf

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

      1. lower-*.f64 N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower-*.f64 79.2

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

   7. Applied rewrites 79.2%

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

4. Final simplification 80.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \left(x \cdot 9\right) \leq -4 \cdot 10^{-47}:\\ \;\;\;\;\frac{\mathsf{fma}\left(9, x \cdot y, b\right)}{z \cdot c}\\ \mathbf{elif}\;y \cdot \left(x \cdot 9\right) \leq 5 \cdot 10^{-39}:\\ \;\;\;\;\mathsf{fma}\left(a, t \cdot \frac{-4}{c}, \frac{b}{z \cdot c}\right)\\ \mathbf{elif}\;y \cdot \left(x \cdot 9\right) \leq 4 \cdot 10^{+301}:\\ \;\;\;\;\frac{\mathsf{fma}\left(9, x \cdot y, b\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;9 \cdot \left(x \cdot \frac{y}{z \cdot c}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 74.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot 9\right)\\ t_2 := \frac{\mathsf{fma}\left(9, x \cdot y, b\right)}{z \cdot c}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{-87}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{-39}:\\ \;\;\;\;\frac{\frac{b}{z} - 4 \cdot \left(t \cdot a\right)}{c}\\ \mathbf{elif}\;t\_1 \leq 4 \cdot 10^{+301}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;9 \cdot \left(x \cdot \frac{y}{z \cdot c}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* y (* x 9.0))) (t_2 (/ (fma 9.0 (* x y) b) (* z c))))
   (if (<= t_1 -2e-87)
     t_2
     (if (<= t_1 5e-39)
       (/ (- (/ b z) (* 4.0 (* t a))) c)
       (if (<= t_1 4e+301) t_2 (* 9.0 (* x (/ y (* z c)))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = y * (x * 9.0);
	double t_2 = fma(9.0, (x * y), b) / (z * c);
	double tmp;
	if (t_1 <= -2e-87) {
		tmp = t_2;
	} else if (t_1 <= 5e-39) {
		tmp = ((b / z) - (4.0 * (t * a))) / c;
	} else if (t_1 <= 4e+301) {
		tmp = t_2;
	} else {
		tmp = 9.0 * (x * (y / (z * c)));
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(y * Float64(x * 9.0))
	t_2 = Float64(fma(9.0, Float64(x * y), b) / Float64(z * c))
	tmp = 0.0
	if (t_1 <= -2e-87)
		tmp = t_2;
	elseif (t_1 <= 5e-39)
		tmp = Float64(Float64(Float64(b / z) - Float64(4.0 * Float64(t * a))) / c);
	elseif (t_1 <= 4e+301)
		tmp = t_2;
	else
		tmp = Float64(9.0 * Float64(x * Float64(y / Float64(z * c))));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(y * N[(x * 9.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(9.0 * N[(x * y), $MachinePrecision] + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e-87], t$95$2, If[LessEqual[t$95$1, 5e-39], N[(N[(N[(b / z), $MachinePrecision] - N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[t$95$1, 4e+301], t$95$2, N[(9.0 * N[(x * N[(y / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -2.00000000000000004e-87 or 4.9999999999999998e-39 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 4.00000000000000021e301

   1. Initial program 86.6%

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

   3. Taylor expanded in z 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. lower-fma.f64 N/A

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

      3. lower-*.f64 74.8

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

   5. Applied rewrites 74.8%

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

   if -2.00000000000000004e-87 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 4.9999999999999998e-39

   1. Initial program 79.8%

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

   3. Taylor expanded in x 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. cancel-sign-sub-inv N/A

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. associate-/l* N/A

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

      6. associate-*r* N/A

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

      7. *-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. *-commutative N/A

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

      10. associate-*l/ N/A

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

      11. associate-/l* N/A

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

      12. lower-*.f64 N/A

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

      13. lower-/.f64 N/A

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

      14. *-commutative N/A

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

      15. associate-/l* N/A

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

      16. associate-*l* N/A

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

      17. *-commutative N/A

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

   5. Applied rewrites 86.4%

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

   6. Taylor expanded in c around -inf

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

   8. Applied rewrites 87.6%

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

   9. Taylor expanded in x around 0

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

   11. Applied rewrites 86.6%

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

   if 4.00000000000000021e301 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 54.4%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l/ N/A

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

      4. lower-/.f64 N/A

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

   4. Applied rewrites 48.5%

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

   5. Taylor expanded in x around inf

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

      1. lower-*.f64 N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower-*.f64 79.2

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

   7. Applied rewrites 79.2%

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

4. Final simplification 79.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \left(x \cdot 9\right) \leq -2 \cdot 10^{-87}:\\ \;\;\;\;\frac{\mathsf{fma}\left(9, x \cdot y, b\right)}{z \cdot c}\\ \mathbf{elif}\;y \cdot \left(x \cdot 9\right) \leq 5 \cdot 10^{-39}:\\ \;\;\;\;\frac{\frac{b}{z} - 4 \cdot \left(t \cdot a\right)}{c}\\ \mathbf{elif}\;y \cdot \left(x \cdot 9\right) \leq 4 \cdot 10^{+301}:\\ \;\;\;\;\frac{\mathsf{fma}\left(9, x \cdot y, b\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;9 \cdot \left(x \cdot \frac{y}{z \cdot c}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 72.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot 9\right)\\ t_2 := \frac{\mathsf{fma}\left(9, x \cdot y, b\right)}{z \cdot c}\\ \mathbf{if}\;t\_1 \leq -4 \cdot 10^{-47}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{-39}:\\ \;\;\;\;\frac{\mathsf{fma}\left(a \cdot \left(z \cdot -4\right), t, b\right)}{z \cdot c}\\ \mathbf{elif}\;t\_1 \leq 4 \cdot 10^{+301}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;9 \cdot \left(x \cdot \frac{y}{z \cdot c}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* y (* x 9.0))) (t_2 (/ (fma 9.0 (* x y) b) (* z c))))
   (if (<= t_1 -4e-47)
     t_2
     (if (<= t_1 5e-39)
       (/ (fma (* a (* z -4.0)) t b) (* z c))
       (if (<= t_1 4e+301) t_2 (* 9.0 (* x (/ y (* z c)))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = y * (x * 9.0);
	double t_2 = fma(9.0, (x * y), b) / (z * c);
	double tmp;
	if (t_1 <= -4e-47) {
		tmp = t_2;
	} else if (t_1 <= 5e-39) {
		tmp = fma((a * (z * -4.0)), t, b) / (z * c);
	} else if (t_1 <= 4e+301) {
		tmp = t_2;
	} else {
		tmp = 9.0 * (x * (y / (z * c)));
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(y * Float64(x * 9.0))
	t_2 = Float64(fma(9.0, Float64(x * y), b) / Float64(z * c))
	tmp = 0.0
	if (t_1 <= -4e-47)
		tmp = t_2;
	elseif (t_1 <= 5e-39)
		tmp = Float64(fma(Float64(a * Float64(z * -4.0)), t, b) / Float64(z * c));
	elseif (t_1 <= 4e+301)
		tmp = t_2;
	else
		tmp = Float64(9.0 * Float64(x * Float64(y / Float64(z * c))));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(y * N[(x * 9.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(9.0 * N[(x * y), $MachinePrecision] + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -4e-47], t$95$2, If[LessEqual[t$95$1, 5e-39], N[(N[(N[(a * N[(z * -4.0), $MachinePrecision]), $MachinePrecision] * t + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 4e+301], t$95$2, N[(9.0 * N[(x * N[(y / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -3.9999999999999999e-47 or 4.9999999999999998e-39 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 4.00000000000000021e301

   1. Initial program 85.7%

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

   3. Taylor expanded in z 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. lower-fma.f64 N/A

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

      3. lower-*.f64 75.3

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

   5. Applied rewrites 75.3%

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

   if -3.9999999999999999e-47 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 4.9999999999999998e-39

   1. Initial program 81.4%

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

   3. Taylor expanded in x 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. *-commutative N/A

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

      5. associate-*l* N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower-*.f64 77.3

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

   5. Applied rewrites 77.3%

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

   7. Applied rewrites 75.5%

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

   if 4.00000000000000021e301 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 54.4%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l/ N/A

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

      4. lower-/.f64 N/A

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

   4. Applied rewrites 48.5%

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

   5. Taylor expanded in x around inf

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

      1. lower-*.f64 N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower-*.f64 79.2

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

   7. Applied rewrites 79.2%

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

4. Final simplification 75.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \left(x \cdot 9\right) \leq -4 \cdot 10^{-47}:\\ \;\;\;\;\frac{\mathsf{fma}\left(9, x \cdot y, b\right)}{z \cdot c}\\ \mathbf{elif}\;y \cdot \left(x \cdot 9\right) \leq 5 \cdot 10^{-39}:\\ \;\;\;\;\frac{\mathsf{fma}\left(a \cdot \left(z \cdot -4\right), t, b\right)}{z \cdot c}\\ \mathbf{elif}\;y \cdot \left(x \cdot 9\right) \leq 4 \cdot 10^{+301}:\\ \;\;\;\;\frac{\mathsf{fma}\left(9, x \cdot y, b\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;9 \cdot \left(x \cdot \frac{y}{z \cdot c}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 71.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot 9\right)\\ t_2 := \frac{\mathsf{fma}\left(9, x \cdot y, b\right)}{z \cdot c}\\ \mathbf{if}\;t\_1 \leq -4 \cdot 10^{-47}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{-39}:\\ \;\;\;\;\frac{\mathsf{fma}\left(a, -4 \cdot \left(z \cdot t\right), b\right)}{z \cdot c}\\ \mathbf{elif}\;t\_1 \leq 4 \cdot 10^{+301}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;9 \cdot \left(x \cdot \frac{y}{z \cdot c}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* y (* x 9.0))) (t_2 (/ (fma 9.0 (* x y) b) (* z c))))
   (if (<= t_1 -4e-47)
     t_2
     (if (<= t_1 5e-39)
       (/ (fma a (* -4.0 (* z t)) b) (* z c))
       (if (<= t_1 4e+301) t_2 (* 9.0 (* x (/ y (* z c)))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = y * (x * 9.0);
	double t_2 = fma(9.0, (x * y), b) / (z * c);
	double tmp;
	if (t_1 <= -4e-47) {
		tmp = t_2;
	} else if (t_1 <= 5e-39) {
		tmp = fma(a, (-4.0 * (z * t)), b) / (z * c);
	} else if (t_1 <= 4e+301) {
		tmp = t_2;
	} else {
		tmp = 9.0 * (x * (y / (z * c)));
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(y * Float64(x * 9.0))
	t_2 = Float64(fma(9.0, Float64(x * y), b) / Float64(z * c))
	tmp = 0.0
	if (t_1 <= -4e-47)
		tmp = t_2;
	elseif (t_1 <= 5e-39)
		tmp = Float64(fma(a, Float64(-4.0 * Float64(z * t)), b) / Float64(z * c));
	elseif (t_1 <= 4e+301)
		tmp = t_2;
	else
		tmp = Float64(9.0 * Float64(x * Float64(y / Float64(z * c))));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(y * N[(x * 9.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(9.0 * N[(x * y), $MachinePrecision] + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -4e-47], t$95$2, If[LessEqual[t$95$1, 5e-39], N[(N[(a * N[(-4.0 * N[(z * t), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 4e+301], t$95$2, N[(9.0 * N[(x * N[(y / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -3.9999999999999999e-47 or 4.9999999999999998e-39 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 4.00000000000000021e301

   1. Initial program 85.7%

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

   3. Taylor expanded in z 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. lower-fma.f64 N/A

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

      3. lower-*.f64 75.3

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

   5. Applied rewrites 75.3%

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

   if -3.9999999999999999e-47 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 4.9999999999999998e-39

   1. Initial program 81.4%

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

   3. Taylor expanded in x 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. *-commutative N/A

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

      5. associate-*l* N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower-*.f64 77.3

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

   5. Applied rewrites 77.3%

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

   if 4.00000000000000021e301 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 54.4%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l/ N/A

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

      4. lower-/.f64 N/A

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

   4. Applied rewrites 48.5%

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

   5. Taylor expanded in x around inf

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

      1. lower-*.f64 N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower-*.f64 79.2

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

   7. Applied rewrites 79.2%

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

4. Final simplification 76.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \left(x \cdot 9\right) \leq -4 \cdot 10^{-47}:\\ \;\;\;\;\frac{\mathsf{fma}\left(9, x \cdot y, b\right)}{z \cdot c}\\ \mathbf{elif}\;y \cdot \left(x \cdot 9\right) \leq 5 \cdot 10^{-39}:\\ \;\;\;\;\frac{\mathsf{fma}\left(a, -4 \cdot \left(z \cdot t\right), b\right)}{z \cdot c}\\ \mathbf{elif}\;y \cdot \left(x \cdot 9\right) \leq 4 \cdot 10^{+301}:\\ \;\;\;\;\frac{\mathsf{fma}\left(9, x \cdot y, b\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;9 \cdot \left(x \cdot \frac{y}{z \cdot c}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 53.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \frac{y}{z \cdot c}\\ t_2 := y \cdot \left(x \cdot 9\right)\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{+49}:\\ \;\;\;\;9 \cdot \left(x \cdot t\_1\right)\\ \mathbf{elif}\;t\_2 \leq -2 \cdot 10^{-207}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+134}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(9 \cdot t\_1\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ y (* z c))) (t_2 (* y (* x 9.0))))
   (if (<= t_2 -1e+49)
     (* 9.0 (* x t_1))
     (if (<= t_2 -2e-207)
       (/ b (* z c))
       (if (<= t_2 2e+134) (* -4.0 (* t (/ a c))) (* x (* 9.0 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 = y / (z * c);
	double t_2 = y * (x * 9.0);
	double tmp;
	if (t_2 <= -1e+49) {
		tmp = 9.0 * (x * t_1);
	} else if (t_2 <= -2e-207) {
		tmp = b / (z * c);
	} else if (t_2 <= 2e+134) {
		tmp = -4.0 * (t * (a / c));
	} else {
		tmp = x * (9.0 * 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) :: t_2
    real(8) :: tmp
    t_1 = y / (z * c)
    t_2 = y * (x * 9.0d0)
    if (t_2 <= (-1d+49)) then
        tmp = 9.0d0 * (x * t_1)
    else if (t_2 <= (-2d-207)) then
        tmp = b / (z * c)
    else if (t_2 <= 2d+134) then
        tmp = (-4.0d0) * (t * (a / c))
    else
        tmp = x * (9.0d0 * 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 = y / (z * c);
	double t_2 = y * (x * 9.0);
	double tmp;
	if (t_2 <= -1e+49) {
		tmp = 9.0 * (x * t_1);
	} else if (t_2 <= -2e-207) {
		tmp = b / (z * c);
	} else if (t_2 <= 2e+134) {
		tmp = -4.0 * (t * (a / c));
	} else {
		tmp = x * (9.0 * 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 = y / (z * c)
	t_2 = y * (x * 9.0)
	tmp = 0
	if t_2 <= -1e+49:
		tmp = 9.0 * (x * t_1)
	elif t_2 <= -2e-207:
		tmp = b / (z * c)
	elif t_2 <= 2e+134:
		tmp = -4.0 * (t * (a / c))
	else:
		tmp = x * (9.0 * 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(y / Float64(z * c))
	t_2 = Float64(y * Float64(x * 9.0))
	tmp = 0.0
	if (t_2 <= -1e+49)
		tmp = Float64(9.0 * Float64(x * t_1));
	elseif (t_2 <= -2e-207)
		tmp = Float64(b / Float64(z * c));
	elseif (t_2 <= 2e+134)
		tmp = Float64(-4.0 * Float64(t * Float64(a / c)));
	else
		tmp = Float64(x * Float64(9.0 * 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 = y / (z * c);
	t_2 = y * (x * 9.0);
	tmp = 0.0;
	if (t_2 <= -1e+49)
		tmp = 9.0 * (x * t_1);
	elseif (t_2 <= -2e-207)
		tmp = b / (z * c);
	elseif (t_2 <= 2e+134)
		tmp = -4.0 * (t * (a / c));
	else
		tmp = x * (9.0 * 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[(y / N[(z * c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(x * 9.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -1e+49], N[(9.0 * N[(x * t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, -2e-207], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 2e+134], N[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(9.0 * t$95$1), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -9.99999999999999946e48

   1. Initial program 79.8%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l/ N/A

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

      4. lower-/.f64 N/A

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

   4. Applied rewrites 81.9%

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

   5. Taylor expanded in x around inf

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

      1. lower-*.f64 N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower-*.f64 69.3

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

   7. Applied rewrites 69.3%

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

   if -9.99999999999999946e48 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -1.99999999999999985e-207

   1. Initial program 86.5%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. 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. *-commutative N/A

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

      3. lower-*.f64 49.6

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

   5. Applied rewrites 49.6%

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

   if -1.99999999999999985e-207 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 1.99999999999999984e134

   1. Initial program 84.8%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l/ N/A

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

      4. lower-/.f64 N/A

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

   4. Applied rewrites 83.8%

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

   5. Taylor expanded in a around inf

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   6. 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. lower-*.f64 45.8

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

   7. Applied rewrites 45.8%

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

   9. Applied rewrites 46.9%

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

   if 1.99999999999999984e134 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 72.5%

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

   3. Taylor expanded in x 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. *-commutative N/A

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

      5. associate-*l* N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower-*.f64 28.4

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

   5. Applied rewrites 28.4%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/r* N/A

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

      4. lower-/.f64 N/A

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

   7. Applied rewrites 24.0%

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

   8. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. associate-*r* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 61.5

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

   10. Applied rewrites 61.5%

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

4. Final simplification 54.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \left(x \cdot 9\right) \leq -1 \cdot 10^{+49}:\\ \;\;\;\;9 \cdot \left(x \cdot \frac{y}{z \cdot c}\right)\\ \mathbf{elif}\;y \cdot \left(x \cdot 9\right) \leq -2 \cdot 10^{-207}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;y \cdot \left(x \cdot 9\right) \leq 2 \cdot 10^{+134}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(9 \cdot \frac{y}{z \cdot c}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 53.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot 9\right)\\ t_2 := 9 \cdot \left(x \cdot \frac{y}{z \cdot c}\right)\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+49}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq -2 \cdot 10^{-207}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+134}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

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 (* y (* x 9.0))) (t_2 (* 9.0 (* x (/ y (* z c))))))
   (if (<= t_1 -1e+49)
     t_2
     (if (<= t_1 -2e-207)
       (/ b (* z c))
       (if (<= t_1 2e+134) (* -4.0 (* t (/ a c))) 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 = y * (x * 9.0);
	double t_2 = 9.0 * (x * (y / (z * c)));
	double tmp;
	if (t_1 <= -1e+49) {
		tmp = t_2;
	} else if (t_1 <= -2e-207) {
		tmp = b / (z * c);
	} else if (t_1 <= 2e+134) {
		tmp = -4.0 * (t * (a / c));
	} 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 = y * (x * 9.0d0)
    t_2 = 9.0d0 * (x * (y / (z * c)))
    if (t_1 <= (-1d+49)) then
        tmp = t_2
    else if (t_1 <= (-2d-207)) then
        tmp = b / (z * c)
    else if (t_1 <= 2d+134) then
        tmp = (-4.0d0) * (t * (a / c))
    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 = y * (x * 9.0);
	double t_2 = 9.0 * (x * (y / (z * c)));
	double tmp;
	if (t_1 <= -1e+49) {
		tmp = t_2;
	} else if (t_1 <= -2e-207) {
		tmp = b / (z * c);
	} else if (t_1 <= 2e+134) {
		tmp = -4.0 * (t * (a / c));
	} 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 = y * (x * 9.0)
	t_2 = 9.0 * (x * (y / (z * c)))
	tmp = 0
	if t_1 <= -1e+49:
		tmp = t_2
	elif t_1 <= -2e-207:
		tmp = b / (z * c)
	elif t_1 <= 2e+134:
		tmp = -4.0 * (t * (a / c))
	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(y * Float64(x * 9.0))
	t_2 = Float64(9.0 * Float64(x * Float64(y / Float64(z * c))))
	tmp = 0.0
	if (t_1 <= -1e+49)
		tmp = t_2;
	elseif (t_1 <= -2e-207)
		tmp = Float64(b / Float64(z * c));
	elseif (t_1 <= 2e+134)
		tmp = Float64(-4.0 * Float64(t * Float64(a / c)));
	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 = y * (x * 9.0);
	t_2 = 9.0 * (x * (y / (z * c)));
	tmp = 0.0;
	if (t_1 <= -1e+49)
		tmp = t_2;
	elseif (t_1 <= -2e-207)
		tmp = b / (z * c);
	elseif (t_1 <= 2e+134)
		tmp = -4.0 * (t * (a / c));
	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[(y * N[(x * 9.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(9.0 * N[(x * N[(y / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+49], t$95$2, If[LessEqual[t$95$1, -2e-207], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+134], N[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -9.99999999999999946e48 or 1.99999999999999984e134 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 76.5%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l/ N/A

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

      4. lower-/.f64 N/A

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

   4. Applied rewrites 74.9%

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

   5. Taylor expanded in x around inf

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

      1. lower-*.f64 N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower-*.f64 65.8

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

   7. Applied rewrites 65.8%

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

   if -9.99999999999999946e48 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -1.99999999999999985e-207

   1. Initial program 86.5%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. 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. *-commutative N/A

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

      3. lower-*.f64 49.6

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

   5. Applied rewrites 49.6%

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

   if -1.99999999999999985e-207 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 1.99999999999999984e134

   1. Initial program 84.8%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l/ N/A

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

      4. lower-/.f64 N/A

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

   4. Applied rewrites 83.8%

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

   5. Taylor expanded in a around inf

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   6. 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. lower-*.f64 45.8

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

   7. Applied rewrites 45.8%

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

   9. Applied rewrites 46.9%

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

4. Final simplification 54.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \left(x \cdot 9\right) \leq -1 \cdot 10^{+49}:\\ \;\;\;\;9 \cdot \left(x \cdot \frac{y}{z \cdot c}\right)\\ \mathbf{elif}\;y \cdot \left(x \cdot 9\right) \leq -2 \cdot 10^{-207}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;y \cdot \left(x \cdot 9\right) \leq 2 \cdot 10^{+134}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;9 \cdot \left(x \cdot \frac{y}{z \cdot c}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 85.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \mathsf{fma}\left(x, 9 \cdot y, b\right)\\ \mathbf{if}\;z \leq -5.5 \cdot 10^{+43}:\\ \;\;\;\;\mathsf{fma}\left(9, y \cdot \frac{x}{z \cdot c}, a \cdot \frac{t \cdot -4}{c}\right)\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-68}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(a \cdot \left(z \cdot -4\right), t, t\_1\right)}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(z, t \cdot \left(a \cdot -4\right), t\_1\right)}{z}}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (fma x (* 9.0 y) b)))
   (if (<= z -5.5e+43)
     (fma 9.0 (* y (/ x (* z c))) (* a (/ (* t -4.0) c)))
     (if (<= z 9.5e-68)
       (/ (/ (fma (* a (* z -4.0)) t t_1) c) z)
       (/ (/ (fma z (* t (* a -4.0)) t_1) z) c)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = fma(x, (9.0 * y), b);
	double tmp;
	if (z <= -5.5e+43) {
		tmp = fma(9.0, (y * (x / (z * c))), (a * ((t * -4.0) / c)));
	} else if (z <= 9.5e-68) {
		tmp = (fma((a * (z * -4.0)), t, t_1) / c) / z;
	} else {
		tmp = (fma(z, (t * (a * -4.0)), t_1) / z) / c;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = fma(x, Float64(9.0 * y), b)
	tmp = 0.0
	if (z <= -5.5e+43)
		tmp = fma(9.0, Float64(y * Float64(x / Float64(z * c))), Float64(a * Float64(Float64(t * -4.0) / c)));
	elseif (z <= 9.5e-68)
		tmp = Float64(Float64(fma(Float64(a * Float64(z * -4.0)), t, t_1) / c) / z);
	else
		tmp = Float64(Float64(fma(z, Float64(t * Float64(a * -4.0)), t_1) / z) / c);
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(x * N[(9.0 * y), $MachinePrecision] + b), $MachinePrecision]}, If[LessEqual[z, -5.5e+43], N[(9.0 * N[(y * N[(x / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * N[(N[(t * -4.0), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9.5e-68], N[(N[(N[(N[(a * N[(z * -4.0), $MachinePrecision]), $MachinePrecision] * t + t$95$1), $MachinePrecision] / c), $MachinePrecision] / z), $MachinePrecision], N[(N[(N[(z * N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision] / z), $MachinePrecision] / c), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.49999999999999989e43

   1. Initial program 51.6%

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

   3. Taylor expanded in x 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. cancel-sign-sub-inv N/A

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. associate-/l* N/A

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

      6. associate-*r* N/A

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

      7. *-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. *-commutative N/A

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

      10. associate-*l/ N/A

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

      11. associate-/l* N/A

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

      12. lower-*.f64 N/A

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

      13. lower-/.f64 N/A

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

      14. *-commutative N/A

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

      15. associate-/l* N/A

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

      16. associate-*l* N/A

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

      17. *-commutative N/A

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

   5. Applied rewrites 83.3%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 70.7%

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

   if -5.49999999999999989e43 < z < 9.4999999999999997e-68

   1. Initial program 96.7%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l/ N/A

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

      4. lower-/.f64 N/A

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

   4. Applied rewrites 97.1%

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

      1. lift-fma.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-fma.f64 N/A

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

      4. associate-+l+ N/A

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

      5. lift-*.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. associate-*r* N/A

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

      8. *-commutative N/A

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

      9. lift-*.f64 N/A

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

      10. associate-*r* N/A

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

      11. *-commutative N/A

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

      12. lift-*.f64 N/A

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

      13. +-commutative N/A

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

      14. lift-fma.f64 N/A

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

      15. lift-fma.f64 96.6

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

   6. Applied rewrites 96.6%

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

   if 9.4999999999999997e-68 < z

   1. Initial program 79.5%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. sub-neg N/A

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

      4. +-commutative N/A

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

      5. associate-+l+ N/A

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

      6. lift-*.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. associate-*l* N/A

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

      9. distribute-lft-neg-in N/A

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

      10. *-commutative N/A

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

      11. associate-*r* N/A

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

      12. lower-fma.f64 N/A

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

      13. lower-*.f64 N/A

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

      14. lift-*.f64 N/A

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

      15. distribute-rgt-neg-in N/A

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

      16. lower-*.f64 N/A

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

      17. metadata-eval N/A

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

      18. lift-*.f64 N/A

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

      19. lift-*.f64 N/A

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

      20. associate-*l* N/A

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

   4. Applied rewrites 73.6%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/r* N/A

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

      4. lower-/.f64 N/A

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

   6. Applied rewrites 87.0%

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

4. Final simplification 88.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{+43}:\\ \;\;\;\;\mathsf{fma}\left(9, y \cdot \frac{x}{z \cdot c}, a \cdot \frac{t \cdot -4}{c}\right)\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-68}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(a \cdot \left(z \cdot -4\right), t, \mathsf{fma}\left(x, 9 \cdot y, b\right)\right)}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(z, t \cdot \left(a \cdot -4\right), \mathsf{fma}\left(x, 9 \cdot y, b\right)\right)}{z}}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 84.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \mathsf{fma}\left(9, y \cdot \frac{x}{z \cdot c}, a \cdot \frac{t \cdot -4}{c}\right)\\ \mathbf{if}\;z \leq -2.25 \cdot 10^{+49}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+225}:\\ \;\;\;\;\frac{\mathsf{fma}\left(a \cdot \left(z \cdot -4\right), t, \mathsf{fma}\left(x, 9 \cdot y, b\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (fma 9.0 (* y (/ x (* z c))) (* a (/ (* t -4.0) c)))))
   (if (<= z -2.25e+49)
     t_1
     (if (<= z 2e+225)
       (/ (fma (* a (* z -4.0)) t (fma x (* 9.0 y) b)) (* z c))
       t_1))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = fma(9.0, (y * (x / (z * c))), (a * ((t * -4.0) / c)));
	double tmp;
	if (z <= -2.25e+49) {
		tmp = t_1;
	} else if (z <= 2e+225) {
		tmp = fma((a * (z * -4.0)), t, fma(x, (9.0 * y), b)) / (z * c);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = fma(9.0, Float64(y * Float64(x / Float64(z * c))), Float64(a * Float64(Float64(t * -4.0) / c)))
	tmp = 0.0
	if (z <= -2.25e+49)
		tmp = t_1;
	elseif (z <= 2e+225)
		tmp = Float64(fma(Float64(a * Float64(z * -4.0)), t, fma(x, Float64(9.0 * y), b)) / Float64(z * c));
	else
		tmp = t_1;
	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[(9.0 * N[(y * N[(x / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * N[(N[(t * -4.0), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.25e+49], t$95$1, If[LessEqual[z, 2e+225], N[(N[(N[(a * N[(z * -4.0), $MachinePrecision]), $MachinePrecision] * t + N[(x * N[(9.0 * y), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -2.24999999999999991e49 or 1.99999999999999986e225 < z

   1. Initial program 52.6%

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

   3. Taylor expanded in x 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. cancel-sign-sub-inv N/A

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. associate-/l* N/A

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

      6. associate-*r* N/A

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

      7. *-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. *-commutative N/A

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

      10. associate-*l/ N/A

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

      11. associate-/l* N/A

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

      12. lower-*.f64 N/A

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

      13. lower-/.f64 N/A

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

      14. *-commutative N/A

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

      15. associate-/l* N/A

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

      16. associate-*l* N/A

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

      17. *-commutative N/A

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

   5. Applied rewrites 81.7%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 72.5%

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

   if -2.24999999999999991e49 < z < 1.99999999999999986e225

   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. Step-by-step derivation

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. sub-neg N/A

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

      4. +-commutative N/A

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

      5. associate-+l+ N/A

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

      6. lift-*.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. associate-*l* N/A

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

      9. distribute-lft-neg-in N/A

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

      10. *-commutative N/A

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

      11. associate-*r* N/A

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

      12. lower-fma.f64 N/A

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

      13. lower-*.f64 N/A

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

      14. lift-*.f64 N/A

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

      15. distribute-rgt-neg-in N/A

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

      16. lower-*.f64 N/A

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

      17. metadata-eval N/A

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

      18. lift-*.f64 N/A

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

      19. lift-*.f64 N/A

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

      20. associate-*l* N/A

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

   4. Applied rewrites 91.3%

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

4. Final simplification 85.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.25 \cdot 10^{+49}:\\ \;\;\;\;\mathsf{fma}\left(9, y \cdot \frac{x}{z \cdot c}, a \cdot \frac{t \cdot -4}{c}\right)\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+225}:\\ \;\;\;\;\frac{\mathsf{fma}\left(a \cdot \left(z \cdot -4\right), t, \mathsf{fma}\left(x, 9 \cdot y, b\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(9, y \cdot \frac{x}{z \cdot c}, a \cdot \frac{t \cdot -4}{c}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 67.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -1.75 \cdot 10^{+161}:\\ \;\;\;\;a \cdot \frac{t \cdot -4}{c}\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{+37}:\\ \;\;\;\;\mathsf{fma}\left(x, 9 \cdot y, b\right) \cdot \frac{1}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= t -1.75e+161)
   (* a (/ (* t -4.0) c))
   (if (<= t 3.4e+37)
     (* (fma x (* 9.0 y) b) (/ 1.0 (* z c)))
     (* -4.0 (* t (/ a 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 (t <= -1.75e+161) {
		tmp = a * ((t * -4.0) / c);
	} else if (t <= 3.4e+37) {
		tmp = fma(x, (9.0 * y), b) * (1.0 / (z * c));
	} else {
		tmp = -4.0 * (t * (a / 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 (t <= -1.75e+161)
		tmp = Float64(a * Float64(Float64(t * -4.0) / c));
	elseif (t <= 3.4e+37)
		tmp = Float64(fma(x, Float64(9.0 * y), b) * Float64(1.0 / Float64(z * c)));
	else
		tmp = Float64(-4.0 * Float64(t * Float64(a / 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[t, -1.75e+161], N[(a * N[(N[(t * -4.0), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.4e+37], N[(N[(x * N[(9.0 * y), $MachinePrecision] + b), $MachinePrecision] * N[(1.0 / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.74999999999999994e161

   1. Initial program 76.1%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l/ N/A

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

      4. lower-/.f64 N/A

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

   4. Applied rewrites 76.1%

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

   5. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-*.f64 32.9

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

   7. Applied rewrites 32.9%

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

   8. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. associate-*r* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. associate-*r/ N/A

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

      7. lower-/.f64 N/A

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

      8. lower-*.f64 84.6

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

   10. Applied rewrites 84.6%

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

   if -1.74999999999999994e161 < t < 3.40000000000000006e37

   1. Initial program 84.4%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l/ N/A

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

      4. lower-/.f64 N/A

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

   4. Applied rewrites 83.2%

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

   5. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-*.f64 69.0

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

   7. Applied rewrites 69.0%

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

      1. lift-/.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-/l/ N/A

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

      4. lift-*.f64 N/A

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

      5. div-inv N/A

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

      6. lift-/.f64 N/A

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

      7. lower-*.f64 71.4

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

   9. Applied rewrites 71.5%

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

   if 3.40000000000000006e37 < t

   1. Initial program 78.2%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l/ N/A

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

      4. lower-/.f64 N/A

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

   4. Applied rewrites 75.4%

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

   5. Taylor expanded in a around inf

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   6. 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. lower-*.f64 30.3

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

   7. Applied rewrites 30.3%

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

   9. Applied rewrites 38.7%

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

4. Final simplification 66.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.75 \cdot 10^{+161}:\\ \;\;\;\;a \cdot \frac{t \cdot -4}{c}\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{+37}:\\ \;\;\;\;\mathsf{fma}\left(x, 9 \cdot y, b\right) \cdot \frac{1}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 67.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -1.75 \cdot 10^{+161}:\\ \;\;\;\;a \cdot \frac{t \cdot -4}{c}\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{+37}:\\ \;\;\;\;\frac{\mathsf{fma}\left(9, x \cdot y, b\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= t -1.75e+161)
   (* a (/ (* t -4.0) c))
   (if (<= t 3.4e+37) (/ (fma 9.0 (* x y) b) (* z c)) (* -4.0 (* t (/ a 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 (t <= -1.75e+161) {
		tmp = a * ((t * -4.0) / c);
	} else if (t <= 3.4e+37) {
		tmp = fma(9.0, (x * y), b) / (z * c);
	} else {
		tmp = -4.0 * (t * (a / 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 (t <= -1.75e+161)
		tmp = Float64(a * Float64(Float64(t * -4.0) / c));
	elseif (t <= 3.4e+37)
		tmp = Float64(fma(9.0, Float64(x * y), b) / Float64(z * c));
	else
		tmp = Float64(-4.0 * Float64(t * Float64(a / 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[t, -1.75e+161], N[(a * N[(N[(t * -4.0), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.4e+37], N[(N[(9.0 * N[(x * y), $MachinePrecision] + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.74999999999999994e161

   1. Initial program 76.1%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l/ N/A

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

      4. lower-/.f64 N/A

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

   4. Applied rewrites 76.1%

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

   5. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-*.f64 32.9

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

   7. Applied rewrites 32.9%

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

   8. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. associate-*r* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. associate-*r/ N/A

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

      7. lower-/.f64 N/A

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

      8. lower-*.f64 84.6

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

   10. Applied rewrites 84.6%

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

   if -1.74999999999999994e161 < t < 3.40000000000000006e37

   1. Initial program 84.4%

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

   3. Taylor expanded in z 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. lower-fma.f64 N/A

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

      3. lower-*.f64 71.5

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

   5. Applied rewrites 71.5%

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

   if 3.40000000000000006e37 < t

   1. Initial program 78.2%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l/ N/A

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

      4. lower-/.f64 N/A

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

   4. Applied rewrites 75.4%

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

   5. Taylor expanded in a around inf

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   6. 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. lower-*.f64 30.3

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

   7. Applied rewrites 30.3%

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

   9. Applied rewrites 38.7%

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

4. Final simplification 66.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.75 \cdot 10^{+161}:\\ \;\;\;\;a \cdot \frac{t \cdot -4}{c}\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{+37}:\\ \;\;\;\;\frac{\mathsf{fma}\left(9, x \cdot y, b\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 50.5% accurate, 1.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{+49}:\\ \;\;\;\;a \cdot \frac{t \cdot -4}{c}\\ \mathbf{elif}\;z \leq 0.0008:\\ \;\;\;\;b \cdot \frac{1}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= z -3.8e+49)
   (* a (/ (* t -4.0) c))
   (if (<= z 0.0008) (* b (/ 1.0 (* z c))) (* -4.0 (* t (/ a 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 <= -3.8e+49) {
		tmp = a * ((t * -4.0) / c);
	} else if (z <= 0.0008) {
		tmp = b * (1.0 / (z * c));
	} else {
		tmp = -4.0 * (t * (a / c));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (z <= (-3.8d+49)) then
        tmp = a * ((t * (-4.0d0)) / c)
    else if (z <= 0.0008d0) then
        tmp = b * (1.0d0 / (z * c))
    else
        tmp = (-4.0d0) * (t * (a / c))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (z <= -3.8e+49) {
		tmp = a * ((t * -4.0) / c);
	} else if (z <= 0.0008) {
		tmp = b * (1.0 / (z * c));
	} else {
		tmp = -4.0 * (t * (a / c));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if z <= -3.8e+49:
		tmp = a * ((t * -4.0) / c)
	elif z <= 0.0008:
		tmp = b * (1.0 / (z * c))
	else:
		tmp = -4.0 * (t * (a / 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 <= -3.8e+49)
		tmp = Float64(a * Float64(Float64(t * -4.0) / c));
	elseif (z <= 0.0008)
		tmp = Float64(b * Float64(1.0 / Float64(z * c)));
	else
		tmp = Float64(-4.0 * Float64(t * Float64(a / c)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (z <= -3.8e+49)
		tmp = a * ((t * -4.0) / c);
	elseif (z <= 0.0008)
		tmp = b * (1.0 / (z * c));
	else
		tmp = -4.0 * (t * (a / c));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[z, -3.8e+49], N[(a * N[(N[(t * -4.0), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.0008], N[(b * N[(1.0 / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.7999999999999999e49

   1. Initial program 51.6%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l/ N/A

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

      4. lower-/.f64 N/A

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

   4. Applied rewrites 55.9%

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

   5. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-*.f64 34.3

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

   7. Applied rewrites 34.3%

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

   8. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. associate-*r* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. associate-*r/ N/A

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

      7. lower-/.f64 N/A

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

      8. lower-*.f64 56.2

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

   10. Applied rewrites 56.2%

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

   if -3.7999999999999999e49 < z < 8.00000000000000038e-4

   1. Initial program 96.3%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   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. *-commutative N/A

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

      3. lower-*.f64 46.5

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

   5. Applied rewrites 46.5%

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

   7. Applied rewrites 46.5%

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

   if 8.00000000000000038e-4 < z

   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. Step-by-step derivation

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l/ N/A

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

      4. lower-/.f64 N/A

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

   4. Applied rewrites 66.6%

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

   5. Taylor expanded in a around inf

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   6. 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. lower-*.f64 53.9

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

   7. Applied rewrites 53.9%

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

   9. Applied rewrites 50.5%

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

4. Final simplification 49.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{+49}:\\ \;\;\;\;a \cdot \frac{t \cdot -4}{c}\\ \mathbf{elif}\;z \leq 0.0008:\\ \;\;\;\;b \cdot \frac{1}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 50.6% accurate, 1.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := -4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{if}\;z \leq -3.95 \cdot 10^{+49}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 0.0008:\\ \;\;\;\;b \cdot \frac{1}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* -4.0 (* t (/ a c)))))
   (if (<= z -3.95e+49) t_1 (if (<= z 0.0008) (* b (/ 1.0 (* z c))) t_1))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = -4.0 * (t * (a / c));
	double tmp;
	if (z <= -3.95e+49) {
		tmp = t_1;
	} else if (z <= 0.0008) {
		tmp = b * (1.0 / (z * c));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (-4.0d0) * (t * (a / c))
    if (z <= (-3.95d+49)) then
        tmp = t_1
    else if (z <= 0.0008d0) then
        tmp = b * (1.0d0 / (z * c))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = -4.0 * (t * (a / c));
	double tmp;
	if (z <= -3.95e+49) {
		tmp = t_1;
	} else if (z <= 0.0008) {
		tmp = b * (1.0 / (z * c));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	t_1 = -4.0 * (t * (a / c))
	tmp = 0
	if z <= -3.95e+49:
		tmp = t_1
	elif z <= 0.0008:
		tmp = b * (1.0 / (z * c))
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(-4.0 * Float64(t * Float64(a / c)))
	tmp = 0.0
	if (z <= -3.95e+49)
		tmp = t_1;
	elseif (z <= 0.0008)
		tmp = Float64(b * Float64(1.0 / Float64(z * c)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = -4.0 * (t * (a / c));
	tmp = 0.0;
	if (z <= -3.95e+49)
		tmp = t_1;
	elseif (z <= 0.0008)
		tmp = b * (1.0 / (z * c));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.95e+49], t$95$1, If[LessEqual[z, 0.0008], N[(b * N[(1.0 / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -3.9500000000000002e49 or 8.00000000000000038e-4 < z

   1. Initial program 65.5%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l/ N/A

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

      4. lower-/.f64 N/A

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

   4. Applied rewrites 62.1%

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

   5. Taylor expanded in a around inf

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   6. 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. lower-*.f64 54.8

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

   7. Applied rewrites 54.8%

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

   9. Applied rewrites 54.3%

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

   if -3.9500000000000002e49 < z < 8.00000000000000038e-4

   1. Initial program 96.3%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   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. *-commutative N/A

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

      3. lower-*.f64 46.5

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

   5. Applied rewrites 46.5%

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

   7. Applied rewrites 46.5%

      \[\leadsto \frac{1}{z \cdot c} \cdot \color{blue}{b} \]
3. Recombined 2 regimes into one program.

4. Final simplification 50.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.95 \cdot 10^{+49}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;z \leq 0.0008:\\ \;\;\;\;b \cdot \frac{1}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 50.1% accurate, 1.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \frac{-4 \cdot \left(t \cdot a\right)}{c}\\ \mathbf{if}\;z \leq -4.2 \cdot 10^{+49}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 0.0008:\\ \;\;\;\;b \cdot \frac{1}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (* -4.0 (* t a)) c)))
   (if (<= z -4.2e+49) t_1 (if (<= z 0.0008) (* b (/ 1.0 (* z c))) t_1))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (-4.0 * (t * a)) / c;
	double tmp;
	if (z <= -4.2e+49) {
		tmp = t_1;
	} else if (z <= 0.0008) {
		tmp = b * (1.0 / (z * c));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((-4.0d0) * (t * a)) / c
    if (z <= (-4.2d+49)) then
        tmp = t_1
    else if (z <= 0.0008d0) then
        tmp = b * (1.0d0 / (z * c))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (-4.0 * (t * a)) / c;
	double tmp;
	if (z <= -4.2e+49) {
		tmp = t_1;
	} else if (z <= 0.0008) {
		tmp = b * (1.0 / (z * c));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	t_1 = (-4.0 * (t * a)) / c
	tmp = 0
	if z <= -4.2e+49:
		tmp = t_1
	elif z <= 0.0008:
		tmp = b * (1.0 / (z * c))
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(-4.0 * Float64(t * a)) / c)
	tmp = 0.0
	if (z <= -4.2e+49)
		tmp = t_1;
	elseif (z <= 0.0008)
		tmp = Float64(b * Float64(1.0 / Float64(z * c)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (-4.0 * (t * a)) / c;
	tmp = 0.0;
	if (z <= -4.2e+49)
		tmp = t_1;
	elseif (z <= 0.0008)
		tmp = b * (1.0 / (z * c));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]}, If[LessEqual[z, -4.2e+49], t$95$1, If[LessEqual[z, 0.0008], N[(b * N[(1.0 / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -4.20000000000000022e49 or 8.00000000000000038e-4 < z

   1. Initial program 65.5%

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

   3. Taylor expanded in z around inf

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 54.8

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

   5. Applied rewrites 54.8%

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

   if -4.20000000000000022e49 < z < 8.00000000000000038e-4

   1. Initial program 96.3%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   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. *-commutative N/A

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

      3. lower-*.f64 46.5

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

   5. Applied rewrites 46.5%

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

   7. Applied rewrites 46.5%

      \[\leadsto \frac{1}{z \cdot c} \cdot \color{blue}{b} \]
3. Recombined 2 regimes into one program.

4. Final simplification 50.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{+49}:\\ \;\;\;\;\frac{-4 \cdot \left(t \cdot a\right)}{c}\\ \mathbf{elif}\;z \leq 0.0008:\\ \;\;\;\;b \cdot \frac{1}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{-4 \cdot \left(t \cdot a\right)}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 35.5% accurate, 2.8× speedup

Math

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

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c) :precision binary64 (/ b (* z c)))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	return b / (z * c);
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    code = b / (z * c)
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	return b / (z * c);
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	return b / (z * c)

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	return Float64(b / Float64(z * c))
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp = code(x, y, z, t, a, b, c)
	tmp = b / (z * c);
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 82.0%

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

3. Taylor expanded in b around 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. *-commutative N/A

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

   3. lower-*.f64 34.6

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

5. Applied rewrites 34.6%

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

Developer Target 1: 80.5% 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 2024232 
(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)))