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

Percentage Accurate: 95.4% → 97.6%

Time: 24.7s

Alternatives: 12

Speedup: 0.9×

• 27.7% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ \left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (+ (- (* x 2.0) (* (* (* y 9.0) z) t)) (* (* a 27.0) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	return ((x * 2.0) - (((y * 9.0) * z) * t)) + ((a * 27.0) * b);
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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
    code = ((x * 2.0d0) - (((y * 9.0d0) * z) * t)) + ((a * 27.0d0) * b)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return ((x * 2.0) - (((y * 9.0) * z) * t)) + ((a * 27.0) * b);
}

Python

def code(x, y, z, t, a, b):
	return ((x * 2.0) - (((y * 9.0) * z) * t)) + ((a * 27.0) * b)

Julia

function code(x, y, z, t, a, b)
	return Float64(Float64(Float64(x * 2.0) - Float64(Float64(Float64(y * 9.0) * z) * t)) + Float64(Float64(a * 27.0) * b))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = ((x * 2.0) - (((y * 9.0) * z) * t)) + ((a * 27.0) * b);
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(N[(x * 2.0), $MachinePrecision] - N[(N[(N[(y * 9.0), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision] + N[(N[(a * 27.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]

Initial Program: 95.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (+ (- (* x 2.0) (* (* (* y 9.0) z) t)) (* (* a 27.0) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	return ((x * 2.0) - (((y * 9.0) * z) * t)) + ((a * 27.0) * b);
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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
    code = ((x * 2.0d0) - (((y * 9.0d0) * z) * t)) + ((a * 27.0d0) * b)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return ((x * 2.0) - (((y * 9.0) * z) * t)) + ((a * 27.0) * b);
}

Python

def code(x, y, z, t, a, b):
	return ((x * 2.0) - (((y * 9.0) * z) * t)) + ((a * 27.0) * b)

Julia

function code(x, y, z, t, a, b)
	return Float64(Float64(Float64(x * 2.0) - Float64(Float64(Float64(y * 9.0) * z) * t)) + Float64(Float64(a * 27.0) * b))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = ((x * 2.0) - (((y * 9.0) * z) * t)) + ((a * 27.0) * b);
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(N[(x * 2.0), $MachinePrecision] - N[(N[(N[(y * 9.0), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision] + N[(N[(a * 27.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]

Alternative 1: 97.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;y \cdot 9 \leq -4 \cdot 10^{+66}:\\ \;\;\;\;y \cdot \mathsf{fma}\left(27 \cdot b, \frac{a}{y}, \mathsf{fma}\left(t, z \cdot -9, \frac{x \cdot 2}{y}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y \cdot t, z \cdot -9, \mathsf{fma}\left(a, 27 \cdot b, x \cdot 2\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= (* y 9.0) -4e+66)
   (* y (fma (* 27.0 b) (/ a y) (fma t (* z -9.0) (/ (* x 2.0) y))))
   (fma (* y t) (* z -9.0) (fma a (* 27.0 b) (* x 2.0)))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y * 9.0) <= -4e+66) {
		tmp = y * fma((27.0 * b), (a / y), fma(t, (z * -9.0), ((x * 2.0) / y)));
	} else {
		tmp = fma((y * t), (z * -9.0), fma(a, (27.0 * b), (x * 2.0)));
	}
	return tmp;
}

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (Float64(y * 9.0) <= -4e+66)
		tmp = Float64(y * fma(Float64(27.0 * b), Float64(a / y), fma(t, Float64(z * -9.0), Float64(Float64(x * 2.0) / y))));
	else
		tmp = fma(Float64(y * t), Float64(z * -9.0), fma(a, Float64(27.0 * b), Float64(x * 2.0)));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[N[(y * 9.0), $MachinePrecision], -4e+66], N[(y * N[(N[(27.0 * b), $MachinePrecision] * N[(a / y), $MachinePrecision] + N[(t * N[(z * -9.0), $MachinePrecision] + N[(N[(x * 2.0), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * t), $MachinePrecision] * N[(z * -9.0), $MachinePrecision] + N[(a * N[(27.0 * b), $MachinePrecision] + N[(x * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 y #s(literal 9 binary64)) < -3.99999999999999978e66

   1. Initial program 92.5%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(\left(2 \cdot \frac{x}{y} + 27 \cdot \frac{a \cdot b}{y}\right) - 9 \cdot \left(t \cdot z\right)\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{y \cdot \left(\left(2 \cdot \frac{x}{y} + 27 \cdot \frac{a \cdot b}{y}\right) - 9 \cdot \left(t \cdot z\right)\right)} \]

      2. +-commutative N/A

         \[\leadsto y \cdot \left(\color{blue}{\left(27 \cdot \frac{a \cdot b}{y} + 2 \cdot \frac{x}{y}\right)} - 9 \cdot \left(t \cdot z\right)\right) \]

      3. associate--l+ N/A

         \[\leadsto y \cdot \color{blue}{\left(27 \cdot \frac{a \cdot b}{y} + \left(2 \cdot \frac{x}{y} - 9 \cdot \left(t \cdot z\right)\right)\right)} \]

      4. sub-neg N/A

         \[\leadsto y \cdot \left(27 \cdot \frac{a \cdot b}{y} + \color{blue}{\left(2 \cdot \frac{x}{y} + \left(\mathsf{neg}\left(9 \cdot \left(t \cdot z\right)\right)\right)\right)}\right) \]

      5. metadata-eval N/A

         \[\leadsto y \cdot \left(27 \cdot \frac{a \cdot b}{y} + \left(\color{blue}{\left(\mathsf{neg}\left(-2\right)\right)} \cdot \frac{x}{y} + \left(\mathsf{neg}\left(9 \cdot \left(t \cdot z\right)\right)\right)\right)\right) \]

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

         \[\leadsto y \cdot \left(27 \cdot \frac{a \cdot b}{y} + \left(\color{blue}{\left(\mathsf{neg}\left(-2 \cdot \frac{x}{y}\right)\right)} + \left(\mathsf{neg}\left(9 \cdot \left(t \cdot z\right)\right)\right)\right)\right) \]

      7. distribute-neg-in N/A

         \[\leadsto y \cdot \left(27 \cdot \frac{a \cdot b}{y} + \color{blue}{\left(\mathsf{neg}\left(\left(-2 \cdot \frac{x}{y} + 9 \cdot \left(t \cdot z\right)\right)\right)\right)}\right) \]

      8. metadata-eval N/A

         \[\leadsto y \cdot \left(27 \cdot \frac{a \cdot b}{y} + \left(\mathsf{neg}\left(\left(-2 \cdot \frac{x}{y} + \color{blue}{\left(\mathsf{neg}\left(-9\right)\right)} \cdot \left(t \cdot z\right)\right)\right)\right)\right) \]

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

         \[\leadsto y \cdot \left(27 \cdot \frac{a \cdot b}{y} + \left(\mathsf{neg}\left(\color{blue}{\left(-2 \cdot \frac{x}{y} - -9 \cdot \left(t \cdot z\right)\right)}\right)\right)\right) \]

      10. lower-fma.f64 N/A

          \[\leadsto y \cdot \color{blue}{\mathsf{fma}\left(27, \frac{a \cdot b}{y}, \mathsf{neg}\left(\left(-2 \cdot \frac{x}{y} - -9 \cdot \left(t \cdot z\right)\right)\right)\right)} \]

      11. lower-/.f64 N/A

          \[\leadsto y \cdot \mathsf{fma}\left(27, \color{blue}{\frac{a \cdot b}{y}}, \mathsf{neg}\left(\left(-2 \cdot \frac{x}{y} - -9 \cdot \left(t \cdot z\right)\right)\right)\right) \]

      12. lower-*.f64 N/A

          \[\leadsto y \cdot \mathsf{fma}\left(27, \frac{\color{blue}{a \cdot b}}{y}, \mathsf{neg}\left(\left(-2 \cdot \frac{x}{y} - -9 \cdot \left(t \cdot z\right)\right)\right)\right) \]

      13. neg-sub0 N/A

          \[\leadsto y \cdot \mathsf{fma}\left(27, \frac{a \cdot b}{y}, \color{blue}{0 - \left(-2 \cdot \frac{x}{y} - -9 \cdot \left(t \cdot z\right)\right)}\right) \]

      14. associate--r- N/A

          \[\leadsto y \cdot \mathsf{fma}\left(27, \frac{a \cdot b}{y}, \color{blue}{\left(0 - -2 \cdot \frac{x}{y}\right) + -9 \cdot \left(t \cdot z\right)}\right) \]

   5. Applied rewrites 98.0%

      \[\leadsto \color{blue}{y \cdot \mathsf{fma}\left(27, \frac{a \cdot b}{y}, \mathsf{fma}\left(t, z \cdot -9, 2 \cdot \frac{x}{y}\right)\right)} \]
   6. Step-by-step derivation

   7. Applied rewrites 99.5%

      \[\leadsto y \cdot \mathsf{fma}\left(27 \cdot b, \color{blue}{\frac{a}{y}}, \mathsf{fma}\left(t, z \cdot -9, \frac{2 \cdot x}{y}\right)\right) \]

   if -3.99999999999999978e66 < (*.f64 y #s(literal 9 binary64))

   1. Initial program 96.7%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b} \]

      2. lift--.f64 N/A

         \[\leadsto \color{blue}{\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)} + \left(a \cdot 27\right) \cdot b \]

      3. sub-neg N/A

         \[\leadsto \color{blue}{\left(x \cdot 2 + \left(\mathsf{neg}\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right)\right)} + \left(a \cdot 27\right) \cdot b \]

      4. +-commutative N/A

         \[\leadsto \color{blue}{\left(\left(\mathsf{neg}\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right) + x \cdot 2\right)} + \left(a \cdot 27\right) \cdot b \]

      5. associate-+l+ N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right) + \left(x \cdot 2 + \left(a \cdot 27\right) \cdot b\right)} \]

      6. lift-*.f64 N/A

         \[\leadsto \left(\mathsf{neg}\left(\color{blue}{\left(\left(y \cdot 9\right) \cdot z\right) \cdot t}\right)\right) + \left(x \cdot 2 + \left(a \cdot 27\right) \cdot b\right) \]

      7. *-commutative N/A

         \[\leadsto \left(\mathsf{neg}\left(\color{blue}{t \cdot \left(\left(y \cdot 9\right) \cdot z\right)}\right)\right) + \left(x \cdot 2 + \left(a \cdot 27\right) \cdot b\right) \]

      8. lift-*.f64 N/A

         \[\leadsto \left(\mathsf{neg}\left(t \cdot \color{blue}{\left(\left(y \cdot 9\right) \cdot z\right)}\right)\right) + \left(x \cdot 2 + \left(a \cdot 27\right) \cdot b\right) \]

      9. lift-*.f64 N/A

         \[\leadsto \left(\mathsf{neg}\left(t \cdot \left(\color{blue}{\left(y \cdot 9\right)} \cdot z\right)\right)\right) + \left(x \cdot 2 + \left(a \cdot 27\right) \cdot b\right) \]

      10. associate-*l* N/A

          \[\leadsto \left(\mathsf{neg}\left(t \cdot \color{blue}{\left(y \cdot \left(9 \cdot z\right)\right)}\right)\right) + \left(x \cdot 2 + \left(a \cdot 27\right) \cdot b\right) \]

      11. associate-*r* N/A

          \[\leadsto \left(\mathsf{neg}\left(\color{blue}{\left(t \cdot y\right) \cdot \left(9 \cdot z\right)}\right)\right) + \left(x \cdot 2 + \left(a \cdot 27\right) \cdot b\right) \]

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

          \[\leadsto \color{blue}{\left(t \cdot y\right) \cdot \left(\mathsf{neg}\left(9 \cdot z\right)\right)} + \left(x \cdot 2 + \left(a \cdot 27\right) \cdot b\right) \]

      13. +-commutative N/A

          \[\leadsto \left(t \cdot y\right) \cdot \left(\mathsf{neg}\left(9 \cdot z\right)\right) + \color{blue}{\left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right)} \]

      14. lower-fma.f64 N/A

          \[\leadsto \color{blue}{\mathsf{fma}\left(t \cdot y, \mathsf{neg}\left(9 \cdot z\right), \left(a \cdot 27\right) \cdot b + x \cdot 2\right)} \]

      15. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{y \cdot t}, \mathsf{neg}\left(9 \cdot z\right), \left(a \cdot 27\right) \cdot b + x \cdot 2\right) \]

      16. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{y \cdot t}, \mathsf{neg}\left(9 \cdot z\right), \left(a \cdot 27\right) \cdot b + x \cdot 2\right) \]

      17. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(y \cdot t, \mathsf{neg}\left(\color{blue}{z \cdot 9}\right), \left(a \cdot 27\right) \cdot b + x \cdot 2\right) \]

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

          \[\leadsto \mathsf{fma}\left(y \cdot t, \color{blue}{z \cdot \left(\mathsf{neg}\left(9\right)\right)}, \left(a \cdot 27\right) \cdot b + x \cdot 2\right) \]

      19. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(y \cdot t, \color{blue}{z \cdot \left(\mathsf{neg}\left(9\right)\right)}, \left(a \cdot 27\right) \cdot b + x \cdot 2\right) \]

      20. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(y \cdot t, z \cdot \color{blue}{-9}, \left(a \cdot 27\right) \cdot b + x \cdot 2\right) \]

   4. Applied rewrites 99.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y \cdot t, z \cdot -9, \mathsf{fma}\left(a, 27 \cdot b, x \cdot 2\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 99.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot 9 \leq -4 \cdot 10^{+66}:\\ \;\;\;\;y \cdot \mathsf{fma}\left(27 \cdot b, \frac{a}{y}, \mathsf{fma}\left(t, z \cdot -9, \frac{x \cdot 2}{y}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y \cdot t, z \cdot -9, \mathsf{fma}\left(a, 27 \cdot b, x \cdot 2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 56.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := \left(y \cdot z\right) \cdot \left(t \cdot -9\right)\\ t_2 := t \cdot \left(\left(y \cdot 9\right) \cdot z\right)\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{+45}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq -2 \cdot 10^{-79}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;t\_2 \leq 4 \cdot 10^{-210}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+57}:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (* y z) (* t -9.0))) (t_2 (* t (* (* y 9.0) z))))
   (if (<= t_2 -1e+45)
     t_1
     (if (<= t_2 -2e-79)
       (* x 2.0)
       (if (<= t_2 4e-210)
         (* 27.0 (* a b))
         (if (<= t_2 5e+57) (* x 2.0) t_1))))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (y * z) * (t * -9.0);
	double t_2 = t * ((y * 9.0) * z);
	double tmp;
	if (t_2 <= -1e+45) {
		tmp = t_1;
	} else if (t_2 <= -2e-79) {
		tmp = x * 2.0;
	} else if (t_2 <= 4e-210) {
		tmp = 27.0 * (a * b);
	} else if (t_2 <= 5e+57) {
		tmp = x * 2.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (y * z) * (t * (-9.0d0))
    t_2 = t * ((y * 9.0d0) * z)
    if (t_2 <= (-1d+45)) then
        tmp = t_1
    else if (t_2 <= (-2d-79)) then
        tmp = x * 2.0d0
    else if (t_2 <= 4d-210) then
        tmp = 27.0d0 * (a * b)
    else if (t_2 <= 5d+57) then
        tmp = x * 2.0d0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (y * z) * (t * -9.0);
	double t_2 = t * ((y * 9.0) * z);
	double tmp;
	if (t_2 <= -1e+45) {
		tmp = t_1;
	} else if (t_2 <= -2e-79) {
		tmp = x * 2.0;
	} else if (t_2 <= 4e-210) {
		tmp = 27.0 * (a * b);
	} else if (t_2 <= 5e+57) {
		tmp = x * 2.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	t_1 = (y * z) * (t * -9.0)
	t_2 = t * ((y * 9.0) * z)
	tmp = 0
	if t_2 <= -1e+45:
		tmp = t_1
	elif t_2 <= -2e-79:
		tmp = x * 2.0
	elif t_2 <= 4e-210:
		tmp = 27.0 * (a * b)
	elif t_2 <= 5e+57:
		tmp = x * 2.0
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(y * z) * Float64(t * -9.0))
	t_2 = Float64(t * Float64(Float64(y * 9.0) * z))
	tmp = 0.0
	if (t_2 <= -1e+45)
		tmp = t_1;
	elseif (t_2 <= -2e-79)
		tmp = Float64(x * 2.0);
	elseif (t_2 <= 4e-210)
		tmp = Float64(27.0 * Float64(a * b));
	elseif (t_2 <= 5e+57)
		tmp = Float64(x * 2.0);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (y * z) * (t * -9.0);
	t_2 = t * ((y * 9.0) * z);
	tmp = 0.0;
	if (t_2 <= -1e+45)
		tmp = t_1;
	elseif (t_2 <= -2e-79)
		tmp = x * 2.0;
	elseif (t_2 <= 4e-210)
		tmp = 27.0 * (a * b);
	elseif (t_2 <= 5e+57)
		tmp = x * 2.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(y * z), $MachinePrecision] * N[(t * -9.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(N[(y * 9.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -1e+45], t$95$1, If[LessEqual[t$95$2, -2e-79], N[(x * 2.0), $MachinePrecision], If[LessEqual[t$95$2, 4e-210], N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 5e+57], N[(x * 2.0), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < -9.9999999999999993e44 or 4.99999999999999972e57 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)

   1. Initial program 90.6%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(t \cdot \left(y \cdot z\right)\right) \cdot -9} \]

      2. associate-*l* N/A

         \[\leadsto \color{blue}{t \cdot \left(\left(y \cdot z\right) \cdot -9\right)} \]

      3. *-commutative N/A

         \[\leadsto t \cdot \color{blue}{\left(-9 \cdot \left(y \cdot z\right)\right)} \]

      4. lower-*.f64 N/A

         \[\leadsto \color{blue}{t \cdot \left(-9 \cdot \left(y \cdot z\right)\right)} \]

      5. *-commutative N/A

         \[\leadsto t \cdot \color{blue}{\left(\left(y \cdot z\right) \cdot -9\right)} \]

      6. lower-*.f64 N/A

         \[\leadsto t \cdot \color{blue}{\left(\left(y \cdot z\right) \cdot -9\right)} \]

      7. lower-*.f64 69.4

         \[\leadsto t \cdot \left(\color{blue}{\left(y \cdot z\right)} \cdot -9\right) \]

   5. Applied rewrites 69.4%

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

   7. Applied rewrites 69.4%

      \[\leadsto \left(y \cdot z\right) \cdot \color{blue}{\left(-9 \cdot t\right)} \]

   if -9.9999999999999993e44 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < -2e-79 or 4.0000000000000002e-210 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < 4.99999999999999972e57

   1. Initial program 99.6%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{2 \cdot x} \]
   4. Step-by-step derivation

      1. lower-*.f64 38.2

         \[\leadsto \color{blue}{2 \cdot x} \]

   5. Applied rewrites 38.2%

      \[\leadsto \color{blue}{2 \cdot x} \]

   if -2e-79 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < 4.0000000000000002e-210

   1. Initial program 99.1%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{27 \cdot \left(a \cdot b\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{27 \cdot \left(a \cdot b\right)} \]

      2. lower-*.f64 50.3

         \[\leadsto 27 \cdot \color{blue}{\left(a \cdot b\right)} \]

   5. Applied rewrites 50.3%

      \[\leadsto \color{blue}{27 \cdot \left(a \cdot b\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 56.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \cdot \left(\left(y \cdot 9\right) \cdot z\right) \leq -1 \cdot 10^{+45}:\\ \;\;\;\;\left(y \cdot z\right) \cdot \left(t \cdot -9\right)\\ \mathbf{elif}\;t \cdot \left(\left(y \cdot 9\right) \cdot z\right) \leq -2 \cdot 10^{-79}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;t \cdot \left(\left(y \cdot 9\right) \cdot z\right) \leq 4 \cdot 10^{-210}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;t \cdot \left(\left(y \cdot 9\right) \cdot z\right) \leq 5 \cdot 10^{+57}:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot z\right) \cdot \left(t \cdot -9\right)\\ \end{array} \]
5. Add Preprocessing

Developer Target 1: 94.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y < 7.590524218811189 \cdot 10^{-161}:\\ \;\;\;\;\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + a \cdot \left(27 \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot 2 - 9 \cdot \left(y \cdot \left(t \cdot z\right)\right)\right) + \left(a \cdot 27\right) \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (< y 7.590524218811189e-161)
   (+ (- (* x 2.0) (* (* (* y 9.0) z) t)) (* a (* 27.0 b)))
   (+ (- (* x 2.0) (* 9.0 (* y (* t z)))) (* (* a 27.0) b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y < 7.590524218811189e-161) {
		tmp = ((x * 2.0) - (((y * 9.0) * z) * t)) + (a * (27.0 * b));
	} else {
		tmp = ((x * 2.0) - (9.0 * (y * (t * z)))) + ((a * 27.0) * b);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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) :: tmp
    if (y < 7.590524218811189d-161) then
        tmp = ((x * 2.0d0) - (((y * 9.0d0) * z) * t)) + (a * (27.0d0 * b))
    else
        tmp = ((x * 2.0d0) - (9.0d0 * (y * (t * z)))) + ((a * 27.0d0) * b)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y < 7.590524218811189e-161) {
		tmp = ((x * 2.0) - (((y * 9.0) * z) * t)) + (a * (27.0 * b));
	} else {
		tmp = ((x * 2.0) - (9.0 * (y * (t * z)))) + ((a * 27.0) * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y < 7.590524218811189e-161:
		tmp = ((x * 2.0) - (((y * 9.0) * z) * t)) + (a * (27.0 * b))
	else:
		tmp = ((x * 2.0) - (9.0 * (y * (t * z)))) + ((a * 27.0) * b)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y < 7.590524218811189e-161)
		tmp = Float64(Float64(Float64(x * 2.0) - Float64(Float64(Float64(y * 9.0) * z) * t)) + Float64(a * Float64(27.0 * b)));
	else
		tmp = Float64(Float64(Float64(x * 2.0) - Float64(9.0 * Float64(y * Float64(t * z)))) + Float64(Float64(a * 27.0) * b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y < 7.590524218811189e-161)
		tmp = ((x * 2.0) - (((y * 9.0) * z) * t)) + (a * (27.0 * b));
	else
		tmp = ((x * 2.0) - (9.0 * (y * (t * z)))) + ((a * 27.0) * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Less[y, 7.590524218811189e-161], N[(N[(N[(x * 2.0), $MachinePrecision] - N[(N[(N[(y * 9.0), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision] + N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x * 2.0), $MachinePrecision] - N[(9.0 * N[(y * N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(a * 27.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]]

Reproduce

herbie shell --seed 2024223 
(FPCore (x y z t a b)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, A"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< y 7590524218811189/100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (+ (- (* x 2) (* (* (* y 9) z) t)) (* a (* 27 b))) (+ (- (* x 2) (* 9 (* y (* t z)))) (* (* a 27) b))))

  (+ (- (* x 2.0) (* (* (* y 9.0) z) t)) (* (* a 27.0) b)))