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

Percentage Accurate: 95.5% → 98.0%

Time: 24.2s

Alternatives: 12

Speedup: 0.8×

• 27.2% 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: 95.5% 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: 98.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := z \cdot \left(9 \cdot y\right)\\ \mathbf{if}\;t\_1 \leq 4 \cdot 10^{+14}:\\ \;\;\;\;b \cdot \left(27 \cdot a\right) + \left(2 \cdot x - t \cdot t\_1\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(\frac{b \cdot 27}{y}, a, \left(-9 \cdot t\right) \cdot z\right), y, 2 \cdot x\right)\\ \end{array} \end{array} \]

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
 (let* ((t_1 (* z (* 9.0 y))))
   (if (<= t_1 4e+14)
     (+ (* b (* 27.0 a)) (- (* 2.0 x) (* t t_1)))
     (fma (fma (/ (* b 27.0) y) a (* (* -9.0 t) z)) y (* 2.0 x)))))

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 = z * (9.0 * y);
	double tmp;
	if (t_1 <= 4e+14) {
		tmp = (b * (27.0 * a)) + ((2.0 * x) - (t * t_1));
	} else {
		tmp = fma(fma(((b * 27.0) / y), a, ((-9.0 * t) * z)), y, (2.0 * x));
	}
	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(z * Float64(9.0 * y))
	tmp = 0.0
	if (t_1 <= 4e+14)
		tmp = Float64(Float64(b * Float64(27.0 * a)) + Float64(Float64(2.0 * x) - Float64(t * t_1)));
	else
		tmp = fma(fma(Float64(Float64(b * 27.0) / y), a, Float64(Float64(-9.0 * t) * z)), y, Float64(2.0 * x));
	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_] := Block[{t$95$1 = N[(z * N[(9.0 * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 4e+14], N[(N[(b * N[(27.0 * a), $MachinePrecision]), $MachinePrecision] + N[(N[(2.0 * x), $MachinePrecision] - N[(t * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(b * 27.0), $MachinePrecision] / y), $MachinePrecision] * a + N[(N[(-9.0 * t), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] * y + N[(2.0 * x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 y #s(literal 9 binary64)) z) < 4e14

   1. Initial program 98.9%

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

   if 4e14 < (*.f64 (*.f64 y #s(literal 9 binary64)) z)

   1. Initial program 89.5%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 14.3

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

   5. Applied rewrites 14.3%

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

   6. Taylor expanded in y around inf

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

      1. associate--l+ N/A

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

      2. +-commutative N/A

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

      3. distribute-rgt-in N/A

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

      4. associate-*r/ N/A

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

      5. associate-*l/ N/A

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

      6. associate-/l* N/A

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

      7. *-inverses N/A

         \[\leadsto \left(27 \cdot \frac{a \cdot b}{y} - 9 \cdot \left(t \cdot z\right)\right) \cdot y + \left(2 \cdot x\right) \cdot \color{blue}{1} \]

      8. *-inverses N/A

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

      9. associate-/l* N/A

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

      10. *-commutative N/A

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

      11. associate-*r/ N/A

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

      12. associate-*r/ N/A

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

      13. lower-fma.f64 N/A

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

   8. Applied rewrites 98.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(\frac{b \cdot 27}{y}, a, \left(t \cdot -9\right) \cdot z\right), y, \left(x \cdot 2\right) \cdot 1\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 98.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot \left(9 \cdot y\right) \leq 4 \cdot 10^{+14}:\\ \;\;\;\;b \cdot \left(27 \cdot a\right) + \left(2 \cdot x - t \cdot \left(z \cdot \left(9 \cdot y\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(\frac{b \cdot 27}{y}, a, \left(-9 \cdot t\right) \cdot z\right), y, 2 \cdot x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 54.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := \left(\left(z \cdot y\right) \cdot t\right) \cdot -9\\ t_2 := t \cdot \left(z \cdot \left(9 \cdot y\right)\right)\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{+90}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq -5 \cdot 10^{-21}:\\ \;\;\;\;b \cdot \left(27 \cdot a\right)\\ \mathbf{elif}\;t\_2 \leq 10^{-40}:\\ \;\;\;\;2 \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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 (* (* (* z y) t) -9.0)) (t_2 (* t (* z (* 9.0 y)))))
   (if (<= t_2 -1e+90)
     t_1
     (if (<= t_2 -5e-21) (* b (* 27.0 a)) (if (<= t_2 1e-40) (* 2.0 x) 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 = ((z * y) * t) * -9.0;
	double t_2 = t * (z * (9.0 * y));
	double tmp;
	if (t_2 <= -1e+90) {
		tmp = t_1;
	} else if (t_2 <= -5e-21) {
		tmp = b * (27.0 * a);
	} else if (t_2 <= 1e-40) {
		tmp = 2.0 * x;
	} 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 = ((z * y) * t) * (-9.0d0)
    t_2 = t * (z * (9.0d0 * y))
    if (t_2 <= (-1d+90)) then
        tmp = t_1
    else if (t_2 <= (-5d-21)) then
        tmp = b * (27.0d0 * a)
    else if (t_2 <= 1d-40) then
        tmp = 2.0d0 * x
    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 = ((z * y) * t) * -9.0;
	double t_2 = t * (z * (9.0 * y));
	double tmp;
	if (t_2 <= -1e+90) {
		tmp = t_1;
	} else if (t_2 <= -5e-21) {
		tmp = b * (27.0 * a);
	} else if (t_2 <= 1e-40) {
		tmp = 2.0 * x;
	} 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 = ((z * y) * t) * -9.0
	t_2 = t * (z * (9.0 * y))
	tmp = 0
	if t_2 <= -1e+90:
		tmp = t_1
	elif t_2 <= -5e-21:
		tmp = b * (27.0 * a)
	elif t_2 <= 1e-40:
		tmp = 2.0 * x
	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(Float64(z * y) * t) * -9.0)
	t_2 = Float64(t * Float64(z * Float64(9.0 * y)))
	tmp = 0.0
	if (t_2 <= -1e+90)
		tmp = t_1;
	elseif (t_2 <= -5e-21)
		tmp = Float64(b * Float64(27.0 * a));
	elseif (t_2 <= 1e-40)
		tmp = Float64(2.0 * x);
	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 = ((z * y) * t) * -9.0;
	t_2 = t * (z * (9.0 * y));
	tmp = 0.0;
	if (t_2 <= -1e+90)
		tmp = t_1;
	elseif (t_2 <= -5e-21)
		tmp = b * (27.0 * a);
	elseif (t_2 <= 1e-40)
		tmp = 2.0 * x;
	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[(N[(z * y), $MachinePrecision] * t), $MachinePrecision] * -9.0), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(z * N[(9.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -1e+90], t$95$1, If[LessEqual[t$95$2, -5e-21], N[(b * N[(27.0 * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 1e-40], N[(2.0 * x), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < -9.99999999999999966e89 or 9.9999999999999993e-41 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)

   1. Initial program 91.4%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 14.3

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

   5. Applied rewrites 14.3%

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

   6. Taylor expanded in y around inf

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 65.7

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

   8. Applied rewrites 65.7%

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

   10. Applied rewrites 65.8%

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

   if -9.99999999999999966e89 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < -4.99999999999999973e-21

   1. Initial program 99.7%

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

   3. Taylor expanded in a around inf

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 38.1

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

   5. Applied rewrites 38.1%

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

   if -4.99999999999999973e-21 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < 9.9999999999999993e-41

   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 x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 45.7

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

   5. Applied rewrites 45.7%

      \[\leadsto \color{blue}{x \cdot 2} \]
3. Recombined 3 regimes into one program.

4. Final simplification 54.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \cdot \left(z \cdot \left(9 \cdot y\right)\right) \leq -1 \cdot 10^{+90}:\\ \;\;\;\;\left(\left(z \cdot y\right) \cdot t\right) \cdot -9\\ \mathbf{elif}\;t \cdot \left(z \cdot \left(9 \cdot y\right)\right) \leq -5 \cdot 10^{-21}:\\ \;\;\;\;b \cdot \left(27 \cdot a\right)\\ \mathbf{elif}\;t \cdot \left(z \cdot \left(9 \cdot y\right)\right) \leq 10^{-40}:\\ \;\;\;\;2 \cdot x\\ \mathbf{else}:\\ \;\;\;\;\left(\left(z \cdot y\right) \cdot t\right) \cdot -9\\ \end{array} \]
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 2024230 
(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)))