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

Average Error: 0.3 → 0.3

Time: 1.4s

Precision: binary64

\[ \begin{array}{c}[x, y] = \mathsf{sort}([x, y])\\ \end{array} \]

Math

\[\left(x \cdot 27\right) \cdot y \]

↓

\[x \cdot \left(27 \cdot y\right) \]

FPCore

(FPCore (x y) :precision binary64 (* (* x 27.0) y))

↓

(FPCore (x y) :precision binary64 (* x (* 27.0 y)))

C

double code(double x, double y) {
	return (x * 27.0) * y;
}

↓

double code(double x, double y) {
	return x * (27.0 * y);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (x * 27.0d0) * y
end function

↓

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = x * (27.0d0 * y)
end function

Java

public static double code(double x, double y) {
	return (x * 27.0) * y;
}

↓

public static double code(double x, double y) {
	return x * (27.0 * y);
}

Python

def code(x, y):
	return (x * 27.0) * y

↓

def code(x, y):
	return x * (27.0 * y)

Julia

function code(x, y)
	return Float64(Float64(x * 27.0) * y)
end

↓

function code(x, y)
	return Float64(x * Float64(27.0 * y))
end

MATLAB

function tmp = code(x, y)
	tmp = (x * 27.0) * y;
end

↓

function tmp = code(x, y)
	tmp = x * (27.0 * y);
end

Wolfram

code[x_, y_] := N[(N[(x * 27.0), $MachinePrecision] * y), $MachinePrecision]

↓

code[x_, y_] := N[(x * N[(27.0 * y), $MachinePrecision]), $MachinePrecision]

Error

Bits error versus x

Bits error versus y

Derivation

1. Initial program 0.3

   \[\left(x \cdot 27\right) \cdot y \]

2. Simplified 0.3

   \[\leadsto \color{blue}{x \cdot \left(27 \cdot y\right)} \]

3. Final simplification 0.3

   \[\leadsto x \cdot \left(27 \cdot y\right) \]

Reproduce

herbie shell --seed 2022150 
(FPCore (x y)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, F"
  :precision binary64
  (* (* x 27.0) y))