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

Average Accuracy: 99.5% → 99.6%

Time: 2.8s

Precision: binary64

Cost: 320

Math

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

↓

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

FPCore

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

↓

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

C

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

↓

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

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 = 27.0d0 * (y * x)
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 27.0 * (y * x);
}

Python

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

↓

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

Julia

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

↓

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

MATLAB

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

↓

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

Wolfram

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

↓

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

Derivation

1. Initial program 99.5%

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

2. Simplified 99.5%

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

   [Start] 99.5	\[ \left(x \cdot 27\right) \cdot y \]
   associate-*l* [=>] 99.5	\[ \color{blue}{x \cdot \left(27 \cdot y\right)} \]

3. Taylor expanded in x around 0 99.6%

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

4. Final simplification 99.6%

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

Reproduce

herbie shell --seed 2023146 
(FPCore (x y)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, F"
  :precision binary64
  (* (* x 27.0) y))