Data.HyperLogLog.Config:hll from hyperloglog-0.3.4

Average Error: 0.2 → 0.2

Time: 1.6s

Precision: binary64

Math

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

↓

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

FPCore

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

↓

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

C

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

↓

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

Fortran

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

↓

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

Java

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

↓

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

Python

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

↓

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

Julia

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

↓

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

MATLAB

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

↓

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

Wolfram

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

↓

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

Error

Bits error versus x

Bits error versus y

Derivation

1. Initial program 0.2

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

2. Final simplification 0.2

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

Reproduce

herbie shell --seed 2022150 
(FPCore (x y)
  :name "Data.HyperLogLog.Config:hll from hyperloglog-0.3.4"
  :precision binary64
  (* (* x y) y))