Statistics.Distribution.Binomial:directEntropy from math-functions-0.1.5.2

Average Error: 0.3 → 0.3

Time: 4.6s

Precision: binary64

Cost: 6784

Math

\[x \cdot \log x \]

↓

\[\log \left(\frac{1}{x}\right) \cdot \left(-x\right) \]

FPCore

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

↓

(FPCore (x) :precision binary64 (* (log (/ 1.0 x)) (- x)))

C

double code(double x) {
	return x * log(x);
}

↓

double code(double x) {
	return log((1.0 / x)) * -x;
}

Fortran

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

↓

real(8) function code(x)
    real(8), intent (in) :: x
    code = log((1.0d0 / x)) * -x
end function

Java

public static double code(double x) {
	return x * Math.log(x);
}

↓

public static double code(double x) {
	return Math.log((1.0 / x)) * -x;
}

Python

def code(x):
	return x * math.log(x)

↓

def code(x):
	return math.log((1.0 / x)) * -x

Julia

function code(x)
	return Float64(x * log(x))
end

↓

function code(x)
	return Float64(log(Float64(1.0 / x)) * Float64(-x))
end

MATLAB

function tmp = code(x)
	tmp = x * log(x);
end

↓

function tmp = code(x)
	tmp = log((1.0 / x)) * -x;
end

Wolfram

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

↓

code[x_] := N[(N[Log[N[(1.0 / x), $MachinePrecision]], $MachinePrecision] * (-x)), $MachinePrecision]

Derivation

1. Initial program 0.3

   \[x \cdot \log x \]

2. Taylor expanded in x around inf 0.3

   \[\leadsto \color{blue}{-1 \cdot \left(\log \left(\frac{1}{x}\right) \cdot x\right)} \]

3. Final simplification 0.3

   \[\leadsto \log \left(\frac{1}{x}\right) \cdot \left(-x\right) \]

Alternatives

Alternative 1
Error	0.3
Cost	6592

\[x \cdot \log x \]

Alternative 2
Error	61.6
Cost	64

\[0 \]

Reproduce

herbie shell --seed 2023039 
(FPCore (x)
  :name "Statistics.Distribution.Binomial:directEntropy from math-functions-0.1.5.2"
  :precision binary64
  (* x (log x)))