Jmat.Real.lambertw, estimator

Average Error: 0.3 → 0.3

Time: 44.2s

Precision: binary64

Cost: 19648

Math

\[\log x - \log \log x \]

↓

\[\left(\left(\log x + 1\right) - \log \log x\right) - 1 \]

FPCore

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

↓

(FPCore (x) :precision binary64 (- (- (+ (log x) 1.0) (log (log x))) 1.0))

C

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

↓

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

Fortran

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

↓

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

Java

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

↓

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

Python

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

↓

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

Julia

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

↓

function code(x)
	return Float64(Float64(Float64(log(x) + 1.0) - log(log(x))) - 1.0)
end

MATLAB

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

↓

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

Wolfram

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

↓

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

Derivation

1. Initial program 0.3

   \[\log x - \log \log x \]

2. Applied egg-rr 0.3

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

3. Applied egg-rr 0.3

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

4. Final simplification 0.3

   \[\leadsto \left(\left(\log x + 1\right) - \log \log x\right) - 1 \]

Alternatives

Alternative 1
Error	0.3
Cost	19648

\[-2 + \left(\left(\log x - \log \log x\right) + 2\right) \]

Alternative 2
Error	0.3
Cost	19584

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

Alternative 3
Error	0.3
Cost	19392

\[\log x - \log \log x \]

Reproduce

herbie shell --seed 2023099 
(FPCore (x)
  :name "Jmat.Real.lambertw, estimator"
  :precision binary64
  (- (log x) (log (log x))))