Average Error: 0.3 → 0.0
Time: 6.4s
Precision: 64
Internal Precision: 128
\[\log x - \log \left(\log x\right)\]
↓
\[\log \left(\frac{x}{\log x}\right)\]

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.3

    \[\log x - \log \left(\log x\right)\]
  2. Using strategy rm

  3. Applied diff-log0.0

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2019007 
(FPCore (x)
  :name "Jmat.Real.lambertw, estimator"
  (- (log x) (log (log x))))

Details

Time bar (total: 6.1s)Debug log

sample79.0ms

Algorithm
intervals

simplify3.0ms

Counts
1 → 1
Calls

1 calls. Slowest were:

3.0ms
(- (log x) (log (log x)))

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize27.0ms

Local error

Found 2 expressions with local error:

0.3b
(- (log x) (log (log x)))
0.1b
(log (log x))

rewrite11.0ms

Algorithm
rewrite-expression-head
Counts
2 → 30
Calls

2 calls. Slowest were:

9.0ms
(- (log x) (log (log x)))
2.0ms
(log (log x))

series709.0ms

Counts
2 → 6
Calls

2 calls. Slowest were:

416.0ms
(- (log x) (log (log x)))
292.0ms
(log (log x))

simplify332.0ms

Counts
18 → 36
Calls

18 calls. Slowest were:

259.0ms
(- (log -1) (+ (log (- (log -1) (log (/ -1 x)))) (log (/ -1 x))))
33.0ms
(log (- (log -1) (log (/ -1 x))))
13.0ms
(- (+ (log (/ 1 x)) (log (- (log (/ 1 x))))))

prune372.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize12.0ms

Local error

Found 2 expressions with local error:

0.2b
(/ x (log x))
0.0b
(log (/ x (log x)))

rewrite2.0ms

Algorithm
rewrite-expression-head
Counts
2 → 27
Calls

2 calls. Slowest were:

1.0ms
(log (/ x (log x)))
1.0ms
(/ x (log x))

series635.0ms

Counts
2 → 6
Calls

2 calls. Slowest were:

349.0ms
(log (/ x (log x)))
286.0ms
(/ x (log x))

simplify842.0ms

Counts
15 → 33
Calls

15 calls. Slowest were:

696.0ms
(- (log (/ -1 (- (log -1) (log (/ -1 x))))) (log (/ -1 x)))
49.0ms
(- (log (/ -1 (log (/ 1 x)))) (log (/ 1 x)))
45.0ms
(/ x (- (log -1) (log (/ -1 x))))

prune218.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes89.0ms

Accuracy

0% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 0.0b

bsearch0.0ms

end0.0ms

sample2.8s

Algorithm
intervals