Average Error: 0.3 → 0.0
Time: 5.7s
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 2019004 +o rules:numerics
(FPCore (x)
  :name "Jmat.Real.lambertw, estimator"
  (- (log x) (log (log x))))

Details

Time bar (total: 5.5s)Debug log

sample108.0ms

Algorithm
intervals

simplify6.0ms

Counts
1 → 1
Calls

1 calls. Slowest were:

6.0ms
(- (log x) (log (log x)))

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize19.0ms

Local error

Found 2 expressions with local error:

0.2b
(- (log x) (log (log x)))
0.0b
(log (log x))

rewrite12.0ms

Algorithm
rewrite-expression-head
Counts
2 → 49
Calls

2 calls. Slowest were:

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

series681.0ms

Counts
2 → 6
Calls

2 calls. Slowest were:

429.0ms
(- (log x) (log (log x)))
252.0ms
(log (log x))

simplify1.1s

Counts
44 → 55
Calls

44 calls. Slowest were:

293.0ms
(- (log -1) (+ (log (- (log -1) (log (/ -1 x)))) (log (/ -1 x))))
58.0ms
(fma (sqrt (log x)) (sqrt (log x)) (- (* (log (log x)) 1)))
51.0ms
(fma 1 (log x) (- (* (log (log x)) 1)))

prune343.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize8.0ms

Local error

Found 1 expressions with local error:

0.3b
(/ x (log x))

rewrite1.0ms

Algorithm
rewrite-expression-head
Counts
1 → 15
Calls

1 calls. Slowest were:

1.0ms
(/ x (log x))

series243.0ms

Counts
1 → 3
Calls

1 calls. Slowest were:

243.0ms
(/ x (log x))

simplify85.0ms

Counts
6 → 18
Calls

6 calls. Slowest were:

46.0ms
(/ x (- (log -1) (log (/ -1 x))))
34.0ms
(* -1 (/ x (log (/ 1 x))))
1.0ms
(cbrt (log x))

prune157.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes92.0ms

Accuracy

0% (0.0b remaining)

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

bsearch1.0ms

end0.0ms

sample2.6s

Algorithm
intervals