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 2018360 +o rules:numerics
(FPCore (x)
  :name "Jmat.Real.lambertw, estimator"
  (- (log x) (log (log x))))

Details

Time bar (total: 2.8s)Debug log

start53.0ms

Algorithm
intervals

setup20.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize9.0ms

Local error

Found 2 expressions with local error:

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

rewrite7.0ms

Algorithm
rewrite-expression-head
Counts
2 → 49
Calls

2 calls. Slowest were:

5.0ms
(- (log x) (log (log x)))
1.0ms
(log (log x))

series709.0ms

Counts
2 → 6
Calls

2 calls. Slowest were:

443.0ms
(- (log x) (log (log x)))
265.0ms
(log (log x))

simplify995.0ms

Counts
44 → 55
Calls

44 calls. Slowest were:

257.0ms
(- (log -1) (+ (log (- (log -1) (log (/ -1 x)))) (log (/ -1 x))))
61.0ms
(log (- (log -1) (log (/ -1 x))))
50.0ms
(fma (sqrt (log x)) (sqrt (log x)) (- (* (log (log x)) 1)))

prune494.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize6.0ms

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))

series292.0ms

Counts
1 → 3
Calls

1 calls. Slowest were:

291.0ms
(/ x (log x))

simplify104.0ms

Counts
6 → 18
Calls

6 calls. Slowest were:

61.0ms
(/ x (- (log -1) (log (/ -1 x))))
36.0ms
(* -1 (/ x (log (/ 1 x))))
1.0ms
(/ x (log x))

prune141.0ms

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b