Average Error: 0.3 → 0.0
Time: 7.2s
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 2018362 +o rules:numerics
(FPCore (x)
  :name "Jmat.Real.lambertw, estimator"
  (- (log x) (log (log x))))

Details

Time bar (total: 4.3s)Debug log

start99.0ms

Algorithm
intervals

setup18.0ms

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)))
0.1b
(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))

series738.0ms

Counts
2 → 6
Calls

2 calls. Slowest were:

463.0ms
(- (log x) (log (log x)))
275.0ms
(log (log x))

simplify1.2s

Counts
44 → 55
Calls

44 calls. Slowest were:

246.0ms
(- (log -1) (+ (log (- (log -1) (log (/ -1 x)))) (log (/ -1 x))))
62.0ms
(fma (sqrt (log x)) (sqrt (log x)) (- (* (log (log x)) 1)))
59.0ms
(fma (sqrt (log x)) (sqrt (log x)) (- (* (log (log x)) 1)))

prune514.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize13.0ms

Local error

Found 2 expressions with local error:

0.3b
(/ x (log x))
0.0b
(log (/ x (log x)))

rewrite3.0ms

Algorithm
rewrite-expression-head
Counts
2 → 31
Calls

2 calls. Slowest were:

2.0ms
(log (/ x (log x)))
1.0ms
(/ x (log x))

series596.0ms

Counts
2 → 6
Calls

2 calls. Slowest were:

322.0ms
(log (/ x (log x)))
274.0ms
(/ x (log x))

simplify754.0ms

Counts
15 → 37
Calls

15 calls. Slowest were:

614.0ms
(- (log (/ -1 (- (log -1) (log (/ -1 x))))) (log (/ -1 x)))
47.0ms
(- (log (/ -1 (log (/ 1 x)))) (log (/ 1 x)))
34.0ms
(/ x (- (log -1) (log (/ -1 x))))

prune332.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes65.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms