Details

Time bar (total: 3.1s)

analyze425.0ms

Algorithm
search

sample68.0ms

Algorithm
intervals
Results
25.0ms115×body2560nan
14.0ms86×body1280nan
10.0ms256×body80valid
5.0ms39×body640nan
2.0ms17×body320nan
0.0ms12×body80nan
0.0msbody160nan

simplify4.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0105
1115
2115

prune3.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 29.9b

Counts
2 → 1

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b
(+ x (sqrt (- (* x x) 1.0)))
27.8b
(sqrt (- (* x x) 1.0))

rewrite11.0ms

Algorithm
rewrite-expression-head
Rules
add-sqr-sqrt *-un-lft-identity
sqrt-prod add-log-exp
pow1 add-cube-cbrt
add-exp-log sqrt-div add-cbrt-cube
+-commutative rem-sqrt-square flip3-- sqrt-pow1 flip3-+ pow1/2 sum-log flip-- flip-+ distribute-lft-out difference-of-squares
Counts
2 → 28
Calls
2 calls:
6.0ms
(+ x (sqrt (- (* x x) 1.0)))
4.0ms
(sqrt (- (* x x) 1.0))

series9.0ms

Counts
2 → 6
Calls
2 calls:
5.0ms
(+ x (sqrt (- (* x x) 1.0)))
4.0ms
(sqrt (- (* x x) 1.0))

simplify77.0ms

Algorithm
egg-herbie
Counts
34 → 34
Iterations

Useful iterations: 3 (73.0ms)

IterNodesCost
0217221
1657211
22555205
35001204

prune63.0ms

Filtered
29 candidates to 34 candidates (-17.2%)
Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New33134
Fresh000
Picked101
Done000
Total34135

Merged error: 0b

Counts
35 → 1

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
0.0b
(sqrt (- x (sqrt 1.0)))
0.5b
(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
25×add-sqr-sqrt
22×sqrt-prod
14×*-un-lft-identity sqrt-div
associate-*r*
pow1 add-cube-cbrt
associate-*l*
add-exp-log add-cbrt-cube add-log-exp
frac-times flip3-- flip3-+ flip-- flip-+ difference-of-squares unswap-sqr
sqrt-pow1 pow1/2 pow-prod-down
associate-*r/ associate-*l/ distribute-lft-out--
+-commutative rem-sqrt-square sqrt-unprod prod-exp sum-log *-commutative cbrt-unprod distribute-lft-out
Counts
3 → 71
Calls
3 calls:
2.0ms
(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
4.0ms
(sqrt (- x (sqrt 1.0)))
13.0ms
(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

series28.0ms

Counts
3 → 9
Calls
3 calls:
9.0ms
(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
5.0ms
(sqrt (- x (sqrt 1.0)))
14.0ms
(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

simplify46.0ms

Algorithm
egg-herbie
Counts
80 → 80
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
0418800
11612762
25002748

prune187.0ms

Filtered
60 candidates to 80 candidates (-33.3%)
Pruning

1 alts after pruning (0 fresh and 1 done)

PrunedKeptTotal
New80080
Fresh000
Picked011
Done000
Total80181

Merged error: 0b

Counts
81 → 1

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0139
1139

end0.0ms

analyze275.0ms

Algorithm
search

sample1.8s

Algorithm
intervals
Results
600.0ms3071×body2560nan
410.0ms2463×body1280nan
329.0ms8000×body80valid
158.0ms1231×body640nan
62.0ms634×body320nan
19.0ms270×body160nan
15.0ms330×body80nan

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