Details

Time bar (total: 3.6s)

sample85.0ms

Algorithm
intervals
Results
19.0ms495×body80nan
19.0ms103×body2560nan
11.0ms72×body1280nan
10.0ms256×body80valid
6.0ms46×body640nan
2.0ms18×body320nan
1.0ms18×body160nan

simplify5.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0105
1115
2115

prune2.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 32.9b

Counts
2 → 1

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b
(+ x (sqrt (- (* x x) 1.0)))
30.6b
(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))

series120.0ms

Counts
2 → 6
Calls
2 calls:
65.0ms
(+ x (sqrt (- (* x x) 1.0)))
55.0ms
(sqrt (- (* x x) 1.0))

simplify86.0ms

Algorithm
egg-herbie
Counts
34 → 34
Iterations

Useful iterations: 3 (75.0ms)

IterNodesCost
0217221
1657211
22555205
35001204

prune77.0ms

Filtered
34 candidates to 29 candidates (85.3%)
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
(sqrt (+ x (sqrt 1.0)))
0.0b
(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
0.5b
(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
21×add-sqr-sqrt
19×sqrt-prod
14×*-un-lft-identity sqrt-div
associate-*r*
pow1 add-cube-cbrt
associate-*l*
add-exp-log flip3-+ add-cbrt-cube flip-+ add-log-exp
frac-times unswap-sqr
flip3-- sqrt-pow1 pow1/2 pow-prod-down flip--
associate-*r/ associate-*l/ distribute-lft-out difference-of-squares
+-commutative rem-sqrt-square sqrt-unprod prod-exp sum-log *-commutative cbrt-unprod distribute-lft-out--
Counts
3 → 69
Calls
3 calls:
4.0ms
(sqrt (+ x (sqrt 1.0)))
3.0ms
(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
13.0ms
(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

series422.0ms

Counts
3 → 9
Calls
3 calls:
67.0ms
(sqrt (+ x (sqrt 1.0)))
154.0ms
(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
201.0ms
(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

simplify45.0ms

Algorithm
egg-herbie
Counts
78 → 78
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
0411796
11435742
25002724

prune178.0ms

Filtered
78 candidates to 58 candidates (74.4%)
Pruning

1 alts after pruning (0 fresh and 1 done)

PrunedKeptTotal
New78078
Fresh000
Picked011
Done000
Total78179

Merged error: 0b

Counts
79 → 1

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0139
1139

end0.0ms

sample2.5s

Algorithm
intervals
Results
602.0ms3062×body2560nan
549.0ms16092×body80nan
388.0ms2414×body1280nan
326.0ms8000×body80valid
162.0ms1285×body640nan
64.0ms658×body320nan
20.0ms300×body160nan

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