Details

Time bar (total: 3.4s)

sample81.0ms

Algorithm
intervals
Results
21.0ms103×body2560nan
16.0ms495×body80nan
10.0ms72×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
0115
1125
2125

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))

rewrite12.0ms

Algorithm
rewrite-expression-head
Rules
add-sqr-sqrt *-un-lft-identity
add-cube-cbrt sqrt-prod add-log-exp
pow1 fma-def
add-exp-log expm1-log1p-u sqrt-div add-cbrt-cube log1p-expm1-u
+-commutative rem-sqrt-square flip3-- sqrt-pow1 flip3-+ pow1/2 sum-log flip-- flip-+ distribute-lft-out difference-of-squares
Counts
2 → 35
Calls
2 calls:
6.0ms
(+ x (sqrt (- (* x x) 1.0)))
5.0ms
(sqrt (- (* x x) 1.0))

series117.0ms

Counts
2 → 6
Calls
2 calls:
62.0ms
(+ x (sqrt (- (* x x) 1.0)))
55.0ms
(sqrt (- (* x x) 1.0))

simplify79.0ms

Algorithm
egg-herbie
Counts
41 → 41
Iterations

Useful iterations: 3 (75.0ms)

IterNodesCost
0235239
1739223
22858218
35001216

prune89.0ms

Filtered
41 candidates to 36 candidates (87.8%)
Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New40141
Fresh000
Picked101
Done000
Total41142

Merged error: 0b

Counts
42 → 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))))

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
26×add-sqr-sqrt
20×sqrt-prod
15×*-un-lft-identity
14×sqrt-div
add-cube-cbrt associate-*r*
pow1
associate-*l*
add-exp-log flip3-+ add-cbrt-cube flip-+ add-log-exp
frac-times unswap-sqr
expm1-log1p-u flip3-- fma-def sqrt-pow1 pow1/2 pow-prod-down flip-- log1p-expm1-u
associate-*r/ associate-*l/ hypot-def distribute-lft-out difference-of-squares
+-commutative rem-sqrt-square sqrt-unprod prod-exp sum-log *-commutative cbrt-unprod distribute-lft-out--
Counts
3 → 80
Calls
3 calls:
4.0ms
(sqrt (+ x (sqrt 1.0)))
3.0ms
(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
12.0ms
(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

series396.0ms

Counts
3 → 9
Calls
3 calls:
62.0ms
(sqrt (+ x (sqrt 1.0)))
138.0ms
(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
195.0ms
(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

simplify43.0ms

Algorithm
egg-herbie
Counts
89 → 89
Iterations

Useful iterations: 2 (35.0ms)

IterNodesCost
0439856
11551780
25001760

prune194.0ms

Filtered
89 candidates to 68 candidates (76.4%)
Pruning

1 alts after pruning (0 fresh and 1 done)

PrunedKeptTotal
New89089
Fresh000
Picked011
Done000
Total89190

Merged error: 0b

Counts
90 → 1

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0139
1139

end0.0ms

sample2.4s

Algorithm
intervals
Results
564.0ms3062×body2560nan
525.0ms16092×body80nan
363.0ms2414×body1280nan
307.0ms8000×body80valid
159.0ms1285×body640nan
60.0ms658×body320nan
19.0ms300×body160nan

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