Details

Time bar (total: 8.7s)

sample14.0ms

Algorithm
intervals
Results
7.0ms257×body80valid

simplify5.0ms

Counts
1 → 1
Iterations

Useful iterations: 1 (1.0ms)

IterNodesCost
048
186
2126
3136
done136

prune5.0ms

Filtered
1 candidates to 1 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New011
Fresh101
Picked000
Done000
Total112

Merged error: 28.1b

Counts
2 → 1

localize4.0ms

Local error

Found 1 expressions with local error:

27.0b
(sqrt (* x (+ x x)))

rewrite5.0ms

Algorithm
rewrite-expression-head
Rules
4×pow1
2×sqrt-pow1 sqrt-div associate-*r/
1×add-exp-log add-sqr-sqrt add-cube-cbrt *-un-lft-identity flip3-+ pow1/2 pow-prod-down sqrt-prod add-cbrt-cube flip-+ add-log-exp
Counts
1 → 13
Calls
1 calls:
5.0ms
(sqrt (* x (+ x x)))

series4.0ms

Counts
1 → 3
Calls
1 calls:
4.0ms
(sqrt (* x (+ x x)))

simplify2.3s

Counts
16 → 16
Iterations

Useful iterations: 3 (50.0ms)

IterNodesCost
033132
16699
212791
334489
4157589
done500089

prune44.0ms

Filtered
13 candidates to 16 candidates (-23.1%)
Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New9716
Fresh000
Picked101
Done000
Total10717

Merged error: 0.1b

Counts
17 → 7

localize6.0ms

Local error

Found 1 expressions with local error:

27.0b
(pow (* x (+ x x)) 1/2)

rewrite7.0ms

Algorithm
rewrite-expression-head
Rules
4×pow1 add-exp-log
3×pow-unpow
2×add-sqr-sqrt add-cube-cbrt pow-pow *-un-lft-identity pow-exp
1×pow-to-exp unpow-prod-down pow-prod-down prod-exp add-cbrt-cube unpow1/2 add-log-exp sqr-pow
Counts
1 → 18
Calls
1 calls:
6.0ms
(pow (* x (+ x x)) 1/2)

series25.0ms

Counts
1 → 3
Calls
1 calls:
25.0ms
(pow (* x (+ x x)) 1/2)

simplify1.8s

Counts
21 → 21
Iterations

Useful iterations: 4 (613.0ms)

IterNodesCost
049197
1110162
2232158
3603149
42231119
done5001119

prune45.0ms

Filtered
13 candidates to 21 candidates (-61.5%)
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New19221
Fresh066
Picked011
Done000
Total19928

Merged error: 0.1b

Counts
28 → 9

localize6.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (sqrt (* x (+ x x))))
0.5b
(* (sqrt (sqrt (* x (+ x x)))) (sqrt (sqrt (* x (+ x x)))))
27.0b
(sqrt (* x (+ x x)))
27.0b
(sqrt (* x (+ x x)))

rewrite41.0ms

Algorithm
rewrite-expression-head
Rules
84×sqrt-pow1
71×pow1
33×sqrt-prod
32×sqrt-div
26×add-sqr-sqrt
25×pow-prod-down
22×pow1/2
20×associate-*r/
14×pow-prod-up
13×add-cube-cbrt *-un-lft-identity
9×flip3-+ swap-sqr flip-+
8×pow-sqr
7×associate-*r* associate-*l*
6×add-exp-log add-cbrt-cube
4×frac-times add-log-exp unswap-sqr
2×associate-*l/
1×pow2 rem-sqrt-square pow-plus sqrt-unprod prod-exp rem-square-sqrt *-commutative cbrt-unprod
Counts
4 → 124
Calls
4 calls:
6.0ms
(sqrt (sqrt (* x (+ x x))))
18.0ms
(* (sqrt (sqrt (* x (+ x x)))) (sqrt (sqrt (* x (+ x x)))))
5.0ms
(sqrt (* x (+ x x)))
6.0ms
(sqrt (* x (+ x x)))

series19.0ms

Counts
4 → 12
Calls
4 calls:
6.0ms
(sqrt (sqrt (* x (+ x x))))
5.0ms
(* (sqrt (sqrt (* x (+ x x)))) (sqrt (sqrt (* x (+ x x)))))
4.0ms
(sqrt (* x (+ x x)))
4.0ms
(sqrt (* x (+ x x)))

simplify2.0s

Counts
136 → 136
Iterations

Useful iterations: 3 (788.0ms)

IterNodesCost
01271941
12511121
27341013
33509917
done5000917

prune103.0ms

Filtered
70 candidates to 136 candidates (-94.3%)
Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New1351136
Fresh257
Picked011
Done011
Total1378145

Merged error: 0.1b

Counts
145 → 8

localize3.0ms

Local error

Found 1 expressions with local error:

0.4b
(* x (sqrt 2))

rewrite6.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt
6×associate-*r*
4×add-cube-cbrt *-un-lft-identity sqrt-prod
3×pow1 add-exp-log associate-*l* add-cbrt-cube
2×unswap-sqr
1×pow-prod-down prod-exp *-commutative cbrt-unprod add-log-exp
Counts
1 → 22
Calls
1 calls:
5.0ms
(* x (sqrt 2))

series7.0ms

Counts
1 → 3
Calls
1 calls:
7.0ms
(* x (sqrt 2))

simplify1.8s

Counts
25 → 25
Iterations

Useful iterations: 2 (15.0ms)

IterNodesCost
037158
169141
2121133
3157133
4214133
5351133
6770133
72304133
done5001133

prune28.0ms

Filtered
13 candidates to 25 candidates (-92.3%)
Pruning

10 alts after pruning (7 fresh and 3 done)

PrunedKeptTotal
New23225
Fresh055
Picked011
Done022
Total231033

Merged error: 0.1b

Counts
33 → 10

regimes55.0ms

Accuracy

99.1% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 30.7b

bsearch12.0ms

Steps
ItersRangePoint
8
-7.67443757966827e-305
8.126837495347253e-308
1.9786006080648e-310

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01216
11816
22016
done2016

end0.0ms

sample335.0ms

Algorithm
intervals
Results
201.0ms8006×body80valid

Profiling

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