Details

Time bar (total: 6.0s)

sample13.0ms

Algorithm
intervals
Results
6.0ms257×body80valid

simplify4.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
056
196
2106
done106

prune2.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 28.1b

Counts
2 → 1

localize4.0ms

Local error

Found 1 expressions with local error:

27.0b
(sqrt (* (* 2.0 x) x))

rewrite4.0ms

Algorithm
rewrite-expression-head
Rules
7×pow1
3×sqrt-pow1 pow-prod-down
1×add-exp-log add-sqr-sqrt add-cube-cbrt *-un-lft-identity pow1/2 sqrt-prod add-cbrt-cube add-log-exp
Counts
1 → 12
Calls
1 calls:
4.0ms
(sqrt (* (* 2.0 x) x))

series4.0ms

Counts
1 → 3
Calls
1 calls:
4.0ms
(sqrt (* (* 2.0 x) x))

simplify959.0ms

Counts
15 → 15
Iterations

Useful iterations: 2 (11.0ms)

IterNodesCost
02199
13484
26480
38280
49080
510280
613480
721580
846480
9149380
done500080

prune48.0ms

Filtered
11 candidates to 15 candidates (-36.4%)
Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New8715
Fresh000
Picked101
Done000
Total9716

Merged error: 0.1b

Counts
16 → 7

localize7.0ms

Local error

Found 1 expressions with local error:

27.0b
(pow (* (* 2.0 x) x) 1/2)

rewrite7.0ms

Algorithm
rewrite-expression-head
Rules
7×pow1 add-exp-log
3×pow-unpow pow-pow pow-prod-down pow-exp prod-exp
2×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
1×pow-to-exp unpow-prod-down add-cbrt-cube unpow1/2 add-log-exp sqr-pow
Counts
1 → 20
Calls
1 calls:
6.0ms
(pow (* (* 2.0 x) x) 1/2)

series26.0ms

Counts
1 → 3
Calls
1 calls:
26.0ms
(pow (* (* 2.0 x) x) 1/2)

simplify1.5s

Counts
23 → 23
Iterations

Useful iterations: 4 (467.0ms)

IterNodesCost
053210
1120177
2253164
3728155
43554125
done5000125

prune51.0ms

Filtered
14 candidates to 23 candidates (-64.3%)
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New21223
Fresh066
Picked011
Done000
Total21930

Merged error: 0.1b

Counts
30 → 9

localize6.0ms

Local error

Found 2 expressions with local error:

0.3b
(pow (/ -1 x) -2)
27.0b
(sqrt (* (pow (/ -1 x) -2) 2.0))

rewrite12.0ms

Algorithm
rewrite-expression-head
Rules
13×unpow-prod-down
10×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
9×times-frac
5×add-exp-log
4×pow1
3×pow-unpow
2×pow-exp add-cbrt-cube add-log-exp
1×pow-to-exp pow-pow sqrt-pow1 pow1/2 div-exp sqrt-prod div-inv sqr-pow
Counts
2 → 38
Calls
2 calls:
5.0ms
(pow (/ -1 x) -2)
6.0ms
(sqrt (* (pow (/ -1 x) -2) 2.0))

series8.0ms

Counts
2 → 6
Calls
2 calls:
4.0ms
(pow (/ -1 x) -2)
4.0ms
(sqrt (* (pow (/ -1 x) -2) 2.0))

simplify1.7s

Counts
44 → 44
Iterations

Useful iterations: done (1.7s)

IterNodesCost
092417
1185377
2458367
31200354
44680324
done5000321

prune79.0ms

Filtered
30 candidates to 44 candidates (-46.7%)
Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New44044
Fresh077
Picked011
Done011
Total44953

Merged error: 0.1b

Counts
53 → 9

localize7.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (sqrt (* (* 2.0 x) x)))
0.5b
(* (sqrt (sqrt (* (* 2.0 x) x))) (sqrt (sqrt (* (* 2.0 x) x))))
27.0b
(sqrt (* (* 2.0 x) x))
27.0b
(sqrt (* (* 2.0 x) x))

rewrite37.0ms

Algorithm
rewrite-expression-head
Rules
158×pow1
154×sqrt-pow1
82×pow-prod-down
33×sqrt-prod
26×add-sqr-sqrt
24×pow1/2
21×pow-prod-up
13×add-cube-cbrt *-un-lft-identity pow-sqr
9×swap-sqr
7×associate-*r* associate-*l*
6×add-exp-log add-cbrt-cube
4×add-log-exp unswap-sqr
1×pow2 rem-sqrt-square pow-plus sqrt-unprod prod-exp rem-square-sqrt *-commutative cbrt-unprod
Counts
4 → 130
Calls
4 calls:
5.0ms
(sqrt (sqrt (* (* 2.0 x) x)))
16.0ms
(* (sqrt (sqrt (* (* 2.0 x) x))) (sqrt (sqrt (* (* 2.0 x) x))))
4.0ms
(sqrt (* (* 2.0 x) x))
4.0ms
(sqrt (* (* 2.0 x) x))

series19.0ms

Counts
4 → 12
Calls
4 calls:
6.0ms
(sqrt (sqrt (* (* 2.0 x) x)))
5.0ms
(* (sqrt (sqrt (* (* 2.0 x) x))) (sqrt (sqrt (* (* 2.0 x) x))))
4.0ms
(sqrt (* (* 2.0 x) x))
4.0ms
(sqrt (* (* 2.0 x) x))

simplify762.0ms

Counts
142 → 142
Iterations

Useful iterations: done (758.0ms)

IterNodesCost
01001759
12121092
2703978
32729911
done5000899

prune136.0ms

Filtered
58 candidates to 142 candidates (-144.8%)
Pruning

9 alts after pruning (6 fresh and 3 done)

PrunedKeptTotal
New1420142
Fresh066
Picked011
Done022
Total1429151

Merged error: 0.1b

Counts
151 → 9

regimes237.0ms

Accuracy

99.2% (0.3b remaining)

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

bsearch15.0ms

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

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01216
11916
22116
done2116

end0.0ms

sample338.0ms

Algorithm
intervals
Results
198.0ms8006×body80valid

Profiling

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