Details

Time bar (total: 13.4s)

sample118.0ms

Algorithm
intervals
Results
41.0ms85×body1280valid
24.0ms78×body640valid
19.0ms239×body80valid
9.0ms38×body320valid
2.0ms11×body160valid

simplify71.0ms

Counts
1 → 1
Iterations

Useful iterations: 1 (2.0ms)

IterNodesCost
01219
12513
24513
36513
48413
510213
611513
done11513

prune11.0ms

Filtered
1 candidates to 1 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New101
Fresh011
Picked000
Done000
Total112

Merged error: 0.5b

Counts
2 → 1

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
0.3b
(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
0.7b
(/ (cos th) (sqrt 2.0))
0.7b
(/ (cos th) (sqrt 2.0))

rewrite38.0ms

Algorithm
rewrite-expression-head
Rules
76×times-frac
70×add-sqr-sqrt
60×add-cube-cbrt *-un-lft-identity
44×associate-*l* sqrt-prod
32×add-exp-log add-cbrt-cube
14×pow1
12×prod-exp associate-/r* cbrt-unprod
6×cbrt-undiv div-exp pow-prod-down associate-/l* unswap-sqr
4×div-inv add-log-exp
2×frac-2neg associate-*r* associate-*l/ clear-num *-commutative
Counts
4 → 168
Calls
4 calls:
10.0ms
(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
10.0ms
(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
5.0ms
(/ (cos th) (sqrt 2.0))
6.0ms
(/ (cos th) (sqrt 2.0))

series50.0ms

Counts
4 → 12
Calls
4 calls:
19.0ms
(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
17.0ms
(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
6.0ms
(/ (cos th) (sqrt 2.0))
7.0ms
(/ (cos th) (sqrt 2.0))

simplify961.0ms

Counts
180 → 180
Iterations

Useful iterations: done (956.0ms)

IterNodesCost
01812118
14932012
215991832
done50001812

prune364.0ms

Filtered
116 candidates to 180 candidates (-55.2%)
Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New17010180
Fresh000
Picked101
Done000
Total17110181

Merged error: 0.0b

Counts
181 → 10

localize15.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (* a2 a2))
0.6b
(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
0.6b
(/ (cos th) (sqrt (sqrt 2.0)))
0.7b
(/ (cos th) (sqrt 2.0))

rewrite151.0ms

Algorithm
rewrite-expression-head
Rules
1149×sqrt-prod
1137×times-frac
626×add-sqr-sqrt
592×add-cube-cbrt *-un-lft-identity
283×associate-*l*
37×associate-/l*
34×add-exp-log add-cbrt-cube
24×associate-/r*
23×div-inv
13×unswap-sqr
11×cbrt-undiv div-exp
9×pow1 prod-exp cbrt-unprod
4×add-log-exp
3×frac-2neg pow-prod-down clear-num
1×associate-*r* associate-*l/ *-commutative associate-/l/
Counts
4 → 744
Calls
4 calls:
47.0ms
(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (* a2 a2))
19.0ms
(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
6.0ms
(/ (cos th) (sqrt (sqrt 2.0)))
5.0ms
(/ (cos th) (sqrt 2.0))

series37.0ms

Counts
4 → 12
Calls
4 calls:
16.0ms
(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (* a2 a2))
6.0ms
(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
9.0ms
(/ (cos th) (sqrt (sqrt 2.0)))
6.0ms
(/ (cos th) (sqrt 2.0))

simplify1.6s

Counts
756 → 756
Iterations

Useful iterations: done (1.5s)

IterNodesCost
056014715
1153813041
2371512044
done500112042

prune1.5s

Filtered
352 candidates to 756 candidates (-114.8%)
Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New7542756
Fresh279
Picked011
Done000
Total75610766

Merged error: 0.0b

Counts
766 → 10

localize29.0ms

Local error

Found 4 expressions with local error:

0.7b
(/ (cos th) (sqrt 2.0))
1.0b
(cbrt 2.0)
1.0b
(cbrt 2.0)
1.0b
(cbrt 2.0)

rewrite12.0ms

Algorithm
rewrite-expression-head
Rules
22×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
18×times-frac
12×sqrt-prod
9×cbrt-prod
6×add-exp-log associate-/r* add-cbrt-cube
4×pow1 add-log-exp
3×pow1/3 associate-/l*
1×cbrt-undiv frac-2neg div-exp clear-num div-inv
Counts
4 → 72
Calls
4 calls:
5.0ms
(/ (cos th) (sqrt 2.0))
2.0ms
(cbrt 2.0)
1.0ms
(cbrt 2.0)
2.0ms
(cbrt 2.0)

series6.0ms

Counts
4 → 6
Calls
4 calls:
6.0ms
(/ (cos th) (sqrt 2.0))
0.0ms
(cbrt 2.0)
0.0ms
(cbrt 2.0)
0.0ms
(cbrt 2.0)

simplify2.2s

Counts
78 → 78
Iterations

Useful iterations: 3 (218.0ms)

IterNodesCost
099710
1175655
2397629
31069612
43824612
done5000612

prune279.0ms

Filtered
55 candidates to 78 candidates (-41.8%)
Pruning

10 alts after pruning (8 fresh and 2 done)

PrunedKeptTotal
New78078
Fresh088
Picked011
Done011
Total781088

Merged error: 0.0b

Counts
88 → 10

localize15.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
0.6b
(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
0.6b
(/ (cos th) (sqrt (sqrt 2.0)))
0.7b
(/ (cos th) (sqrt 2.0))

rewrite76.0ms

Algorithm
rewrite-expression-head
Rules
616×sqrt-prod
614×times-frac
345×add-sqr-sqrt
340×add-cube-cbrt *-un-lft-identity
37×associate-/l*
25×add-exp-log add-cbrt-cube
24×associate-/r*
22×associate-*l*
14×div-inv
9×pow1
7×cbrt-undiv div-exp
6×prod-exp cbrt-unprod
4×add-log-exp
3×frac-2neg pow-prod-down clear-num unswap-sqr
1×associate-*r* associate-*l/ *-commutative associate-/l/
Counts
4 → 469
Calls
4 calls:
10.0ms
(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
17.0ms
(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
6.0ms
(/ (cos th) (sqrt (sqrt 2.0)))
5.0ms
(/ (cos th) (sqrt 2.0))

series37.0ms

Counts
4 → 12
Calls
4 calls:
16.0ms
(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
6.0ms
(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
9.0ms
(/ (cos th) (sqrt (sqrt 2.0)))
6.0ms
(/ (cos th) (sqrt 2.0))

simplify1.1s

Counts
481 → 481
Iterations

Useful iterations: done (1.1s)

IterNodesCost
04779858
111088538
226007929
done50007927

prune828.0ms

Filtered
189 candidates to 481 candidates (-154.5%)
Pruning

10 alts after pruning (7 fresh and 3 done)

PrunedKeptTotal
New4810481
Fresh077
Picked011
Done022
Total48110491

Merged error: 0.0b

Counts
491 → 10

regimes500.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 0.5b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 1 (1.0ms)

IterNodesCost
02537
13135
done3135

end0.0ms

sample3.4s

Algorithm
intervals
Results
1.2s2688×body1280valid
644.0ms2072×body640valid
596.0ms7888×body80valid
244.0ms1030×body320valid
87.0ms543×body160valid

Profiling

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