Details

Time bar (total: 14.1s)

sample111.0ms

Algorithm
intervals
Results
44.0ms54×body1280valid
22.0ms38×body640valid
15.0ms135×body80valid
12.0ms18×body320valid
3.0ms12×body160valid

simplify3.0s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01724
13424
27124
312724
416924
527124
665424
7206924
done500024

prune5.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 19.4b

Counts
2 → 1

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* 2.0 J) (cos (/ K 2.0)))
0.2b
(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
8.3b
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
9.9b
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))

rewrite38.0ms

Algorithm
rewrite-expression-head
Rules
28×add-exp-log
20×pow1
18×add-cbrt-cube
15×*-un-lft-identity
12×add-sqr-sqrt prod-exp
11×add-cube-cbrt
10×associate-*r*
9×pow-prod-down cbrt-unprod
8×sqrt-prod
7×unpow-prod-down
4×sqrt-div pow-exp add-log-exp
3×pow-unpow times-frac div-exp
2×flip3-+ associate-*r/ associate-*l* *-commutative flip-+ distribute-lft-out
1×pow-to-exp rem-sqrt-square pow-pow sqrt-pow1 pow1/2 div-inv sqr-pow
Counts
4 → 85
Calls
4 calls:
6.0ms
(* (* 2.0 J) (cos (/ K 2.0)))
8.0ms
(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
7.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
15.0ms
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))

series130.0ms

Counts
4 → 12
Calls
4 calls:
8.0ms
(* (* 2.0 J) (cos (/ K 2.0)))
37.0ms
(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
36.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
49.0ms
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))

simplify1.2s

Counts
97 → 97
Iterations

Useful iterations: 2 (281.0ms)

IterNodesCost
02022013
14951800
217351613
done50001613

prune263.0ms

Filtered
62 candidates to 97 candidates (-56.5%)
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New89897
Fresh000
Picked011
Done000
Total89998

Merged error: 14.7b

Counts
98 → 9

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* 2.0 J) (cos (/ K 2.0)))
0.2b
(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
8.3b
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
10.0b
(* (* -2.0 J) (* (cos (/ K 2.0)) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))))

rewrite38.0ms

Algorithm
rewrite-expression-head
Rules
31×add-exp-log
23×pow1
21×add-cbrt-cube
14×prod-exp
11×*-un-lft-identity pow-prod-down cbrt-unprod
10×add-sqr-sqrt
9×add-cube-cbrt
7×unpow-prod-down
4×sqrt-div associate-*r/ associate-*r* pow-exp sqrt-prod add-log-exp
3×pow-unpow times-frac div-exp
2×flip3-+ associate-*l* *-commutative flip-+
1×pow-to-exp rem-sqrt-square pow-pow sqrt-pow1 pow1/2 div-inv distribute-lft-out sqr-pow
Counts
4 → 82
Calls
4 calls:
6.0ms
(* (* 2.0 J) (cos (/ K 2.0)))
8.0ms
(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
7.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
14.0ms
(* (* -2.0 J) (* (cos (/ K 2.0)) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))))

series129.0ms

Counts
4 → 12
Calls
4 calls:
8.0ms
(* (* 2.0 J) (cos (/ K 2.0)))
35.0ms
(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
36.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
50.0ms
(* (* -2.0 J) (* (cos (/ K 2.0)) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))))

simplify1.2s

Counts
94 → 94
Iterations

Useful iterations: 2 (237.0ms)

IterNodesCost
02001983
14891775
215851557
done50001557

prune234.0ms

Filtered
58 candidates to 94 candidates (-62.1%)
Pruning

10 alts after pruning (8 fresh and 2 done)

PrunedKeptTotal
New93194
Fresh077
Picked011
Done011
Total9310103

Merged error: 14.7b

Counts
103 → 10

localize19.0ms

Local error

Found 4 expressions with local error:

8.3b
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
8.3b
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
10.0b
(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
10.0b
(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))

rewrite35.0ms

Algorithm
rewrite-expression-head
Rules
32×sqrt-prod
18×*-un-lft-identity
16×add-sqr-sqrt
12×sqrt-div
10×pow1 add-cube-cbrt sqrt-pow1
6×rem-sqrt-square pow1/2
4×add-exp-log flip3-+ add-cbrt-cube flip-+ distribute-lft-out add-log-exp
Counts
4 → 76
Calls
4 calls:
10.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
8.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
8.0ms
(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
8.0ms
(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))

series209.0ms

Counts
4 → 12
Calls
4 calls:
39.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
38.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
68.0ms
(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
64.0ms
(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))

simplify1.4s

Counts
88 → 88
Iterations

Useful iterations: 4 (676.0ms)

IterNodesCost
0971968
11921666
24171612
310251602
432801592
done50011592

prune362.0ms

Filtered
62 candidates to 88 candidates (-41.9%)
Pruning

10 alts after pruning (7 fresh and 3 done)

PrunedKeptTotal
New88088
Fresh077
Picked011
Done022
Total881098

Merged error: 14.7b

Counts
98 → 10

localize19.0ms

Local error

Found 4 expressions with local error:

8.3b
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
9.9b
(* (* (* -2.0 J) (cos (/ K 2.0))) (* (sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))) (sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))))
10.0b
(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
10.0b
(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))

rewrite62.0ms

Algorithm
rewrite-expression-head
Rules
34×sqrt-div
30×pow1
28×sqrt-prod
25×add-exp-log add-cbrt-cube
15×*-un-lft-identity pow-prod-down prod-exp cbrt-unprod
14×add-sqr-sqrt
10×associate-*r/
9×add-cube-cbrt sqrt-pow1 flip3-+ flip-+
5×rem-sqrt-square pow1/2
4×frac-times add-log-exp
3×distribute-lft-out
2×associate-*l/
1×associate-*r* associate-*l* *-commutative
Counts
4 → 96
Calls
4 calls:
7.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
31.0ms
(* (* (* -2.0 J) (cos (/ K 2.0))) (* (sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))) (sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))))
8.0ms
(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
8.0ms
(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))

series217.0ms

Counts
4 → 12
Calls
4 calls:
38.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
47.0ms
(* (* (* -2.0 J) (cos (/ K 2.0))) (* (sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))) (sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))))
66.0ms
(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
66.0ms
(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))

simplify1.1s

Counts
108 → 108
Iterations

Useful iterations: done (1.1s)

IterNodesCost
01683817
14042594
212392336
done50002334

prune328.0ms

Filtered
62 candidates to 108 candidates (-74.2%)
Pruning

10 alts after pruning (6 fresh and 4 done)

PrunedKeptTotal
New1080108
Fresh066
Picked011
Done033
Total10810118

Merged error: 14.7b

Counts
118 → 10

regimes660.0ms

Accuracy

88.9% (0.6b remaining)

Error of 13.7b against oracle of 13.1b and baseline of 18.4b

bsearch1.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
034118
146118
done46118

end0.0ms

sample3.2s

Algorithm
intervals
Results
1.3s1515×body1280valid
742.0ms1268×body640valid
502.0ms4323×body80valid
247.0ms596×body320valid
83.0ms308×body160valid

Profiling

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