Details

Time bar (total: 12.6s)

sample138.0ms

Algorithm
intervals
Results
52.0ms127×body1280valid
21.0ms256×pre80true
17.0ms67×body640valid
5.0ms26×body320valid
2.0ms29×body80valid
1.0ms7×body160valid

simplify3.0s

Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
099
1159
2229
3319
4379
5479
6659
7799
81079
91389
101579
111739
121909
132079
142249
152419
162589
172759
182929
193099
203269
213439
223609
233779
243949
254119
264289
274459
284629
294799
304969
315139
325309
335479
345649
355819
365989
376159
386329
396499
406669
416839
427009
437179
447349
457519
467689
477859
488029
498199
508369
518539
528709
538879
549049
559219
569389
579559
589729
599899
6010069
6110239
6210409
6310579
6410749
6510919
6611089
6711259
6811429
6911599
7011769
7111939
7212109
7312279
7412449
7512619
7612789
7712959
7813129
7913299
8013469
8113639
8213809
8313979
8414149
8514319
8614489
8714659
8814829
8914999
9015169
9115339
9215509
9315679
9415849
9516019
9616189
9716359
9816529
9916699
10016869
10117039
10217209
10317379
10417549
10517719
10617889
10718059
10818229
10918399
11018569
11118739
11218909
11319079
11419249
11519419
11619589
11719759
11819929
11920099
12020269
12120439
12220609
12320779
12420949
12521119
12621289
12721459
12821629
12921799
13021969
13122139
13222309
13322479
13422649
13522819
13622989
13723159
13823329
13923499
14023669
14123839
14224009
14324179
14424349
14524519
14624689
14724859
14825029
14925199
15025369
15125539
15225709
15325879
15426049
15526219
15626389
15726559
15826729
15926899
16027069
16127239
16227409
16327579
16427749
16527919
16628089
16728259
16828429
16928599
17028769
17128939
17229109
17329279
17429449
17529619
17629789
17729959
17830129
17930299
18030469
18130639
18230809
18330979
18431149
18531319
18631489
18731659
18831829
18931999
19032169
19132339
19232509
19332679
19432849
19533019
19633189
19733359
19833529
19933699
20033869
20134039
20234209
20334379
20434549
20534719
20634889
20735059
20835229
20935399
21035569
21135739
21235909
21336079
21436249
21536419
21636589
21736759
21836929
21937099
22037269
22137439
22237609
22337779
22437949
22538119
22638289
22738459
22838629
22938799
23038969
23139139
23239309
23339479
23439649
23539819
23639989
23740159
23840329
23940499
24040669
24140839
24241009
24341179
24441349
24541519
24641689
24741859
24842029
24942199
25042369
25142539
25242709
25342879
25443049
25543219
25643389
25743559
25843729
25943899
26044069
26144239
26244409
26344579
26444749
26544919
26645089
26745259
26845429
26945599
27045769
27145939
27246109
27346279
27446449
27546619
27646789
27746959
27847129
27947299
28047469
28147639
28247809
28347979
28448149
28548319
28648489
28748659
28848829
28948999
29049169
29149339
29249509
29349679
29449849
done50009

prune6.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 14.8b

Counts
2 → 1

localize13.0ms

Local error

Found 3 expressions with local error:

0.1b
(+ x (- (tan (+ y z)) (tan a)))
0.1b
(- (tan (+ y z)) (tan a))
4.3b
(tan (+ y z))

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
10×*-un-lft-identity add-log-exp
5×add-sqr-sqrt
4×tan-quot
3×pow1 add-exp-log add-cube-cbrt add-cbrt-cube
2×sub-neg tan-sum associate-+r+ diff-log sum-log frac-sub distribute-lft-out distribute-lft-out--
1×+-commutative associate-+r- flip3-- flip3-+ flip-- flip-+ difference-of-squares
Counts
3 → 42
Calls
3 calls:
6.0ms
(+ x (- (tan (+ y z)) (tan a)))
8.0ms
(- (tan (+ y z)) (tan a))
6.0ms
(tan (+ y z))

series121.0ms

Counts
3 → 9
Calls
3 calls:
46.0ms
(+ x (- (tan (+ y z)) (tan a)))
46.0ms
(- (tan (+ y z)) (tan a))
29.0ms
(tan (+ y z))

simplify1.1s

Counts
51 → 51
Iterations

Useful iterations: 3 (123.0ms)

IterNodesCost
092627
1199590
2440572
31066570
43773570
done5000570

prune101.0ms

Filtered
39 candidates to 51 candidates (-30.8%)
Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New45651
Fresh000
Picked101
Done000
Total46652

Merged error: 0.1b

Counts
52 → 6

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b
(+ (tan y) (tan z))
0.1b
(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
0.1b
(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
0.2b
(* (tan y) (tan z))

rewrite43.0ms

Algorithm
rewrite-expression-head
Rules
15×*-un-lft-identity
13×add-sqr-sqrt add-log-exp
7×tan-quot
6×pow1 add-exp-log add-cube-cbrt add-cbrt-cube
3×associate-*r* associate-*l* sum-log distribute-lft-out
2×+-commutative sub-neg associate-+r+ flip3-+ diff-log flip-+ distribute-lft-out-- difference-of-squares
1×frac-times associate-+r- flip3-- times-frac associate-*r/ pow-prod-down associate-*l/ frac-add prod-exp *-commutative frac-sub flip-- cbrt-unprod unswap-sqr
Counts
4 → 67
Calls
4 calls:
5.0ms
(+ (tan y) (tan z))
15.0ms
(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
14.0ms
(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
7.0ms
(* (tan y) (tan z))

series340.0ms

Counts
4 → 12
Calls
4 calls:
25.0ms
(+ (tan y) (tan z))
148.0ms
(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
141.0ms
(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
25.0ms
(* (tan y) (tan z))

simplify735.0ms

Counts
79 → 79
Iterations

Useful iterations: 3 (291.0ms)

IterNodesCost
01551433
13771362
29551302
324471291
done50011291

prune170.0ms

Filtered
58 candidates to 79 candidates (-36.2%)
Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New70979
Fresh235
Picked101
Done000
Total731285

Merged error: 0.1b

Counts
85 → 12

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (+ (tan y) (tan z)) (cos a))
0.2b
(* (tan y) (tan z))
0.2b
(* (tan y) (tan z))
0.2b
(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (* (tan y) (tan z))) (cos a)))

rewrite43.0ms

Algorithm
rewrite-expression-head
Rules
19×associate-*l/
18×add-sqr-sqrt
15×add-exp-log add-cbrt-cube
14×tan-quot *-un-lft-identity
12×add-cube-cbrt
10×pow1 associate-*l*
9×associate-*r*
8×associate-/l/
6×frac-sub
5×flip3-- flip--
4×prod-exp cbrt-unprod add-log-exp
3×flip3-+ times-frac pow-prod-down frac-add *-commutative flip-+ associate-/l* unswap-sqr
2×cbrt-undiv frac-times associate-*r/ div-exp associate-/r/
1×frac-2neg div-sub clear-num associate-/r* div-inv distribute-lft-out
Counts
4 → 96
Calls
4 calls:
9.0ms
(* (+ (tan y) (tan z)) (cos a))
7.0ms
(* (tan y) (tan z))
6.0ms
(* (tan y) (tan z))
18.0ms
(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (* (tan y) (tan z))) (cos a)))

series268.0ms

Counts
4 → 12
Calls
4 calls:
40.0ms
(* (+ (tan y) (tan z)) (cos a))
27.0ms
(* (tan y) (tan z))
25.0ms
(* (tan y) (tan z))
175.0ms
(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (* (tan y) (tan z))) (cos a)))

simplify646.0ms

Counts
108 → 108
Iterations

Useful iterations: done (643.0ms)

IterNodesCost
02012138
16192041
223941664
done50001654

prune193.0ms

Filtered
84 candidates to 108 candidates (-28.6%)
Pruning

12 alts after pruning (11 fresh and 1 done)

PrunedKeptTotal
New1071108
Fresh11011
Picked011
Done000
Total10812120

Merged error: 0.1b

Counts
120 → 12

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b
(- (/ (* (+ (tan y) (tan z)) (cos a)) (- 1 (* (tan y) (tan z)))) (/ (sin a) 1))
0.2b
(* (+ (tan y) (tan z)) (cos a))
0.2b
(/ (- (/ (* (+ (tan y) (tan z)) (cos a)) (- 1 (* (tan y) (tan z)))) (/ (sin a) 1)) (cos a))
0.2b
(* (tan y) (tan z))

rewrite57.0ms

Algorithm
rewrite-expression-head
Rules
59×add-sqr-sqrt
37×*-un-lft-identity
31×times-frac
20×add-cube-cbrt
15×difference-of-squares
10×add-exp-log add-cbrt-cube
8×pow1
7×associate-*l* associate-/l*
6×tan-quot associate-*r* add-log-exp
5×distribute-lft-out--
4×associate-*l/
3×associate-/r* associate-/l/
2×flip3-- pow-prod-down prod-exp *-commutative frac-sub flip-- cbrt-unprod unswap-sqr
1×cbrt-undiv frac-times sub-neg frac-2neg flip3-+ diff-log div-sub associate-*r/ div-exp frac-add clear-num flip-+ div-inv distribute-lft-out
Counts
4 → 107
Calls
4 calls:
17.0ms
(- (/ (* (+ (tan y) (tan z)) (cos a)) (- 1 (* (tan y) (tan z)))) (/ (sin a) 1))
9.0ms
(* (+ (tan y) (tan z)) (cos a))
20.0ms
(/ (- (/ (* (+ (tan y) (tan z)) (cos a)) (- 1 (* (tan y) (tan z)))) (/ (sin a) 1)) (cos a))
6.0ms
(* (tan y) (tan z))

series391.0ms

Counts
4 → 12
Calls
4 calls:
145.0ms
(- (/ (* (+ (tan y) (tan z)) (cos a)) (- 1 (* (tan y) (tan z)))) (/ (sin a) 1))
41.0ms
(* (+ (tan y) (tan z)) (cos a))
179.0ms
(/ (- (/ (* (+ (tan y) (tan z)) (cos a)) (- 1 (* (tan y) (tan z)))) (/ (sin a) 1)) (cos a))
25.0ms
(* (tan y) (tan z))

simplify509.0ms

Counts
119 → 119
Iterations

Useful iterations: done (504.0ms)

IterNodesCost
02133148
15292919
215822729
done50012633

prune145.0ms

Filtered
85 candidates to 119 candidates (-40.0%)
Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New1181119
Fresh1910
Picked101
Done101
Total12110131

Merged error: 0.1b

Counts
131 → 10

regimes968.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 0.2b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 1 (1.0ms)

IterNodesCost
02129
12727
done2727

end0.0ms

sample3.6s

Algorithm
intervals
Results
1.6s3963×body1280valid
593.0ms8000×pre80true
503.0ms2013×body640valid
123.0ms666×body320valid
62.0ms1056×body80valid
36.0ms302×body160valid

Profiling

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