Details

Time bar (total: 1.2m)

sample764.0ms

Algorithm
intervals
Results
450.0ms1384×body80nan
175.0ms424×body80valid

simplify874.0ms

Counts
1 → 1
Iterations
IterNodes
done2006
31271
2198
158
022

prune15.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 24.8b

localize81.0ms

Local error

Found 4 expressions with local error:

7.9b
(* (* (pow (/ d h) (/ 1 2)) (pow (/ d l) (/ 1 2))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
9.4b
(pow (/ d h) (/ 1 2))
11.5b
(pow (/ d l) (/ 1 2))
13.2b
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))

rewrite140.0ms

Algorithm
rewrite-expression-head
Rules
331×add-exp-log
179×prod-exp
99×div-exp
60×pow-exp
45×times-frac
42×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
30×add-cbrt-cube
26×pow-unpow unpow-prod-down
18×pow-to-exp
16×associate-*r*
14×rec-exp 1-exp
13×cbrt-unprod
10×pow1
6×prod-diff
5×distribute-rgt-in cbrt-undiv distribute-lft-in div-inv
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×associate-*l/ associate-*r/
2×sub-neg pow-pow associate-*l* pow-prod-down *-commutative sqr-pow
1×frac-times flip3-- flip--
Counts
4 → 222
Calls
4 calls:
74.0ms
(* (* (pow (/ d h) (/ 1 2)) (pow (/ d l) (/ 1 2))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
5.0ms
(pow (/ d h) (/ 1 2))
5.0ms
(pow (/ d l) (/ 1 2))
46.0ms
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))

series674.0ms

Counts
4 → 12
Calls
4 calls:
379.0ms
(* (* (pow (/ d h) (/ 1 2)) (pow (/ d l) (/ 1 2))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
91.0ms
(pow (/ d h) (/ 1 2))
86.0ms
(pow (/ d l) (/ 1 2))
117.0ms
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))

simplify998.0ms

Counts
234 → 234
Iterations
IterNodes
done2002
11360
0461

prune1.4s

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 12.2b

localize83.0ms

Local error

Found 4 expressions with local error:

4.0b
(/ (* M D) (* 2 d))
7.9b
(* (* (* (sqrt (/ 1 (* (cbrt h) (cbrt h)))) (sqrt (/ d (cbrt h)))) (pow (/ d l) (/ 1 2))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
11.5b
(pow (/ d l) (/ 1 2))
13.2b
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))

rewrite674.0ms

Algorithm
rewrite-expression-head
Rules
320×add-exp-log
171×prod-exp
96×div-exp
46×add-cbrt-cube pow-exp
28×add-sqr-sqrt *-un-lft-identity times-frac add-cube-cbrt
20×cbrt-unprod
18×associate-*l/
16×associate-*r*
14×rec-exp 1-exp
13×pow-unpow unpow-prod-down
12×sqrt-div
11×pow-to-exp
10×frac-times
9×pow1 cbrt-undiv
6×prod-diff associate-*r/
5×distribute-rgt-in distribute-lft-in
4×expm1-log1p-u flip3-- insert-posit16 log1p-expm1-u div-inv flip-- add-log-exp
2×sub-neg associate-*l* pow-prod-down *-commutative
1×clear-num associate-/r* pow-pow frac-2neg associate-/l* sqr-pow
Counts
4 → 207
Calls
4 calls:
22.0ms
(/ (* M D) (* 2 d))
579.0ms
(* (* (* (sqrt (/ 1 (* (cbrt h) (cbrt h)))) (sqrt (/ d (cbrt h)))) (pow (/ d l) (/ 1 2))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
5.0ms
(pow (/ d l) (/ 1 2))
59.0ms
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))

series2.7s

Counts
4 → 12
Calls
4 calls:
48.0ms
(/ (* M D) (* 2 d))
2.4s
(* (* (* (sqrt (/ 1 (* (cbrt h) (cbrt h)))) (sqrt (/ d (cbrt h)))) (pow (/ d l) (/ 1 2))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
102.0ms
(pow (/ d l) (/ 1 2))
123.0ms
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))

simplify1.1s

Counts
219 → 219
Iterations
IterNodes
done2012
11503
0495

prune1.8s

Pruning

25 alts after pruning (25 fresh and 0 done)

Merged error: 11.6b

localize98.0ms

Local error

Found 4 expressions with local error:

2.0b
(sqrt (/ d (cbrt l)))
4.0b
(/ (* M D) (* 2 d))
7.9b
(* (* (* (sqrt (/ 1 (* (cbrt h) (cbrt h)))) (sqrt (/ d (cbrt h)))) (* (sqrt (/ (/ 1 (cbrt l)) (cbrt l))) (sqrt (/ d (cbrt l))))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
13.2b
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))

rewrite832.0ms

Algorithm
rewrite-expression-head
Rules
305×add-exp-log
163×prod-exp
97×sqrt-div
93×div-exp
82×frac-times
55×add-cbrt-cube
51×associate-*l/
40×pow-exp
36×associate-*r/
32×add-sqr-sqrt
30×times-frac
27×*-un-lft-identity add-cube-cbrt cbrt-unprod
25×pow1
22×sqrt-prod
16×flip3-- associate-*r* flip--
14×rec-exp 1-exp pow-prod-down
10×cbrt-prod
9×cbrt-undiv
8×pow-to-exp
6×prod-diff
5×distribute-rgt-in distribute-lft-in
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×rem-sqrt-square div-inv
2×sub-neg associate-*l* *-commutative
1×clear-num associate-/r* frac-2neg sqrt-pow1 pow1/2 associate-/l*
Counts
4 → 242
Calls
4 calls:
4.0ms
(sqrt (/ d (cbrt l)))
12.0ms
(/ (* M D) (* 2 d))
755.0ms
(* (* (* (sqrt (/ 1 (* (cbrt h) (cbrt h)))) (sqrt (/ d (cbrt h)))) (* (sqrt (/ (/ 1 (cbrt l)) (cbrt l))) (sqrt (/ d (cbrt l))))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
53.0ms
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))

series2.0s

Counts
4 → 12
Calls
4 calls:
206.0ms
(sqrt (/ d (cbrt l)))
43.0ms
(/ (* M D) (* 2 d))
1.7s
(* (* (* (sqrt (/ 1 (* (cbrt h) (cbrt h)))) (sqrt (/ d (cbrt h)))) (* (sqrt (/ (/ 1 (cbrt l)) (cbrt l))) (sqrt (/ d (cbrt l))))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
126.0ms
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))

simplify2.5s

Counts
254 → 254
Iterations
IterNodes
done2000
11977
0656

prune2.5s

Pruning

27 alts after pruning (27 fresh and 0 done)

Merged error: 8.2b

localize142.0ms

Local error

Found 4 expressions with local error:

4.9b
(/ M (/ 2 (/ D d)))
4.9b
(/ M (/ 2 (/ D d)))
5.9b
(* (* (sqrt (/ 1 (* (cbrt h) (cbrt h)))) (sqrt (/ d (cbrt h)))) (* (* (sqrt (/ d (cbrt l))) (sqrt (/ (/ 1 (cbrt l)) (cbrt l)))) (* (* 1/2 (* (/ M (/ 2 (/ D d))) (/ M (/ 2 (/ D d))))) (- (/ h l)))))
13.4b
(* (* 1/2 (* (/ M (/ 2 (/ D d))) (/ M (/ 2 (/ D d))))) (- (/ h l)))

rewrite2.6s

Algorithm
rewrite-expression-head
Rules
844×add-cbrt-cube add-exp-log
810×times-frac
486×prod-exp cbrt-unprod
389×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
326×frac-times
276×associate-*r/
256×sqrt-div
252×cbrt-undiv div-exp
164×associate-*l/
106×pow1
88×associate-/r*
81×pow-prod-down
68×distribute-neg-frac
36×div-inv
31×associate-*r*
13×distribute-lft-neg-in distribute-rgt-neg-in
10×associate-/r/
6×associate-/l*
4×expm1-log1p-u distribute-rgt-neg-out insert-posit16 log1p-expm1-u add-log-exp
2×clear-num frac-2neg associate-*l* *-commutative
1×neg-mul-1
Counts
4 → 802
Calls
4 calls:
8.0ms
(/ M (/ 2 (/ D d)))
8.0ms
(/ M (/ 2 (/ D d)))
2.4s
(* (* (sqrt (/ 1 (* (cbrt h) (cbrt h)))) (sqrt (/ d (cbrt h)))) (* (* (sqrt (/ d (cbrt l))) (sqrt (/ (/ 1 (cbrt l)) (cbrt l)))) (* (* 1/2 (* (/ M (/ 2 (/ D d))) (/ M (/ 2 (/ D d))))) (- (/ h l)))))
211.0ms
(* (* 1/2 (* (/ M (/ 2 (/ D d))) (/ M (/ 2 (/ D d))))) (- (/ h l)))

series1.3s

Counts
4 → 12
Calls
4 calls:
48.0ms
(/ M (/ 2 (/ D d)))
50.0ms
(/ M (/ 2 (/ D d)))
1.1s
(* (* (sqrt (/ 1 (* (cbrt h) (cbrt h)))) (sqrt (/ d (cbrt h)))) (* (* (sqrt (/ d (cbrt l))) (sqrt (/ (/ 1 (cbrt l)) (cbrt l)))) (* (* 1/2 (* (/ M (/ 2 (/ D d))) (/ M (/ 2 (/ D d))))) (- (/ h l)))))
96.0ms
(* (* 1/2 (* (/ M (/ 2 (/ D d))) (/ M (/ 2 (/ D d))))) (- (/ h l)))

simplify3.6s

Counts
814 → 814
Iterations
IterNodes
done2000
01262

prune11.1s

Pruning

35 alts after pruning (35 fresh and 0 done)

Merged error: 4.2b

regimes3.7s

Accuracy

2.2% (8.2b remaining)

Error of 14.7b against oracle of 6.5b and baseline of 14.8b

bsearch2.7s

Steps
ItersRangePoint
8
8.272578197208453e+94
2.5288413774350296e+97
4.34627183388716e+96
7
3.243406009872032e-163
3.814586161137829e-161
2.582312067182575e-161
7
-4.2718281220796194e-92
-2.0758636028279273e-93
-5.417236322821405e-93
9
-4.3325125160580366e+203
-2.3112651975032648e+195
-8.000109981051055e+199

simplify2.1s

Iterations
IterNodes
done2001
1801998
1791988
1781979
1771969
1761960
1751950
1741940
1731930
1721920
1711910
1701901
1691891
1681882
1671872
1661862
1651852
1641843
1631833
1621823
1611813
1601803
1591793
1581783
1571773
1561763
1551753
1541743
1531733
1521723
1511713
1501703
1491693
1481683
1471673
1461664
1451654
1441644
1431634
1421624
1411614
1401604
1391594
1381584
1371574
1361565
1351555
1341545
1331535
1321525
1311515
1301506
1291496
1281486
1271476
1261466
1251456
1241446
1231436
1221426
1211416
1201407
1191397
1181388
1171378
1161369
1151359
1141349
1131339
1121330
1111320
1101311
1091301
1081291
1071281
1061271
1051261
1041251
1031241
1021232
1011222
1001212
991202
981192
971182
961173
951163
941153
931143
921133
911123
901113
891103
881093
871083
861073
851063
841054
831044
821034
811024
801014
791004
78995
77985
76975
75965
74955
73945
72935
71925
70915
69905
68895
67885
66876
65866
64857
63847
62837
61827
60818
59808
58798
57788
56778
55768
54759
53749
52740
51730
50721
49711
48701
47691
46682
45672
44663
43653
42643
41633
40623
39613
38603
37593
36583
35573
34563
33553
32544
31534
30524
29514
28504
27494
26485
25475
24465
23455
22446
21436
20427
19417
18407
17397
16387
15377
14367
13357
12347
11337
10328
9319
8310
7300
6290
5281
4257
3193
2144
1121
082

end0.0ms

sample22.6s

Algorithm
intervals
Results
14.1s37697×body80nan
5.9s12790×body80valid