Details

Time bar (total: 48.9s)

sample714.0ms

Algorithm
intervals
Results
308.0ms475×body80nan
146.0ms296×body80valid

simplify2.5s

Counts
1 → 1
Iterations
IterNodes
done5000
43618
3693
2157
150
021

prune36.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 30.4b

localize89.0ms

Local error

Found 4 expressions with local error:

6.7b
(* n (pow (/ l Om) 2))
8.3b
(/ (* l l) Om)
11.0b
(* (* (* 2 n) U) (- (- t (* 2 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2)) (- U U*))))
18.8b
(sqrt (* (* (* 2 n) U) (- (- t (* 2 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2)) (- U U*)))))

rewrite307.0ms

Algorithm
rewrite-expression-head
Rules
29×add-sqr-sqrt
26×add-exp-log
23×pow1
21×associate-*r*
20×*-un-lft-identity add-cbrt-cube associate-*r/ add-cube-cbrt
15×unpow-prod-down
13×times-frac
12×prod-diff pow-prod-down
11×prod-exp
10×distribute-rgt-in distribute-lft-in flip3-- associate--l+ flip--
8×frac-sub cbrt-unprod
6×sqrt-div
5×unswap-sqr
4×expm1-log1p-u sub-neg sqrt-pow1 associate-*l* insert-posit16 log1p-expm1-u add-log-exp
3×associate-/r* div-exp
2×cbrt-undiv pow-exp *-commutative div-inv unpow2 sqr-pow
1×pow-to-exp clear-num frac-2neg pow1/2 sqrt-prod associate-/l*
Counts
4 → 138
Calls
4 calls:
13.0ms
(* n (pow (/ l Om) 2))
9.0ms
(/ (* l l) Om)
139.0ms
(* (* (* 2 n) U) (- (- t (* 2 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2)) (- U U*))))
142.0ms
(sqrt (* (* (* 2 n) U) (- (- t (* 2 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2)) (- U U*)))))

series2.4s

Counts
4 → 12
Calls
4 calls:
85.0ms
(* n (pow (/ l Om) 2))
21.0ms
(/ (* l l) Om)
630.0ms
(* (* (* 2 n) U) (- (- t (* 2 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2)) (- U U*))))
1.6s
(sqrt (* (* (* 2 n) U) (- (- t (* 2 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2)) (- U U*)))))

simplify3.1s

Counts
150 → 150
Iterations
IterNodes
done5000
24351
11056
0355

prune1.3s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 17.9b

localize83.0ms

Local error

Found 4 expressions with local error:

4.3b
(* n (/ l Om))
6.8b
(* (* 2 n) (* U (fma -2 (* (/ l Om) l) t)))
7.1b
(* (* U (- (* (/ l Om) (* n (/ l Om))))) (- U U*))
18.8b
(sqrt (+ (* (* 2 n) (* U (fma -2 (* (/ l Om) l) t))) (* (* 2 n) (* (* U (- (* (/ l Om) (* n (/ l Om))))) (- U U*)))))

rewrite139.0ms

Algorithm
rewrite-expression-head
Rules
34×add-sqr-sqrt
28×*-un-lft-identity
26×add-cbrt-cube add-exp-log add-cube-cbrt
24×pow1
21×associate-*r/
19×associate-*r*
18×prod-diff
15×distribute-rgt-in distribute-lft-in
13×prod-exp cbrt-unprod
12×pow-prod-down
10×times-frac
9×frac-times distribute-neg-frac
6×associate-*l/
5×associate-*l*
4×expm1-log1p-u flip3-- sqrt-prod fma-udef insert-posit16 log1p-expm1-u flip-- add-log-exp
3×*-commutative
2×sub-neg sqrt-div unswap-sqr
1×distribute-lft-neg-out cbrt-undiv rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 div-exp distribute-rgt-neg-out flip-+ div-inv distribute-lft-out distribute-lft-out-- difference-of-squares
Counts
4 → 140
Calls
4 calls:
9.0ms
(* n (/ l Om))
30.0ms
(* (* 2 n) (* U (fma -2 (* (/ l Om) l) t)))
55.0ms
(* (* U (- (* (/ l Om) (* n (/ l Om))))) (- U U*))
43.0ms
(sqrt (+ (* (* 2 n) (* U (fma -2 (* (/ l Om) l) t))) (* (* 2 n) (* (* U (- (* (/ l Om) (* n (/ l Om))))) (- U U*)))))

series1.8s

Counts
4 → 12
Calls
4 calls:
36.0ms
(* n (/ l Om))
155.0ms
(* (* 2 n) (* U (fma -2 (* (/ l Om) l) t)))
197.0ms
(* (* U (- (* (/ l Om) (* n (/ l Om))))) (- U U*))
1.4s
(sqrt (+ (* (* 2 n) (* U (fma -2 (* (/ l Om) l) t))) (* (* 2 n) (* (* U (- (* (/ l Om) (* n (/ l Om))))) (- U U*)))))

simplify2.5s

Counts
152 → 152
Iterations
IterNodes
done5005
24006
1992
0335

prune1.3s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 14.1b

localize53.0ms

Local error

Found 4 expressions with local error:

6.2b
(* (- (* (/ l Om) n)) U)
6.8b
(* (* 2 n) (* U (fma -2 (* (/ l Om) l) t)))
7.1b
(* (* (/ l Om) (* (- (* (/ l Om) n)) U)) (- U U*))
18.8b
(sqrt (+ (* (* 2 n) (* U (fma -2 (* (/ l Om) l) t))) (* (* 2 n) (* (* (/ l Om) (* (- (* (/ l Om) n)) U)) (- U U*)))))

rewrite198.0ms

Algorithm
rewrite-expression-head
Rules
36×add-cbrt-cube add-exp-log
28×pow1
25×add-sqr-sqrt
22×*-un-lft-identity
20×associate-*l/ prod-exp add-cube-cbrt cbrt-unprod
18×prod-diff
15×distribute-rgt-in distribute-lft-in pow-prod-down
9×frac-times associate-*r*
8×associate-*l*
7×distribute-neg-frac
5×associate-*r/
4×expm1-log1p-u flip3-- sqrt-prod fma-udef insert-posit16 log1p-expm1-u flip-- add-log-exp
3×distribute-lft-neg-out *-commutative
2×cbrt-undiv sub-neg sqrt-div div-exp
1×distribute-lft-neg-in rem-sqrt-square neg-mul-1 distribute-rgt-neg-in sqrt-pow1 flip3-+ pow1/2 distribute-rgt-neg-out flip-+ distribute-lft-out distribute-lft-out-- difference-of-squares unswap-sqr
Counts
4 → 138
Calls
4 calls:
9.0ms
(* (- (* (/ l Om) n)) U)
33.0ms
(* (* 2 n) (* U (fma -2 (* (/ l Om) l) t)))
104.0ms
(* (* (/ l Om) (* (- (* (/ l Om) n)) U)) (- U U*))
50.0ms
(sqrt (+ (* (* 2 n) (* U (fma -2 (* (/ l Om) l) t))) (* (* 2 n) (* (* (/ l Om) (* (- (* (/ l Om) n)) U)) (- U U*)))))

series1.9s

Counts
4 → 12
Calls
4 calls:
65.0ms
(* (- (* (/ l Om) n)) U)
152.0ms
(* (* 2 n) (* U (fma -2 (* (/ l Om) l) t)))
217.0ms
(* (* (/ l Om) (* (- (* (/ l Om) n)) U)) (- U U*))
1.4s
(sqrt (+ (* (* 2 n) (* U (fma -2 (* (/ l Om) l) t))) (* (* 2 n) (* (* (/ l Om) (* (- (* (/ l Om) n)) U)) (- U U*)))))

simplify2.7s

Counts
150 → 150
Iterations
IterNodes
done5002
23947
1956
0320

prune1.3s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 12.9b

localize86.0ms

Local error

Found 4 expressions with local error:

17.8b
(cbrt (- (* (/ l Om) n)))
17.8b
(cbrt (- (* (/ l Om) n)))
17.8b
(cbrt (- (* (/ l Om) n)))
18.8b
(sqrt (+ (* (* 2 n) (* U (fma -2 (* (/ l Om) l) t))) (* (* 2 n) (* (* (/ l Om) (* (* (cbrt (- (* (/ l Om) n))) (cbrt (- (* (/ l Om) n)))) (* (cbrt (- (* (/ l Om) n))) U))) (- U U*)))))

rewrite63.0ms

Algorithm
rewrite-expression-head
Rules
18×cbrt-prod
9×add-sqr-sqrt
8×*-un-lft-identity add-cube-cbrt
5×pow1
4×expm1-log1p-u add-cbrt-cube add-exp-log sqrt-prod insert-posit16 log1p-expm1-u add-log-exp
3×distribute-lft-neg-in cbrt-div neg-mul-1 distribute-rgt-neg-in pow1/3 associate-*l/ distribute-neg-frac
2×sqrt-div
1×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 flip-+ distribute-lft-out
Counts
4 → 73
Calls
4 calls:
3.0ms
(cbrt (- (* (/ l Om) n)))
3.0ms
(cbrt (- (* (/ l Om) n)))
4.0ms
(cbrt (- (* (/ l Om) n)))
51.0ms
(sqrt (+ (* (* 2 n) (* U (fma -2 (* (/ l Om) l) t))) (* (* 2 n) (* (* (/ l Om) (* (* (cbrt (- (* (/ l Om) n))) (cbrt (- (* (/ l Om) n)))) (* (cbrt (- (* (/ l Om) n))) U))) (- U U*)))))

series2.0s

Counts
4 → 12
Calls
4 calls:
115.0ms
(cbrt (- (* (/ l Om) n)))
146.0ms
(cbrt (- (* (/ l Om) n)))
156.0ms
(cbrt (- (* (/ l Om) n)))
1.6s
(sqrt (+ (* (* 2 n) (* U (fma -2 (* (/ l Om) l) t))) (* (* 2 n) (* (* (/ l Om) (* (* (cbrt (- (* (/ l Om) n))) (cbrt (- (* (/ l Om) n)))) (* (cbrt (- (* (/ l Om) n))) U))) (- U U*)))))

simplify2.2s

Counts
85 → 85
Iterations
IterNodes
done5001
21124
1305
0135

prune949.0ms

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 12.9b

regimes2.0s

Accuracy

-4.8% (13.9b remaining)

Error of 29.7b against oracle of 15.8b and baseline of 29.1b

bsearch1.3s

Steps
ItersRangePoint
7
1.5722377279286372e+171
1.6878560816814095e+173
2.2801453703210546e+171
8
82394.3909005377
346522067.3540806
83934.69895366188
7
1.3305596714023463e-256
3.3027307033904866e-255
3.0731526450190984e-256
8
-8.857405213449995e-178
-5.825023206546193e-182
-6.039684361220293e-180
8
-7.609228664274234e+57
-2.3582671215277715e+54
-1.908160256120522e+56
6
-3.161237838760785e+183
-4.7233346363841123e+182
-1.6760288117773952e+183

simplify9.5s

Iterations
IterNodes
done5000
10624996
10614992
10604987
10594983
10584978
10574974
10564969
10554965
10544960
10534956
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10514947
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2001117
1991113
1981108
1971104
1961099
1951095
1941090
1931086
1921081
1911077
1901072
1891068
1881063
1871059
1861054
1851050
1841045
1831041
1821036
1811032
1801027
1791023
1781018
1771014
1761009
1751005
1741000
173996
172991
171987
170982
169978
168973
167969
166964
165960
164955
163951
162946
161942
160937
159933
158928
157924
156919
155915
154910
153906
152901
151897
150892
149888
148883
147879
146874
145870
144865
143861
142856
141852
140847
139843
138838
137834
136829
135825
134820
133816
132811
131807
130802
129798
128793
127789
126784
125780
124775
123771
122766
121762
120757
119753
118748
117744
116739
115735
114730
113726
112721
111717
110712
109708
108703
107699
106694
105690
104685
103681
102676
101672
100667
99663
98658
97654
96649
95645
94640
93636
92631
91627
90622
89618
88613
87609
86604
85600
84595
83591
82586
81582
80577
79573
78568
77564
76559
75555
74550
73546
72541
71537
70532
69528
68523
67519
66514
65510
64505
63501
62496
61492
60487
59483
58478
57474
56469
55465
54460
53456
52451
51447
50442
49438
48433
47429
46424
45420
44415
43411
42406
41402
40397
39393
38388
37384
36379
35375
34370
33366
32361
31357
30352
29348
28343
27339
26334
25330
24325
23321
22316
21312
20307
19303
18298
17294
16289
15285
14280
13276
12271
11267
10262
9258
8253
7249
6244
5229
4209
3175
2151
1130
082

end0.0ms

sample8.3s

Algorithm
intervals
Results
4.2s14800×body80nan
2.6s9195×body80valid