Details

Time bar (total: 33.4s)

sample457.0ms

Algorithm
intervals
Results
103.0ms369×body80nan
49.0ms164×body80valid
21.0ms31×body1280valid
18.0ms31×body1280nan
12.0ms30×body640nan
10.0ms29×body320valid
10.0ms22×body640valid
5.0ms13×body320nan
2.0ms10×body160valid
1.0msbody160nan

simplify3.2s

Counts
1 → 1
Iterations
IterNodes
done5000
73799
61449
5797
4423
3199
293
139
018

prune22.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 42.4b

localize45.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
0.4b
(* (sqrt 2.0) t)
11.8b
(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
21.1b
(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

rewrite194.0ms

Algorithm
rewrite-expression-head
Rules
17×add-sqr-sqrt
13×sqrt-prod
12×*-un-lft-identity add-cube-cbrt
11×add-cbrt-cube add-exp-log
pow1
associate-/r* times-frac associate-*l* add-log-exp
sqrt-div
flip3-- associate-*r* flip--
cbrt-undiv div-exp prod-exp associate--l+ associate-/r/ cbrt-unprod unswap-sqr
distribute-rgt-in rem-sqrt-square clear-num sub-neg frac-2neg distribute-lft-in sqrt-pow1 pow1/2 diff-log pow-prod-down *-commutative div-inv associate-/l*
Counts
4 → 80
Calls
4 calls:
62.0ms
(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
16.0ms
(* (sqrt 2.0) t)
26.0ms
(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
84.0ms
(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

series2.6s

Counts
4 → 12
Calls
4 calls:
610.0ms
(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
60.0ms
(* (sqrt 2.0) t)
296.0ms
(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
1.7s
(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

simplify1.3s

Counts
92 → 92
Iterations
IterNodes
done5000
22619
1455
0167

prune632.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 6.1b

localize45.0ms

Local error

Found 4 expressions with local error:

3.2b
(+ (* 2.0 (+ (* t t) (/ (* l l) x))) (/ 4.0 (/ x (* t t))))
5.7b
(/ (* l l) x)
9.8b
(/ x (* t t))
27.7b
(sqrt (+ (* 2.0 (+ (* t t) (/ (* l l) x))) (/ 4.0 (/ x (* t t)))))

rewrite135.0ms

Algorithm
rewrite-expression-head
Rules
14×add-cbrt-cube add-exp-log
10×add-sqr-sqrt
*-un-lft-identity add-cube-cbrt
times-frac add-log-exp
pow1
cbrt-undiv associate-/r* flip3-+ sqrt-div div-exp frac-add associate-*r/ flip-+ associate-/l*
sqrt-prod
associate-+l+ clear-num frac-2neg prod-exp cbrt-unprod div-inv
distribute-rgt-in +-commutative rem-sqrt-square sum-log distribute-lft-in sqrt-pow1 pow1/2
Counts
4 → 74
Calls
4 calls:
32.0ms
(+ (* 2.0 (+ (* t t) (/ (* l l) x))) (/ 4.0 (/ x (* t t))))
7.0ms
(/ (* l l) x)
6.0ms
(/ x (* t t))
86.0ms
(sqrt (+ (* 2.0 (+ (* t t) (/ (* l l) x))) (/ 4.0 (/ x (* t t)))))

series525.0ms

Counts
4 → 12
Calls
4 calls:
89.0ms
(+ (* 2.0 (+ (* t t) (/ (* l l) x))) (/ 4.0 (/ x (* t t))))
26.0ms
(/ (* l l) x)
28.0ms
(/ x (* t t))
382.0ms
(sqrt (+ (* 2.0 (+ (* t t) (/ (* l l) x))) (/ 4.0 (/ x (* t t)))))

simplify1.6s

Counts
86 → 86
Iterations
IterNodes
done5001
23089
1509
0168

prune562.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 3.2b

localize50.0ms

Local error

Found 4 expressions with local error:

0.6b
(+ (* t t) (* l (/ l x)))
3.2b
(+ (* 2.0 (+ (* t t) (* l (/ l x)))) (/ 4.0 (/ x (* t t))))
9.8b
(/ x (* t t))
27.7b
(sqrt (+ (* 2.0 (+ (* t t) (* l (/ l x)))) (/ 4.0 (/ x (* t t)))))

rewrite141.0ms

Algorithm
rewrite-expression-head
Rules
add-cbrt-cube add-exp-log
add-sqr-sqrt add-log-exp
*-un-lft-identity add-cube-cbrt
pow1 flip3-+ flip-+
sqrt-div frac-add associate-*r/
times-frac sqrt-prod associate-/l*
cbrt-undiv +-commutative associate-+l+ sum-log div-exp
distribute-rgt-in rem-sqrt-square clear-num associate-/r* frac-2neg distribute-lft-in sqrt-pow1 pow1/2 prod-exp cbrt-unprod div-inv
Counts
4 → 64
Calls
4 calls:
13.0ms
(+ (* t t) (* l (/ l x)))
40.0ms
(+ (* 2.0 (+ (* t t) (* l (/ l x)))) (/ 4.0 (/ x (* t t))))
12.0ms
(/ x (* t t))
73.0ms
(sqrt (+ (* 2.0 (+ (* t t) (* l (/ l x)))) (/ 4.0 (/ x (* t t)))))

series500.0ms

Counts
4 → 12
Calls
4 calls:
52.0ms
(+ (* t t) (* l (/ l x)))
90.0ms
(+ (* 2.0 (+ (* t t) (* l (/ l x)))) (/ 4.0 (/ x (* t t))))
40.0ms
(/ x (* t t))
316.0ms
(sqrt (+ (* 2.0 (+ (* t t) (* l (/ l x)))) (/ 4.0 (/ x (* t t)))))

simplify1.2s

Counts
76 → 76
Iterations
IterNodes
done5001
22158
1435
0150

prune548.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 3.2b

localize47.0ms

Local error

Found 4 expressions with local error:

9.8b
(/ x (* t t))
27.4b
(sqrt (+ (* (/ l x) l) (* t t)))
27.4b
(sqrt (+ (* (/ l x) l) (* t t)))
27.7b
(sqrt (+ (* 2.0 (* (sqrt (+ (* (/ l x) l) (* t t))) (sqrt (+ (* (/ l x) l) (* t t))))) (/ 4.0 (/ x (* t t)))))

rewrite221.0ms

Algorithm
rewrite-expression-head
Rules
26×sqrt-div
12×add-sqr-sqrt
10×associate-*r/
*-un-lft-identity flip3-+ add-cbrt-cube add-exp-log add-cube-cbrt sqrt-prod flip-+
frac-add
pow1
frac-times add-log-exp
rem-sqrt-square sqrt-pow1 times-frac pow1/2 associate-/l*
cbrt-undiv div-exp associate-*l/
clear-num associate-/r* frac-2neg prod-exp cbrt-unprod div-inv
Counts
4 → 74
Calls
4 calls:
6.0ms
(/ x (* t t))
21.0ms
(sqrt (+ (* (/ l x) l) (* t t)))
24.0ms
(sqrt (+ (* (/ l x) l) (* t t)))
168.0ms
(sqrt (+ (* 2.0 (* (sqrt (+ (* (/ l x) l) (* t t))) (sqrt (+ (* (/ l x) l) (* t t))))) (/ 4.0 (/ x (* t t)))))

series1.1s

Counts
4 → 12
Calls
4 calls:
41.0ms
(/ x (* t t))
221.0ms
(sqrt (+ (* (/ l x) l) (* t t)))
232.0ms
(sqrt (+ (* (/ l x) l) (* t t)))
563.0ms
(sqrt (+ (* 2.0 (* (sqrt (+ (* (/ l x) l) (* t t))) (sqrt (+ (* (/ l x) l) (* t t))))) (/ 4.0 (/ x (* t t)))))

simplify1.1s

Counts
86 → 86
Iterations
IterNodes
done5000
22427
1489
0186

prune601.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 3.2b

regimes735.0ms

Accuracy

71.1% (6.8b remaining)

Error of 10.6b against oracle of 3.8b and baseline of 27.2b

bsearch1.7s

Steps
ItersRangePoint
9
9.302190505211976e+16
7.445004787773374e+23
7.30958659336468e+23
10
9.657462100703732e-164
3.031856998694715e-153
8.463507043182295e-160
8
1.567848216510623e-295
4.048090763928206e-293
4.0088796644560363e-293
10
-3.4801109198288895e-286
-4.7771503152615563e-296
-1.6191443127207628e-287
8
-1.185302419643378e-162
-2.4464775612223304e-166
-8.68838282607017e-163
6
-8.884635004656325e+106
-1.469680632787173e+106
-8.435929301784522e+106

simplify7.6s

Iterations
IterNodes
done5000
12204996
12194992
12184988
12174984
12164980
12154976
12144972
12134968
12124964
12114960
12104956
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2731208
2721204
2711200
2701196
2691192
2681188
2671184
2661180
2651176
2641172
2631168
2621164
2611160
2601156
2591152
2581148
2571144
2561140
2551136
2541132
2531128
2521124
2511120
2501116
2491112
2481108
2471104
2461100
2451096
2441092
2431088
2421084
2411080
2401076
2391072
2381068
2371064
2361060
2351056
2341052
2331048
2321044
2311040
2301036
2291032
2281028
2271024
2261020
2251016
2241012
2231008
2221004
2211000
220996
219992
218988
217984
216980
215976
214972
213968
212964
211960
210956
209952
208948
207944
206940
205936
204932
203928
202924
201920
200916
199912
198908
197904
196900
195896
194892
193888
192884
191880
190876
189872
188868
187864
186860
185856
184852
183848
182844
181840
180836
179832
178828
177824
176820
175816
174812
173808
172804
171800
170796
169792
168788
167784
166780
165776
164772
163768
162764
161760
160756
159752
158748
157744
156740
155736
154732
153728
152724
151720
150716
149712
148708
147704
146700
145696
144692
143688
142684
141680
140676
139672
138668
137664
136660
135656
134652
133648
132644
131640
130636
129632
128628
127624
126620
125616
124612
123608
122604
121600
120596
119592
118588
117584
116580
115576
114572
113568
112564
111560
110556
109552
108548
107544
106540
105536
104532
103528
102524
101520
100516
99512
98508
97504
96500
95496
94492
93488
92484
91480
90476
89472
88468
87464
86460
85456
84452
83448
82444
81440
80436
79432
78428
77424
76420
75416
74412
73408
72404
71400
70396
69392
68388
67384
66380
65376
64372
63368
62364
61360
60356
59352
58348
57344
56340
55336
54332
53328
52324
51320
50316
49312
48308
47304
46300
45296
44292
43288
42284
41280
40276
39272
38268
37264
36260
35256
34252
33248
32244
31240
30236
29232
28228
27224
26220
25216
24212
23208
22204
21200
20196
19192
18188
17184
16180
15176
14172
13168
12164
11160
10156
9152
8148
7144
6134
5126
4120
3112
294
170
054

end0.0ms

sample6.6s

Algorithm
intervals
Results
1.3s10213×body80nan
1.0s1064×body640valid
799.0ms5001×body80valid
549.0ms394×body160valid
529.0ms885×body1280valid
468.0ms604×body1280nan
424.0ms624×body640nan
302.0ms656×body320valid
143.0ms338×body320nan
93.0ms202×body160nan