Details

sample114.0ms

Algorithm

intervals

Results

60.0ms	383×	body	80	valid
27.0ms	174×	body	80	nan

simplify2.6s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
6	2300
5	639
4	204
3	87
2	47
1	26
0	12

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 2.0b

localize17.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (+ (* (+ k 10) k) 1) (pow k m))
0.0b	(* (+ k 10) k)
2.0b	(/ a (/ (+ (* (+ k 10) k) 1) (pow k m)))

rewrite75.0ms

Algorithm

rewrite-expression-head

Rules

180×	`times-frac`
105×	`add-sqr-sqrt` `*-un-lft-identity`
103×	`add-cube-cbrt`
48×	`unpow-prod-down`
32×	`associate-/r*`
20×	`add-exp-log`
16×	`sqr-pow`
12×	`add-cbrt-cube`
10×	`div-exp`
6×	`div-inv` `associate-/l*`
5×	`pow1`
4×	`cbrt-undiv` `associate-l`
3×	`associate-r` `insert-posit16` `add-log-exp`
2×	`pow-to-exp` `clear-num` `frac-2neg` `flip3-+` `associate-*l/` `pow-exp` `flip-+` `associate-/l/`
1×	`pow-prod-down` `prod-exp` `associate-/r/` `*-commutative` `cbrt-unprod` `distribute-lft-out` `unswap-sqr`

Counts

3 → 191

Calls

3 calls:

30.0ms	(/ (+ (* (+ k 10) k) 1) (pow k m))
19.0ms	(* (+ k 10) k)
20.0ms	(/ a (/ (+ (* (+ k 10) k) 1) (pow k m)))

series296.0ms

Counts

3 → 9

Calls

3 calls:

81.0ms	(/ (+ (* (+ k 10) k) 1) (pow k m))
50.0ms	(* (+ k 10) k)
165.0ms	(/ a (/ (+ (* (+ k 10) k) 1) (pow k m)))

simplify2.6s

Counts

200 → 200

Iterations

Iter	Nodes
done	5003
2	3028
1	962
0	361

prune1.1s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize36.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sqrt (+ (* (+ k 10) k) 1)) (/ (pow k m) (sqrt (+ (* (+ k 10) k) 1))))
2.0b	(/ a (/ (sqrt (+ (* (+ k 10) k) 1)) (/ (pow k m) (sqrt (+ (* (+ k 10) k) 1)))))
12.2b	(sqrt (+ (* (+ k 10) k) 1))
12.2b	(sqrt (+ (* (+ k 10) k) 1))

rewrite555.0ms

Algorithm

rewrite-expression-head

Rules

3621×	`times-frac`
1625×	`add-sqr-sqrt`
1623×	`*-un-lft-identity` `add-cube-cbrt`
1380×	`sqrt-prod`
558×	`unpow-prod-down`
341×	`associate-/r*`
186×	`sqr-pow`
68×	`sqrt-div` `associate-/r/`
37×	`div-inv`
34×	`flip3-+` `flip-+`
30×	`add-exp-log`
19×	`div-exp`
18×	`add-cbrt-cube`
9×	`cbrt-undiv` `associate-/l*`
6×	`pow1`
4×	`insert-posit16` `add-log-exp`
2×	`pow-to-exp` `rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `pow-exp` `associate-/l/`

Counts

4 → 1589

Calls

4 calls:

57.0ms	(/ (sqrt (+ (* (+ k 10) k) 1)) (/ (pow k m) (sqrt (+ (* (+ k 10) k) 1))))
49.0ms	(/ a (/ (sqrt (+ (* (+ k 10) k) 1)) (/ (pow k m) (sqrt (+ (* (+ k 10) k) 1)))))
11.0ms	(sqrt (+ (* (+ k 10) k) 1))
11.0ms	(sqrt (+ (* (+ k 10) k) 1))

series324.0ms

Counts

4 → 12

Calls

4 calls:

109.0ms	(/ (sqrt (+ (* (+ k 10) k) 1)) (/ (pow k m) (sqrt (+ (* (+ k 10) k) 1))))
153.0ms	(/ a (/ (sqrt (+ (* (+ k 10) k) 1)) (/ (pow k m) (sqrt (+ (* (+ k 10) k) 1)))))
30.0ms	(sqrt (+ (* (+ k 10) k) 1))
32.0ms	(sqrt (+ (* (+ k 10) k) 1))

simplify3.9s

Counts

1601 → 1601

Iterations

Iter	Nodes
done	5001
0	1776

prune8.3s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize80.0ms

Local error

Found 4 expressions with local error:

12.2b	(sqrt (+ (* (+ k 10) k) 1))
12.2b	(sqrt (+ (* (+ k 10) k) 1))
12.6b	(cbrt (+ (* (+ k 10) k) 1))
12.6b	(cbrt (+ (* (+ k 10) k) 1))

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
8×	`*-un-lft-identity` `add-cube-cbrt`
6×	`cbrt-prod` `pow1` `sqrt-prod`
4×	`cbrt-div` `flip3-+` `add-cbrt-cube` `sqrt-div` `add-exp-log` `flip-+` `insert-posit16` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow1/3`

Counts

4 → 60

Calls

4 calls:

26.0ms	(sqrt (+ (* (+ k 10) k) 1))
21.0ms	(sqrt (+ (* (+ k 10) k) 1))
8.0ms	(cbrt (+ (* (+ k 10) k) 1))
6.0ms	(cbrt (+ (* (+ k 10) k) 1))

series217.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(sqrt (+ (* (+ k 10) k) 1))
33.0ms	(sqrt (+ (* (+ k 10) k) 1))
56.0ms	(cbrt (+ (* (+ k 10) k) 1))
77.0ms	(cbrt (+ (* (+ k 10) k) 1))

simplify1.9s

Counts

72 → 72

Iterations

Iter	Nodes
done	5008
4	2569
3	890
2	413
1	181
0	84

prune697.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize33.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (* (/ (+ (* (+ k 10) k) 1) (pow k m)) (/ (+ (* (+ k 10) k) 1) (pow k m))) (/ (+ (* (+ k 10) k) 1) (pow k m)))
0.0b	(* (/ (+ (* (+ k 10) k) 1) (pow k m)) (/ (+ (* (+ k 10) k) 1) (pow k m)))
2.0b	(/ a (cbrt (* (* (/ (+ (* (+ k 10) k) 1) (pow k m)) (/ (+ (* (+ k 10) k) 1) (pow k m))) (/ (+ (* (+ k 10) k) 1) (pow k m)))))
4.7b	(cbrt (* (* (/ (+ (* (+ k 10) k) 1) (pow k m)) (/ (+ (* (+ k 10) k) 1) (pow k m))) (/ (+ (* (+ k 10) k) 1) (pow k m))))

rewrite303.0ms

Algorithm

rewrite-expression-head

Rules

352×	`add-exp-log`
172×	`div-exp`
148×	`prod-exp`
144×	`times-frac`
137×	`add-sqr-sqrt`
83×	`*-un-lft-identity` `add-cube-cbrt`
58×	`add-cbrt-cube`
57×	`pow-to-exp` `pow-exp`
54×	`unpow-prod-down`
50×	`associate-r`
30×	`pow1`
26×	`associate-l`
25×	`swap-sqr`
24×	`sqr-pow`
22×	`cbrt-unprod`
20×	`unswap-sqr`
18×	`cbrt-undiv`
16×	`frac-times` `associate-*l/`
14×	`cbrt-div`
10×	`associate-*r/`
7×	`pow-plus` `associate-/r/` `pow-prod-up`
6×	`div-inv`
5×	`cbrt-prod`
4×	`associate-/r*` `pow-prod-down` `insert-posit16` `add-log-exp`
3×	`pow2` `pow-sqr` `associate-/l*`
2×	`pow3` `*-commutative`
1×	`clear-num` `frac-2neg` `pow1/3` `rem-cbrt-cube`

Counts

4 → 320

Calls

4 calls:

111.0ms	(* (* (/ (+ (* (+ k 10) k) 1) (pow k m)) (/ (+ (* (+ k 10) k) 1) (pow k m))) (/ (+ (* (+ k 10) k) 1) (pow k m)))
72.0ms	(* (/ (+ (* (+ k 10) k) 1) (pow k m)) (/ (+ (* (+ k 10) k) 1) (pow k m)))
10.0ms	(/ a (cbrt (* (* (/ (+ (* (+ k 10) k) 1) (pow k m)) (/ (+ (* (+ k 10) k) 1) (pow k m))) (/ (+ (* (+ k 10) k) 1) (pow k m)))))
101.0ms	(cbrt (* (* (/ (+ (* (+ k 10) k) 1) (pow k m)) (/ (+ (* (+ k 10) k) 1) (pow k m))) (/ (+ (* (+ k 10) k) 1) (pow k m))))

series469.0ms

Counts

4 → 12

Calls

4 calls:

132.0ms	(* (* (/ (+ (* (+ k 10) k) 1) (pow k m)) (/ (+ (* (+ k 10) k) 1) (pow k m))) (/ (+ (* (+ k 10) k) 1) (pow k m)))
102.0ms	(* (/ (+ (* (+ k 10) k) 1) (pow k m)) (/ (+ (* (+ k 10) k) 1) (pow k m)))
145.0ms	(/ a (cbrt (* (* (/ (+ (* (+ k 10) k) 1) (pow k m)) (/ (+ (* (+ k 10) k) 1) (pow k m))) (/ (+ (* (+ k 10) k) 1) (pow k m)))))
89.0ms	(cbrt (* (* (/ (+ (* (+ k 10) k) 1) (pow k m)) (/ (+ (* (+ k 10) k) 1) (pow k m))) (/ (+ (* (+ k 10) k) 1) (pow k m))))

simplify1.8s

Counts

332 → 332

Iterations

Iter	Nodes
done	5001
1	1431
0	451

prune1.5s

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.0b

regimes124.0ms

Accuracy

98.8% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 2.1b

bsearch51.0ms

Steps

Iters	Range		Point
4	1.0646836956296872e+108	1.6495200433389913e+108	1.367410316305712e+108

simplify1.4s

Iterations

Iter	Nodes
done	5001
247	4985
246	4967
245	4945
244	4927
243	4905
242	4887
241	4865
240	4847
239	4825
238	4807
237	4785
236	4767
235	4745
234	4727
233	4705
232	4687
231	4665
230	4647
229	4625
228	4607
227	4585
226	4567
225	4545
224	4527
223	4505
222	4487
221	4465
220	4447
219	4425
218	4407
217	4385
216	4367
215	4345
214	4327
213	4305
212	4287
211	4265
210	4247
209	4225
208	4207
207	4185
206	4167
205	4145
204	4127
203	4105
202	4087
201	4065
200	4047
199	4025
198	4007
197	3985
196	3967
195	3945
194	3927
193	3905
192	3887
191	3865
190	3847
189	3825
188	3807
187	3785
186	3767
185	3745
184	3727
183	3705
182	3687
181	3665
180	3647
179	3625
178	3607
177	3585
176	3567
175	3545
174	3527
173	3505
172	3487
171	3465
170	3447
169	3425
168	3407
167	3385
166	3367
165	3345
164	3327
163	3305
162	3287
161	3265
160	3247
159	3225
158	3207
157	3185
156	3167
155	3145
154	3127
153	3105
152	3087
151	3065
150	3047
149	3025
148	3007
147	2985
146	2967
145	2945
144	2927
143	2905
142	2887
141	2865
140	2847
139	2825
138	2807
137	2785
136	2767
135	2745
134	2727
133	2705
132	2687
131	2665
130	2647
129	2625
128	2607
127	2585
126	2567
125	2545
124	2527
123	2505
122	2487
121	2465
120	2447
119	2425
118	2407
117	2385
116	2367
115	2345
114	2327
113	2305
112	2287
111	2265
110	2247
109	2225
108	2207
107	2185
106	2167
105	2145
104	2127
103	2105
102	2087
101	2065
100	2047
99	2025
98	2007
97	1985
96	1967
95	1945
94	1927
93	1905
92	1887
91	1865
90	1847
89	1825
88	1807
87	1785
86	1767
85	1745
84	1727
83	1705
82	1687
81	1665
80	1647
79	1625
78	1607
77	1585
76	1567
75	1545
74	1527
73	1505
72	1487
71	1465
70	1447
69	1425
68	1407
67	1385
66	1367
65	1345
64	1327
63	1305
62	1287
61	1265
60	1247
59	1225
58	1207
57	1185
56	1167
55	1145
54	1127
53	1105
52	1087
51	1065
50	1047
49	1025
48	1007
47	985
46	967
45	945
44	927
43	905
42	887
41	865
40	847
39	825
38	807
37	785
36	767
35	745
34	727
33	705
32	687
31	665
30	647
29	625
28	607
27	585
26	567
25	545
24	527
23	505
22	487
21	465
20	447
19	425
18	407
17	385
16	367
15	345
14	327
13	305
12	287
11	265
10	247
9	225
8	207
7	185
6	167
5	149
4	109
3	85
2	61
1	51
0	35

end0.0ms

sample3.2s

Algorithm

intervals

Results

2.1s	11968×	body	80	valid
545.0ms	4230×	body	80	nan