Details

sample30.0ms

Algorithm

intervals

Results

9.0ms	55×	body	1280	valid
5.0ms	38×	body	640	valid
5.0ms	130×	body	80	valid
3.0ms	29×	body	320	valid
0.0ms	4×	body	160	valid

simplify7.1s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	7	13
1	12	13
2	16	13
3	19	13
4	21	13
5	27	13
6	39	13
7	60	13
8	78	13
9	99	13
10	147	13
11	192	13
12	204	13
13	218	13
14	245	13
15	269	13
16	296	13
17	320	13
18	347	13
19	371	13
20	398	13
21	421	13
22	448	13
23	471	13
24	498	13
25	522	13
26	549	13
27	573	13
28	600	13
29	624	13
30	651	13
31	675	13
32	702	13
33	726	13
34	753	13
35	777	13
36	804	13
37	827	13
38	854	13
39	878	13
40	905	13
41	929	13
42	956	13
43	980	13
44	1007	13
45	1031	13
46	1058	13
47	1081	13
48	1108	13
49	1132	13
50	1159	13
51	1183	13
52	1210	13
53	1234	13
54	1261	13
55	1285	13
56	1312	13
57	1336	13
58	1363	13
59	1387	13
60	1414	13
61	1438	13
62	1465	13
63	1489	13
64	1516	13
65	1540	13
66	1567	13
67	1591	13
68	1618	13
69	1642	13
70	1669	13
71	1693	13
72	1720	13
73	1744	13
74	1771	13
75	1794	13
76	1821	13
77	1845	13
78	1872	13
79	1895	13
80	1922	13
81	1946	13
82	1973	13
83	1996	13
84	2023	13
85	2047	13
86	2074	13
87	2097	13
88	2124	13
89	2148	13
90	2175	13
91	2198	13
92	2225	13
93	2248	13
94	2275	13
95	2298	13
96	2325	13
97	2349	13
98	2376	13
99	2399	13
100	2426	13
101	2449	13
102	2476	13
103	2499	13
104	2526	13
105	2549	13
106	2576	13
107	2600	13
108	2627	13
109	2651	13
110	2678	13
111	2701	13
112	2728	13
113	2751	13
114	2778	13
115	2802	13
116	2829	13
117	2853	13
118	2880	13
119	2903	13
120	2930	13
121	2953	13
122	2980	13
123	3003	13
124	3030	13
125	3053	13
126	3080	13
127	3104	13
128	3131	13
129	3154	13
130	3181	13
131	3205	13
132	3232	13
133	3256	13
134	3283	13
135	3307	13
136	3334	13
137	3357	13
138	3384	13
139	3408	13
140	3435	13
141	3458	13
142	3485	13
143	3508	13
144	3535	13
145	3558	13
146	3585	13
147	3608	13
148	3635	13
149	3658	13
150	3685	13
151	3709	13
152	3736	13
153	3760	13
154	3787	13
155	3810	13
156	3837	13
157	3861	13
158	3888	13
159	3911	13
160	3938	13
161	3961	13
162	3988	13
163	4011	13
164	4038	13
165	4061	13
166	4088	13
167	4111	13
168	4138	13
169	4161	13
170	4188	13
171	4211	13
172	4238	13
173	4261	13
174	4288	13
175	4312	13
176	4339	13
177	4362	13
178	4389	13
179	4412	13
180	4439	13
181	4462	13
182	4489	13
183	4512	13
184	4539	13
185	4562	13
186	4589	13
187	4613	13
188	4640	13
189	4663	13
190	4690	13
191	4713	13
192	4740	13
193	4763	13
194	4790	13
195	4813	13
196	4840	13
197	4863	13
198	4890	13
199	4913	13
200	4940	13
201	4963	13
202	4990	13
done	5000	13

prune2.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 29.8b

Counts

2 → 1

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (+ x 1.0) (- x 1.0))
0.0b	(/ x (+ x 1.0))
3.1b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

99×	`*-un-lft-identity`
52×	`times-frac`
45×	`add-sqr-sqrt`
23×	`add-cube-cbrt`
18×	`distribute-lft-out` `distribute-lft-out--`
9×	`associate-/r*` `difference-of-squares`
7×	`add-exp-log` `add-cbrt-cube` `associate-/l*`
5×	`add-log-exp`
4×	`associate-/r/`
3×	`pow1`
2×	`cbrt-undiv` `flip3--` `frac-2neg` `flip3-+` `div-exp` `clear-num` `flip--` `flip-+` `div-inv` `associate-/l/`
1×	`sub-neg` `diff-log` `frac-sub`

Counts

3 → 104

Calls

3 calls:

8.0ms	(/ (+ x 1.0) (- x 1.0))
10.0ms	(/ x (+ x 1.0))
30.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series14.0ms

Counts

3 → 9

Calls

3 calls:

3.0ms	(/ (+ x 1.0) (- x 1.0))
3.0ms	(/ x (+ x 1.0))
8.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify726.0ms

Counts

113 → 113

Iterations

Useful iterations: done (722.0ms)

Iter	Nodes	Cost
0	176	1584
1	399	1506
2	1114	1428
3	2960	1418
done	5001	1417

prune199.0ms

Filtered

77 candidates to 113 candidates (-46.8%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	107	6	113
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	108	6	114

Merged error: 0.0b

Counts

114 → 6

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ x (+ x 1.0))
0.0b	(log (exp (/ (+ x 1.0) (- x 1.0))))
0.0b	(exp (/ (+ x 1.0) (- x 1.0)))
3.1b	(- (/ x (+ x 1.0)) (log (exp (/ (+ x 1.0) (- x 1.0)))))

rewrite68.0ms

Algorithm

rewrite-expression-head

Rules

82×	`*-un-lft-identity`
56×	`add-sqr-sqrt`
53×	`times-frac`
52×	`exp-prod`
35×	`add-cube-cbrt`
28×	`log-pow`
14×	`distribute-lft-out`
10×	`distribute-lft-out--` `difference-of-squares`
6×	`pow1` `add-exp-log` `log-prod` `associate-/r/` `add-cbrt-cube` `add-log-exp`
4×	`associate-/r*`
3×	`flip3--` `flip--` `div-inv` `associate-/l*` `associate--r+`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `flip3-+` `diff-log` `div-exp` `rem-log-exp` `clear-num` `flip-+` `rem-exp-log`

Counts

4 → 124

Calls

4 calls:

5.0ms	(/ x (+ x 1.0))
11.0ms	(log (exp (/ (+ x 1.0) (- x 1.0))))
10.0ms	(exp (/ (+ x 1.0) (- x 1.0)))
37.0ms	(- (/ x (+ x 1.0)) (log (exp (/ (+ x 1.0) (- x 1.0)))))

series22.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(/ x (+ x 1.0))
3.0ms	(log (exp (/ (+ x 1.0) (- x 1.0))))
4.0ms	(exp (/ (+ x 1.0) (- x 1.0)))
12.0ms	(- (/ x (+ x 1.0)) (log (exp (/ (+ x 1.0) (- x 1.0)))))

simplify711.0ms

Counts

136 → 136

Iterations

Useful iterations: 3 (281.0ms)

Iter	Nodes	Cost
0	212	1758
1	423	1535
2	1035	1439
3	2677	1412
done	5000	1412

prune227.0ms

Filtered

97 candidates to 136 candidates (-40.2%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	136	0	136
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	136	6	142

Merged error: 0.0b

Counts

142 → 6

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ x (+ x 1.0))
0.0b	(cbrt (pow (/ (+ x 1.0) (- x 1.0)) 3))
0.0b	(pow (/ (+ x 1.0) (- x 1.0)) 3)
3.1b	(- (/ x (+ x 1.0)) (cbrt (pow (/ (+ x 1.0) (- x 1.0)) 3)))

rewrite103.0ms

Algorithm

rewrite-expression-head

Rules

137×	`*-un-lft-identity`
124×	`add-sqr-sqrt`
103×	`times-frac`
70×	`cbrt-prod`
56×	`unpow-prod-down` `cube-prod`
55×	`add-cube-cbrt`
30×	`difference-of-squares`
24×	`distribute-lft-out`
17×	`distribute-lft-out--`
10×	`associate-/r/`
9×	`add-exp-log` `add-cbrt-cube`
6×	`add-log-exp`
5×	`pow1` `flip3--` `flip--` `div-inv`
4×	`associate-/r*` `sqr-pow`
3×	`cube-div` `pow-unpow` `associate-/l*`
2×	`cbrt-undiv` `cube-mult` `cbrt-div` `unpow3` `div-exp` `pow-exp` `rem-cube-cbrt`
1×	`pow-to-exp` `sub-neg` `pow-pow` `frac-2neg` `flip3-+` `pow1/3` `diff-log` `clear-num` `frac-sub` `rem-cbrt-cube` `flip-+`

Counts

4 → 201

Calls

4 calls:

5.0ms	(/ x (+ x 1.0))
12.0ms	(cbrt (pow (/ (+ x 1.0) (- x 1.0)) 3))
11.0ms	(pow (/ (+ x 1.0) (- x 1.0)) 3)
65.0ms	(- (/ x (+ x 1.0)) (cbrt (pow (/ (+ x 1.0) (- x 1.0)) 3)))

series27.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(/ x (+ x 1.0))
5.0ms	(cbrt (pow (/ (+ x 1.0) (- x 1.0)) 3))
4.0ms	(pow (/ (+ x 1.0) (- x 1.0)) 3)
15.0ms	(- (/ x (+ x 1.0)) (cbrt (pow (/ (+ x 1.0) (- x 1.0)) 3)))

simplify569.0ms

Counts

213 → 213

Iterations

Useful iterations: done (556.0ms)

Iter	Nodes	Cost
0	293	4170
1	763	3494
2	2258	3258
done	5000	3225

prune257.0ms

Filtered

113 candidates to 213 candidates (-88.5%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	213	0	213
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	213	6	219

Merged error: 0.0b

Counts

219 → 6

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (+ x 1.0) (- x 1.0))
0.0b	(/ (/ x (sqrt (+ x 1.0))) (sqrt (+ x 1.0)))
0.1b	(/ x (sqrt (+ x 1.0)))
6.8b	(- (/ (/ x (sqrt (+ x 1.0))) (sqrt (+ x 1.0))) (/ (+ x 1.0) (- x 1.0)))

rewrite276.0ms

Algorithm

rewrite-expression-head

Rules

433×	`times-frac`
355×	`*-un-lft-identity`
264×	`add-sqr-sqrt`
234×	`sqrt-prod`
199×	`add-cube-cbrt`
64×	`distribute-lft-out`
34×	`associate-/l*`
22×	`associate-/r/`
20×	`sqrt-div`
19×	`associate-/r*` `difference-of-squares`
13×	`add-exp-log` `add-cbrt-cube`
12×	`distribute-lft-out--`
11×	`flip3-+` `flip-+` `div-inv`
6×	`add-log-exp`
5×	`cbrt-undiv` `div-exp`
4×	`pow1`
3×	`frac-2neg` `clear-num` `associate-/l/`
2×	`flip3--` `flip--`
1×	`sub-neg` `diff-log` `frac-sub`

Counts

4 → 362

Calls

4 calls:

8.0ms	(/ (+ x 1.0) (- x 1.0))
21.0ms	(/ (/ x (sqrt (+ x 1.0))) (sqrt (+ x 1.0)))
7.0ms	(/ x (sqrt (+ x 1.0)))
215.0ms	(- (/ (/ x (sqrt (+ x 1.0))) (sqrt (+ x 1.0))) (/ (+ x 1.0) (- x 1.0)))

series22.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(/ (+ x 1.0) (- x 1.0))
3.0ms	(/ (/ x (sqrt (+ x 1.0))) (sqrt (+ x 1.0)))
8.0ms	(/ x (sqrt (+ x 1.0)))
8.0ms	(- (/ (/ x (sqrt (+ x 1.0))) (sqrt (+ x 1.0))) (/ (+ x 1.0) (- x 1.0)))

simplify709.0ms

Counts

374 → 374

Iterations

Useful iterations: done (695.0ms)

Iter	Nodes	Cost
0	436	8403
1	1030	7396
2	3187	6685
done	5000	6668

prune501.0ms

Filtered

177 candidates to 374 candidates (-111.3%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	374	0	374
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	374	6	380

Merged error: 0.0b

Counts

380 → 6

regimes51.0ms

Accuracy

99.7% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 28.7b

bsearch35.0ms

Steps

Iters	Range		Point
11	901.3230478674768	3.453863445390637e+32	12520.595647862758
9	-174458.2165831976	-0.46594774775336223	-0.9999789100910194

simplify3.0ms

Iterations

Useful iterations: 1 (1.0ms)

Iter	Nodes	Cost
0	26	59
1	33	44
done	33	44

end0.0ms

sample828.0ms

Algorithm

intervals

Results

285.0ms	1718×	body	1280	valid
161.0ms	1194×	body	640	valid
147.0ms	4175×	body	80	valid
62.0ms	606×	body	320	valid
20.0ms	307×	body	160	valid

Details

sample30.0ms

simplify7.1s

prune2.0ms

localize7.0ms

rewrite53.0ms

series14.0ms

simplify726.0ms

prune199.0ms

localize13.0ms

rewrite68.0ms

series22.0ms

simplify711.0ms

prune227.0ms

localize9.0ms

rewrite103.0ms

series27.0ms

simplify569.0ms

prune257.0ms

localize12.0ms

rewrite276.0ms

series22.0ms

simplify709.0ms

prune501.0ms

regimes51.0ms

bsearch35.0ms

simplify3.0ms

end0.0ms

sample828.0ms

Profiling