Details

sample75.0ms

Algorithm

intervals

Results

13.0ms	186×	body	80	valid
9.0ms	23×	body	1280	valid
7.0ms	29×	body	640	valid
6.0ms	115×	body	80	nan
4.0ms	11×	body	1280	nan
3.0ms	14×	body	640	nan
2.0ms	9×	body	320	valid
1.0ms	9×	body	160	valid
1.0ms	5×	body	320	nan
0.0ms	3×	body	160	nan

simplify14.7s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
229	4985
228	4965
227	4945
226	4924
225	4899
224	4880
223	4860
222	4837
221	4816
220	4797
219	4775
218	4754
217	4733
216	4711
215	4691
214	4670
213	4645
212	4626
211	4606
210	4583
209	4562
208	4543
207	4521
206	4500
205	4479
204	4457
203	4437
202	4416
201	4393
200	4374
199	4354
198	4331
197	4310
196	4291
195	4269
194	4248
193	4227
192	4207
191	4187
190	4166
189	4143
188	4124
187	4104
186	4081
185	4060
184	4041
183	4019
182	3998
181	3977
180	3957
179	3937
178	3916
177	3891
176	3872
175	3852
174	3829
173	3808
172	3789
171	3767
170	3746
169	3725
168	3703
167	3683
166	3662
165	3637
164	3618
163	3598
162	3575
161	3554
160	3535
159	3513
158	3492
157	3471
156	3449
155	3429
154	3408
153	3385
152	3366
151	3346
150	3323
149	3302
148	3283
147	3261
146	3240
145	3219
144	3195
143	3175
142	3154
141	3129
140	3110
139	3090
138	3067
137	3046
136	3027
135	3005
134	2984
133	2963
132	2943
131	2923
130	2902
129	2879
128	2860
127	2840
126	2817
125	2796
124	2777
123	2755
122	2734
121	2713
120	2693
119	2673
118	2652
117	2627
116	2608
115	2588
114	2565
113	2544
112	2525
111	2503
110	2482
109	2461
108	2441
107	2421
106	2400
105	2377
104	2358
103	2338
102	2315
101	2294
100	2275
99	2253
98	2232
97	2211
96	2189
95	2169
94	2148
93	2125
92	2106
91	2086
90	2063
89	2042
88	2023
87	2001
86	1980
85	1959
84	1939
83	1919
82	1898
81	1873
80	1854
79	1834
78	1811
77	1790
76	1771
75	1749
74	1728
73	1707
72	1687
71	1667
70	1646
69	1623
68	1604
67	1584
66	1561
65	1540
64	1521
63	1499
62	1478
61	1457
60	1435
59	1415
58	1394
57	1371
56	1352
55	1332
54	1309
53	1288
52	1269
51	1247
50	1226
49	1205
48	1185
47	1165
46	1144
45	1119
44	1100
43	1080
42	1057
41	1036
40	1017
39	995
38	974
37	953
36	933
35	913
34	892
33	867
32	848
31	828
30	805
29	784
28	765
27	743
26	722
25	701
24	681
23	661
22	640
21	617
20	598
19	578
18	555
17	534
16	515
15	493
14	472
13	451
12	428
11	406
10	360
9	273
8	126
7	86
6	75
5	65
4	53
3	40
2	29
1	19
0	9

prune19.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.6b

localize51.0ms

Local error

Found 4 expressions with local error:

0.0b	(- 1.0 (log (- 1.0 (/ (- x y) (- 1.0 y)))))
0.0b	(/ (- x y) (- 1.0 y))
2.5b	(- 1.0 (/ (- x y) (- 1.0 y)))
5.8b	(log (- 1.0 (/ (- x y) (- 1.0 y))))

rewrite402.0ms

Algorithm

rewrite-expression-head

Rules

192×	`add-sqr-sqrt`
184×	`*-un-lft-identity`
105×	`prod-diff`
103×	`times-frac`
91×	`add-cube-cbrt`
49×	`difference-of-squares`
47×	`distribute-lft-out--`
12×	`log-prod`
9×	`pow1` `flip3--` `flip--`
8×	`associate-/r/`
7×	`add-exp-log` `add-log-exp`
6×	`add-cbrt-cube` `fma-neg` `associate--r+`
5×	`associate-/r` `log-pow` `associate-/l`
4×	`expm1-log1p-u` `log-div` `insert-posit16` `log1p-expm1-u` `div-inv`
3×	`associate--r-`
2×	`sub-neg` `diff-log` `div-sub` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `rem-log-exp`

Counts

4 → 231

Calls

4 calls:

106.0ms	(- 1.0 (log (- 1.0 (/ (- x y) (- 1.0 y)))))
37.0ms	(/ (- x y) (- 1.0 y))
117.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))
114.0ms	(log (- 1.0 (/ (- x y) (- 1.0 y))))

series507.0ms

Counts

4 → 12

Calls

4 calls:

181.0ms	(- 1.0 (log (- 1.0 (/ (- x y) (- 1.0 y)))))
68.0ms	(/ (- x y) (- 1.0 y))
106.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))
152.0ms	(log (- 1.0 (/ (- x y) (- 1.0 y))))

simplify5.6s

Counts

243 → 243

Iterations

Iter	Nodes
done	5000
2	2878
1	1027
0	393

prune2.2s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.2b

localize69.0ms

Local error

Found 4 expressions with local error:

0.0b	(log (/ (exp 1.0) (- 1.0 (/ (- x y) (- 1.0 y)))))
0.0b	(/ (- x y) (- 1.0 y))
0.1b	(/ (exp 1.0) (- 1.0 (/ (- x y) (- 1.0 y))))
2.5b	(- 1.0 (/ (- x y) (- 1.0 y)))

rewrite371.0ms

Algorithm

rewrite-expression-head

Rules

226×	`add-sqr-sqrt`
202×	`*-un-lft-identity`
144×	`times-frac`
102×	`add-cube-cbrt`
93×	`prod-diff`
58×	`difference-of-squares`
50×	`distribute-lft-out--`
24×	`log-prod`
12×	`associate-/r/`
11×	`associate-/r*`
9×	`add-exp-log`
8×	`flip3--` `add-cbrt-cube` `flip--` `associate-/l*`
6×	`div-inv` `add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`fma-neg` `div-exp`
2×	`cbrt-undiv` `clear-num` `frac-2neg` `div-sub` `rem-log-exp` `associate-/l/`
1×	`log-div` `sub-neg` `diff-log` `log-pow` `associate--r-`

Counts

4 → 252

Calls

4 calls:

69.0ms	(log (/ (exp 1.0) (- 1.0 (/ (- x y) (- 1.0 y)))))
44.0ms	(/ (- x y) (- 1.0 y))
126.0ms	(/ (exp 1.0) (- 1.0 (/ (- x y) (- 1.0 y))))
93.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))

series679.0ms

Counts

4 → 12

Calls

4 calls:

313.0ms	(log (/ (exp 1.0) (- 1.0 (/ (- x y) (- 1.0 y)))))
69.0ms	(/ (- x y) (- 1.0 y))
199.0ms	(/ (exp 1.0) (- 1.0 (/ (- x y) (- 1.0 y))))
97.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))

simplify5.9s

Counts

264 → 264

Iterations

Iter	Nodes
done	5002
2	3216
1	1126
0	437

prune2.7s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.1b

localize104.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ 1 (sqrt (- 1.0 (/ (- x y) (- 1.0 y))))) (/ (exp 1.0) (sqrt (- 1.0 (/ (- x y) (- 1.0 y))))))
0.1b	(/ (exp 1.0) (sqrt (- 1.0 (/ (- x y) (- 1.0 y)))))
2.5b	(- 1.0 (/ (- x y) (- 1.0 y)))
2.5b	(- 1.0 (/ (- x y) (- 1.0 y)))

rewrite1.1s

Algorithm

rewrite-expression-head

Rules

410×	`add-sqr-sqrt`
334×	`*-un-lft-identity`
265×	`times-frac`
186×	`prod-diff`
184×	`add-cube-cbrt`
84×	`difference-of-squares`
72×	`distribute-lft-out--`
71×	`sqrt-prod`
33×	`associate-r` `associate-l`
23×	`add-exp-log`
18×	`add-cbrt-cube` `associate-/r/`
15×	`unswap-sqr`
11×	`flip3--` `flip--`
9×	`associate-/r*` `div-exp` `div-inv`
8×	`prod-exp` `add-log-exp`
6×	`pow1` `fma-neg` `sqrt-div`
5×	`cbrt-undiv`
4×	`expm1-log1p-u` `cbrt-unprod` `insert-posit16` `log1p-expm1-u`
3×	`associate-/l*`
2×	`rec-exp` `sub-neg` `diff-log` `1-exp` `div-sub` `associate--r-`
1×	`frac-times` `clear-num` `frac-2neg` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative`

Counts

4 → 394

Calls

4 calls:

709.0ms	(* (/ 1 (sqrt (- 1.0 (/ (- x y) (- 1.0 y))))) (/ (exp 1.0) (sqrt (- 1.0 (/ (- x y) (- 1.0 y))))))
121.0ms	(/ (exp 1.0) (sqrt (- 1.0 (/ (- x y) (- 1.0 y)))))
116.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))
85.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))

series786.0ms

Counts

4 → 12

Calls

4 calls:

225.0ms	(* (/ 1 (sqrt (- 1.0 (/ (- x y) (- 1.0 y))))) (/ (exp 1.0) (sqrt (- 1.0 (/ (- x y) (- 1.0 y))))))
336.0ms	(/ (exp 1.0) (sqrt (- 1.0 (/ (- x y) (- 1.0 y)))))
95.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))
129.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))

simplify6.7s

Counts

406 → 406

Iterations

Iter	Nodes
done	5000
2	3866
1	1350
0	489

prune4.2s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize100.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (/ (exp 1.0) (sqrt (- 1.0 (/ (- x y) (- 1.0 y))))) (sqrt (- 1.0 (/ (- x y) (- 1.0 y)))))
0.2b	(expm1 (log1p (/ (/ (exp 1.0) (sqrt (- 1.0 (/ (- x y) (- 1.0 y))))) (sqrt (- 1.0 (/ (- x y) (- 1.0 y)))))))
2.5b	(- 1.0 (/ (- x y) (- 1.0 y)))
2.5b	(- 1.0 (/ (- x y) (- 1.0 y)))

rewrite680.0ms

Algorithm

rewrite-expression-head

Rules

812×	`add-sqr-sqrt`
783×	`times-frac`
614×	`*-un-lft-identity`
384×	`sqrt-prod`
362×	`add-cube-cbrt`
192×	`difference-of-squares`
186×	`prod-diff`
126×	`distribute-lft-out--`
34×	`associate-/r/`
33×	`associate-/l*`
22×	`sqrt-div`
19×	`flip3--` `flip--`
17×	`div-inv`
9×	`associate-/r*` `add-cbrt-cube`
8×	`add-exp-log` `add-log-exp`
6×	`fma-neg`
4×	`expm1-log1p-u` `pow1` `insert-posit16` `log1p-expm1-u`
3×	`cbrt-undiv` `div-exp`
2×	`sub-neg` `diff-log` `div-sub` `associate--r-`
1×	`expm1-log1p` `clear-num` `frac-2neg` `expm1-udef` `associate-/l/`

Counts

4 → 601

Calls

4 calls:

317.0ms	(/ (/ (exp 1.0) (sqrt (- 1.0 (/ (- x y) (- 1.0 y))))) (sqrt (- 1.0 (/ (- x y) (- 1.0 y)))))
1.0ms	(expm1 (log1p (/ (/ (exp 1.0) (sqrt (- 1.0 (/ (- x y) (- 1.0 y))))) (sqrt (- 1.0 (/ (- x y) (- 1.0 y)))))))
97.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))
107.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))

series2.0s

Counts

4 → 12

Calls

4 calls:

243.0ms	(/ (/ (exp 1.0) (sqrt (- 1.0 (/ (- x y) (- 1.0 y))))) (sqrt (- 1.0 (/ (- x y) (- 1.0 y)))))
1.6s	(expm1 (log1p (/ (/ (exp 1.0) (sqrt (- 1.0 (/ (- x y) (- 1.0 y))))) (sqrt (- 1.0 (/ (- x y) (- 1.0 y)))))))
76.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))
95.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))

simplify7.1s

Counts

613 → 613

Iterations

Iter	Nodes
done	5001
2	4342
1	1763
0	735

prune5.7s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

regimes625.0ms

Accuracy

99.5% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 18.9b

bsearch288.0ms

Steps

Iters	Range		Point
10	0.00018705152818348546	24130438545.104744	51921085.77104035
8	-871508905171.6743	-135490375.57476136	-224500362.70196208

simplify29.0ms

Iterations

Iter	Nodes
done	58
2	58
1	53
0	38

end0.0ms

sample2.7s

Algorithm

intervals

Results

790.0ms	832×	body	1280	valid
516.0ms	5628×	body	80	valid
300.0ms	846×	body	640	valid
243.0ms	3796×	body	80	nan
132.0ms	333×	body	1280	nan
90.0ms	455×	body	320	valid
83.0ms	366×	body	640	nan
36.0ms	213×	body	320	nan
31.0ms	239×	body	160	valid
16.0ms	141×	body	160	nan