Details

sample32.0ms

Algorithm

intervals

Results

14.0ms

256×

body

valid

simplify42.6s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
201	4996
200	4991
199	4986
198	4981
197	4976
196	4971
195	4966
194	4961
193	4956
192	4951
191	4946
190	4941
189	4936
188	4931
187	4926
186	4921
185	4916
184	4911
183	4906
182	4901
181	4896
180	4891
179	4886
178	4881
177	4876
176	4871
175	4866
174	4861
173	4856
172	4851
171	4846
170	4841
169	4836
168	4831
167	4826
166	4821
165	4816
164	4811
163	4806
162	4801
161	4796
160	4791
159	4786
158	4781
157	4776
156	4771
155	4766
154	4761
153	4756
152	4751
151	4746
150	4741
149	4736
148	4731
147	4726
146	4721
145	4716
144	4711
143	4706
142	4701
141	4696
140	4691
139	4686
138	4681
137	4676
136	4671
135	4666
134	4661
133	4656
132	4651
131	4646
130	4641
129	4636
128	4631
127	4626
126	4621
125	4616
124	4611
123	4606
122	4601
121	4596
120	4591
119	4586
118	4581
117	4576
116	4571
115	4566
114	4561
113	4556
112	4551
111	4546
110	4541
109	4536
108	4531
107	4526
106	4521
105	4516
104	4511
103	4506
102	4501
101	4496
100	4491
99	4486
98	4481
97	4476
96	4471
95	4466
94	4461
93	4456
92	4451
91	4446
90	4441
89	4436
88	4431
87	4426
86	4421
85	4416
84	4411
83	4406
82	4401
81	4396
80	4391
79	4386
78	4381
77	4376
76	4371
75	4366
74	4361
73	4356
72	4351
71	4346
70	4341
69	4336
68	4331
67	4326
66	4321
65	4316
64	4311
63	4306
62	4301
61	4296
60	4291
59	4286
58	4281
57	4276
56	4271
55	4266
54	4261
53	4256
52	4251
51	4246
50	4241
49	4236
48	4231
47	4226
46	4221
45	4216
44	4211
43	4206
42	4201
41	4196
40	4191
39	4186
38	4181
37	4176
36	4171
35	4166
34	4161
33	4156
32	4151
31	4146
30	4141
29	4136
28	4131
27	4126
26	4121
25	4116
24	4111
23	4106
22	4101
21	4096
20	4091
19	4086
18	4081
17	4076
16	4071
15	4066
14	4061
13	4056
12	4049
11	4021
10	2709
9	1862
8	1482
7	1265
6	1028
5	714
4	349
3	145
2	64
1	35
0	18

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 20.4b

localize31.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ x (/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))
0.1b	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
3.6b	(* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))
19.8b	(/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

rewrite165.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
13×	`add-cbrt-cube` `add-exp-log`
12×	`*-un-lft-identity`
10×	`add-cube-cbrt`
8×	`pow1`
6×	`associate-r` `associate-l` `add-log-exp`
5×	`flip3-+` `flip-+`
4×	`associate-*r/`
3×	`associate-/r*` `times-frac` `prod-exp` `cbrt-unprod`
2×	`cbrt-undiv` `div-exp` `pow-prod-down` `associate-l/` `associate-/r/` `-commutative` `unswap-sqr` `associate-/l/`
1×	`distribute-rgt-in` `+-commutative` `clear-num` `sum-log` `frac-2neg` `distribute-lft-in` `div-inv` `distribute-lft-out` `associate-/l*`

Counts

4 → 79

Calls

4 calls:

38.0ms	(+ x (/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))
28.0ms	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
52.0ms	(* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))
44.0ms	(/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

series544.0ms

Counts

4 → 12

Calls

4 calls:

230.0ms	(+ x (/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))
86.0ms	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
59.0ms	(* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))
169.0ms	(/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

simplify1.9s

Counts

91 → 91

Iterations

Iter	Nodes
done	5000
2	2692
1	561
0	192

prune589.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize45.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ x (* y (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))))
0.1b	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
0.1b	(* y (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))
15.8b	(/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

rewrite191.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
22×	`*-un-lft-identity` `add-cube-cbrt`
19×	`times-frac`
18×	`associate-r`
13×	`add-cbrt-cube` `add-exp-log`
8×	`pow1`
6×	`associate-l` `add-log-exp`
5×	`flip3-+` `flip-+`
4×	`associate-/r/`
3×	`associate-/r` `prod-exp` `cbrt-unprod` `associate-/l` `unswap-sqr`
2×	`cbrt-undiv` `div-exp` `pow-prod-down` `associate-l/` `-commutative` `div-inv` `associate-/l/`
1×	`+-commutative` `clear-num` `sum-log` `frac-2neg` `associate-*r/`

Counts

4 → 96

Calls

4 calls:

11.0ms	(+ x (* y (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))))
30.0ms	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
91.0ms	(* y (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))
57.0ms	(/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

series532.0ms

Counts

4 → 12

Calls

4 calls:

217.0ms	(+ x (* y (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))))
72.0ms	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
153.0ms	(* y (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))
90.0ms	(/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

simplify1.3s

Counts

108 → 108

Iterations

Iter	Nodes
done	5000
2	2641
1	578
0	209

prune682.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize53.0ms

Local error

Found 4 expressions with local error:

0.1b	(* z (+ 0.4917317610505968 (* 0.0692910599291889 z)))
0.1b	(* y (exp (log (/ (+ (* z (+ 0.4917317610505968 (* 0.0692910599291889 z))) 0.279195317918525) (+ 3.350343815022304 (* z (+ z 6.012459259764103)))))))
0.5b	(exp (log (/ (+ (* z (+ 0.4917317610505968 (* 0.0692910599291889 z))) 0.279195317918525) (+ 3.350343815022304 (* z (+ z 6.012459259764103))))))
15.8b	(/ (+ (* z (+ 0.4917317610505968 (* 0.0692910599291889 z))) 0.279195317918525) (+ 3.350343815022304 (* z (+ z 6.012459259764103))))

rewrite151.0ms

Algorithm

rewrite-expression-head

Rules

40×	`add-sqr-sqrt`
32×	`log-prod` `exp-sum`
31×	`*-un-lft-identity` `add-cube-cbrt`
28×	`times-frac`
21×	`associate-r`
10×	`add-cbrt-cube`
9×	`pow1` `add-exp-log`
6×	`associate-l` `associate-/r/`
5×	`flip3-+` `flip-+`
4×	`exp-prod` `add-log-exp` `unswap-sqr`
3×	`associate-/r` `associate-r/` `div-inv` `associate-/l*`
2×	`log-div` `exp-diff` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `associate-/l/`
1×	`distribute-rgt-in` `cbrt-undiv` `clear-num` `frac-2neg` `distribute-lft-in` `div-exp` `log-pow` `rem-exp-log`

Counts

4 → 117

Calls

4 calls:

14.0ms	(* z (+ 0.4917317610505968 (* 0.0692910599291889 z)))
67.0ms	(* y (exp (log (/ (+ (* z (+ 0.4917317610505968 (* 0.0692910599291889 z))) 0.279195317918525) (+ 3.350343815022304 (* z (+ z 6.012459259764103)))))))
20.0ms	(exp (log (/ (+ (* z (+ 0.4917317610505968 (* 0.0692910599291889 z))) 0.279195317918525) (+ 3.350343815022304 (* z (+ z 6.012459259764103))))))
45.0ms	(/ (+ (* z (+ 0.4917317610505968 (* 0.0692910599291889 z))) 0.279195317918525) (+ 3.350343815022304 (* z (+ z 6.012459259764103))))

series404.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(* z (+ 0.4917317610505968 (* 0.0692910599291889 z)))
138.0ms	(* y (exp (log (/ (+ (* z (+ 0.4917317610505968 (* 0.0692910599291889 z))) 0.279195317918525) (+ 3.350343815022304 (* z (+ z 6.012459259764103)))))))
80.0ms	(exp (log (/ (+ (* z (+ 0.4917317610505968 (* 0.0692910599291889 z))) 0.279195317918525) (+ 3.350343815022304 (* z (+ z 6.012459259764103))))))
93.0ms	(/ (+ (* z (+ 0.4917317610505968 (* 0.0692910599291889 z))) 0.279195317918525) (+ 3.350343815022304 (* z (+ z 6.012459259764103))))

simplify1.6s

Counts

129 → 129

Iterations

Iter	Nodes
done	5001
2	2730
1	629
0	256

prune976.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize48.0ms

Local error

Found 4 expressions with local error:

7.3b	(* (/ y (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))) (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))))
15.2b	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
15.2b	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
15.3b	(/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))

rewrite215.0ms

Algorithm

rewrite-expression-head

Rules

79×	`add-sqr-sqrt`
66×	`times-frac`
47×	`*-un-lft-identity` `add-cube-cbrt`
42×	`sqrt-prod`
24×	`associate-r` `associate-l`
18×	`add-cbrt-cube` `add-exp-log`
10×	`sqrt-div`
9×	`unswap-sqr`
8×	`pow1`
6×	`associate-/r*` `flip3-+` `associate-/r/` `flip-+`
5×	`cbrt-undiv` `div-exp`
4×	`prod-exp` `cbrt-unprod` `add-log-exp`
3×	`div-inv` `associate-/l*`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-/l/`
1×	`frac-times` `clear-num` `frac-2neg` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative`

Counts

4 → 150

Calls

4 calls:

126.0ms	(* (/ y (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))) (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))))
13.0ms	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
18.0ms	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
53.0ms	(/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))

series416.0ms

Counts

4 → 12

Calls

4 calls:

162.0ms	(* (/ y (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))) (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))))
69.0ms	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
54.0ms	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
132.0ms	(/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))

simplify2.5s

Counts

162 → 162

Iterations

Iter	Nodes
done	5001
2	3895
1	742
0	258

prune1.2s

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.0b

regimes237.0ms

Accuracy

98.8% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 15.9b

bsearch246.0ms

Steps

Iters	Range		Point
10	1.4175168406832512e-19	0.030359728269424062	0.029920003583066714
10	-3.014988135594576e+22	-33326255562.233612	-1.237026755802593e+20

simplify9.0ms

Iterations

Iter	Nodes
done	46
1	46
0	30

end0.0ms

sample1.7s

Algorithm

intervals

Results

1.2s

8000×

body

valid