Details

sample153.0ms

Algorithm

intervals

Results

45.0ms	56×	body	1280	valid
35.0ms	52×	body	10240	exit
22.0ms	54×	body	640	valid
8.0ms	96×	body	80	valid
7.0ms	28×	body	320	valid
4.0ms	3×	body	2560	valid
4.0ms	81×	body	80	nan
3.0ms	19×	body	160	valid
2.0ms	11×	body	640	nan
1.0ms	2×	body	1280	nan
0.0ms	3×	body	320	nan
0.0ms	2×	body	160	nan

simplify41.2s

Counts

1 → 1

Iterations

Useful iterations: 10 (1.2s)

Iter	Nodes	Cost
0	12	345
1	20	345
2	35	320
3	53	320
4	77	320
5	127	320
6	253	320
7	448	320
8	572	320
9	788	320
10	1206	280
11	1735	280
12	2095	280
13	2139	280
14	2164	280
15	2170	280
16	2187	280
17	2213	280
18	2234	280
19	2240	280
20	2253	280
21	2261	280
22	2286	280
23	2292	280
24	2309	280
25	2319	280
26	2340	280
27	2346	280
28	2359	280
29	2365	280
30	2390	280
31	2396	280
32	2413	280
33	2421	280
34	2442	280
35	2448	280
36	2461	280
37	2469	280
38	2494	280
39	2500	280
40	2517	280
41	2525	280
42	2546	280
43	2552	280
44	2565	280
45	2571	280
46	2596	280
47	2602	280
48	2619	280
49	2629	280
50	2650	280
51	2656	280
52	2669	280
53	2675	280
54	2700	280
55	2706	280
56	2723	280
57	2731	280
58	2752	280
59	2758	280
60	2771	280
61	2779	280
62	2804	280
63	2810	280
64	2827	280
65	2837	280
66	2858	280
67	2864	280
68	2877	280
69	2885	280
70	2910	280
71	2916	280
72	2933	280
73	2939	280
74	2960	280
75	2966	280
76	2979	280
77	2985	280
78	3010	280
79	3016	280
80	3033	280
81	3043	280
82	3064	280
83	3070	280
84	3083	280
85	3089	280
86	3114	280
87	3120	280
88	3137	280
89	3145	280
90	3166	280
91	3172	280
92	3185	280
93	3193	280
94	3218	280
95	3224	280
96	3241	280
97	3251	280
98	3272	280
99	3278	280
100	3291	280
101	3297	280
102	3322	280
103	3328	280
104	3345	280
105	3355	280
106	3376	280
107	3382	280
108	3395	280
109	3405	280
110	3430	280
111	3436	280
112	3453	280
113	3461	280
114	3482	280
115	3488	280
116	3501	280
117	3511	280
118	3536	280
119	3542	280
120	3559	280
121	3565	280
122	3586	280
123	3592	280
124	3605	280
125	3615	280
126	3640	280
127	3646	280
128	3663	280
129	3671	280
130	3692	280
131	3698	280
132	3711	280
133	3719	280
134	3744	280
135	3750	280
136	3767	280
137	3773	280
138	3794	280
139	3800	280
140	3813	280
141	3823	280
142	3848	280
143	3854	280
144	3871	280
145	3877	280
146	3898	280
147	3904	280
148	3917	280
149	3927	280
150	3952	280
151	3958	280
152	3975	280
153	3985	280
154	4006	280
155	4012	280
156	4025	280
157	4035	280
158	4060	280
159	4066	280
160	4083	280
161	4091	280
162	4112	280
163	4118	280
164	4131	280
165	4137	280
166	4162	280
167	4168	280
168	4185	280
169	4195	280
170	4216	280
171	4222	280
172	4235	280
173	4241	280
174	4266	280
175	4272	280
176	4289	280
177	4297	280
178	4318	280
179	4324	280
180	4337	280
181	4343	280
182	4368	280
183	4374	280
184	4391	280
185	4401	280
186	4422	280
187	4428	280
188	4441	280
189	4447	280
190	4472	280
191	4478	280
192	4495	280
193	4501	280
194	4522	280
195	4528	280
196	4541	280
197	4549	280
198	4574	280
199	4580	280
200	4597	280
201	4607	280
202	4628	280
203	4634	280
204	4647	280
205	4653	280
206	4678	280
207	4684	280
208	4701	280
209	4711	280
210	4732	280
211	4738	280
212	4751	280
213	4757	280
214	4782	280
215	4788	280
216	4805	280
217	4815	280
218	4836	280
219	4842	280
220	4855	280
221	4861	280
222	4886	280
223	4892	280
224	4909	280
225	4919	280
226	4940	280
227	4946	280
228	4959	280
229	4969	280
230	4994	280
done	5000	280

prune23.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.4b

localize18.0ms

Local error

Found 2 expressions with local error:

0.1b	(/ (log (fma (expm1 z) y 1.0)) t)
3.4b	(log (fma (expm1 z) y 1.0))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `*-un-lft-identity` `times-frac` `add-cube-cbrt`
7×	`pow1`
5×	`add-exp-log` `log-pow`
4×	`add-cbrt-cube` `associate-/l*`
3×	`log-prod` `associate-/r*`
2×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `rem-log-exp` `div-inv`

Counts

2 → 47

Calls

2 calls:

10.0ms	(/ (log (fma (expm1 z) y 1.0)) t)
1.0ms	(log (fma (expm1 z) y 1.0))

series323.0ms

Counts

2 → 6

Calls

2 calls:

211.0ms	(/ (log (fma (expm1 z) y 1.0)) t)
112.0ms	(log (fma (expm1 z) y 1.0))

simplify2.6s

Counts

53 → 53

Iterations

Useful iterations: done (2.6s)

Iter	Nodes	Cost
0	128	21150
1	281	19323
2	802	18911
3	2469	18806
done	5045	18755

prune465.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 5.1b

localize20.0ms

Local error

Found 2 expressions with local error:

0.1b	(* (log (fma (expm1 z) y 1.0)) (/ 1 t))
3.4b	(log (fma (expm1 z) y 1.0))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
13×	`associate-r`
12×	`*-un-lft-identity` `add-exp-log`
11×	`times-frac` `add-cube-cbrt`
7×	`add-cbrt-cube`
6×	`pow1`
4×	`associate-l` `prod-exp`
3×	`log-prod` `unswap-sqr`
2×	`expm1-log1p-u` `div-exp` `log-pow` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
1×	`cbrt-undiv` `rec-exp` `1-exp` `rem-log-exp` `pow-prod-down` `associate-r/` `un-div-inv` `-commutative` `div-inv`

Counts

2 → 53

Calls

2 calls:

26.0ms	(* (log (fma (expm1 z) y 1.0)) (/ 1 t))
2.0ms	(log (fma (expm1 z) y 1.0))

series263.0ms

Counts

2 → 6

Calls

2 calls:

185.0ms	(* (log (fma (expm1 z) y 1.0)) (/ 1 t))
77.0ms	(log (fma (expm1 z) y 1.0))

simplify2.4s

Counts

59 → 59

Iterations

Useful iterations: done (2.4s)

Iter	Nodes	Cost
0	151	23099
1	376	20230
2	1035	18588
3	2868	18403
done	5000	18378

prune433.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 5.1b

localize39.0ms

Local error

Found 4 expressions with local error:

0.0b	(log1p (log (fma (expm1 z) y 1.0)))
0.1b	(/ (expm1 (log1p (log (fma (expm1 z) y 1.0)))) t)
0.2b	(expm1 (log1p (log (fma (expm1 z) y 1.0))))
3.4b	(log (fma (expm1 z) y 1.0))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
9×	`times-frac`
7×	`add-exp-log`
6×	`add-cbrt-cube`
5×	`expm1-log1p-u` `pow1`
4×	`log1p-expm1-u` `add-log-exp`
3×	`log-prod` `associate-/r` `associate-/l`
2×	`expm1-udef`
1×	`cbrt-undiv` `log1p-udef` `expm1-log1p` `clear-num` `frac-2neg` `div-sub` `div-exp` `rem-log-exp` `log1p-expm1` `log-pow` `div-inv`

Counts

4 → 66

Calls

4 calls:

0.0ms	(log1p (log (fma (expm1 z) y 1.0)))
9.0ms	(/ (expm1 (log1p (log (fma (expm1 z) y 1.0)))) t)
0.0ms	(expm1 (log1p (log (fma (expm1 z) y 1.0))))
2.0ms	(log (fma (expm1 z) y 1.0))

series1.1s

Counts

4 → 12

Calls

4 calls:

224.0ms	(log1p (log (fma (expm1 z) y 1.0)))
449.0ms	(/ (expm1 (log1p (log (fma (expm1 z) y 1.0)))) t)
303.0ms	(expm1 (log1p (log (fma (expm1 z) y 1.0))))
112.0ms	(log (fma (expm1 z) y 1.0))

simplify2.1s

Counts

78 → 78

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	201	40590
1	488	29232
2	1534	28163
done	5000	27948

prune628.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 5.1b

localize42.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sqrt (log (fma (expm1 z) y 1.0))) t)
0.1b	(* (sqrt (log (fma (expm1 z) y 1.0))) (/ (sqrt (log (fma (expm1 z) y 1.0))) t))
3.4b	(log (fma (expm1 z) y 1.0))
3.4b	(log (fma (expm1 z) y 1.0))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

54×	`add-sqr-sqrt`
46×	`times-frac`
38×	`*-un-lft-identity` `add-cube-cbrt`
37×	`sqrt-prod`
25×	`associate-r`
16×	`pow1`
13×	`add-exp-log`
11×	`add-cbrt-cube`
10×	`log-pow`
7×	`associate-l` `associate-/l*`
6×	`log-prod` `unswap-sqr`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r*`
2×	`cbrt-undiv` `div-exp` `rem-log-exp` `prod-exp` `cbrt-unprod` `div-inv`
1×	`clear-num` `frac-2neg` `pow-prod-down` `associate-r/` `-commutative`

Counts

4 → 127

Calls

4 calls:

6.0ms	(/ (sqrt (log (fma (expm1 z) y 1.0))) t)
37.0ms	(* (sqrt (log (fma (expm1 z) y 1.0))) (/ (sqrt (log (fma (expm1 z) y 1.0))) t))
2.0ms	(log (fma (expm1 z) y 1.0))
2.0ms	(log (fma (expm1 z) y 1.0))

series756.0ms

Counts

4 → 12

Calls

4 calls:

443.0ms	(/ (sqrt (log (fma (expm1 z) y 1.0))) t)
147.0ms	(* (sqrt (log (fma (expm1 z) y 1.0))) (/ (sqrt (log (fma (expm1 z) y 1.0))) t))
79.0ms	(log (fma (expm1 z) y 1.0))
87.0ms	(log (fma (expm1 z) y 1.0))

simplify2.2s

Counts

139 → 139

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	211	62760
1	511	57629
2	1607	54695
done	5002	54325

prune990.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 5.1b

regimes444.0ms

Accuracy

45% (3.8b remaining)

Error of 8.5b against oracle of 4.7b and baseline of 11.7b

bsearch83.0ms

Steps

Iters	Range		Point
5	-5.4476459343637906e-92	-1.3848136150427842e-92	-3.4642096152683066e-92

simplify6.0ms

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	26	913
1	31	913
done	31	913

end0.0ms

sample6.9s

Algorithm

intervals

Results

2.0s	1525×	body	10240	exit
1.4s	1503×	body	1280	valid
903.0ms	1504×	body	640	valid
629.0ms	83×	body	2560	valid
395.0ms	3505×	body	80	valid
371.0ms	923×	body	320	valid
243.0ms	2432×	body	80	nan
145.0ms	514×	body	160	valid
99.0ms	284×	body	640	nan
49.0ms	99×	body	1280	nan
37.0ms	150×	body	320	nan
14.0ms	91×	body	160	nan