Details

analyze160.0ms (1.1%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	99.9%	0.1%	0%	0%	0%	0
0%	0%	99.9%	0.1%	0%	0%	0%	1
0%	0%	50%	0.1%	0%	50%	0%	2
0%	0%	50%	0.1%	0%	50%	0%	3
0%	0%	50%	0.1%	0%	50%	0%	4
25%	12.5%	37.5%	0.1%	0%	50%	0%	5
26.7%	12.5%	34.3%	0.1%	0%	53.1%	0%	6
37%	15.6%	26.5%	0.1%	1.6%	54.6%	1.6%	7
40.8%	15.6%	22.6%	0.1%	2.3%	57%	2.3%	8
49.4%	17.2%	17.6%	0.1%	3.5%	58.1%	3.5%	9
53.3%	17.2%	15%	0.1%	4.1%	59.5%	4.1%	10
59.5%	18%	12.2%	0.1%	4.8%	60.2%	4.8%	11
62.5%	18%	10.8%	0.1%	5.1%	60.9%	5.1%	12

Compiler

Compiled 19 to 16 computations (15.8% saved)

sample3.2s (21%)

Results

1.6s	8256×	body	256	valid
919.0ms	1289×	body	1024	invalid
205.0ms	666×	body	512	invalid
194.0ms	1627×	body	256	invalid
169.0ms	468×	body	256	infinite
59.0ms	243×	body	256	unsamplable

Bogosity

preprocess399.0ms (2.6%)

Algorithm

2×	egg-herbie

Rules

11732×	`rational.json-simplify-41`
1774×	`rational.json-simplify-1`
664×	`rational.json-simplify-35`
26×	`rational.json-simplify-2`
8×	`rational.json-simplify-43`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	98
1	40	98
2	58	98
3	84	98
4	118	98
5	212	98
6	472	98
7	616	98
8	626	98
9	636	98
10	646	98
11	656	98
12	1858	98
13	1868	98
14	1878	98
15	1888	98
16	1898	98
17	1908	98
18	2554	98
19	2564	98
20	2574	98
21	2584	98
22	2594	98
23	2604	98
24	2614	98
25	2624	98
26	2634	98
27	2644	98
28	2654	98
29	2664	98
30	2674	98
31	2684	98
32	2694	98
33	2704	98
34	2714	98
35	2724	98
36	2734	98
37	2744	98
38	2754	98
39	2764	98
40	2774	98
41	2784	98
42	2794	98
43	2804	98
44	2814	98
45	2824	98
46	2834	98
47	2844	98
48	2854	98
49	2864	98
50	2874	98
51	2884	98
52	2894	98
53	2904	98
54	2914	98
55	2924	98
56	2934	98
57	2944	98
58	2954	98
59	2964	98
60	2974	98
61	2984	98
62	2994	98
63	3004	98
64	3014	98
65	3024	98
66	3034	98
67	3044	98
68	3054	98
69	3064	98
70	3074	98
71	3084	98
72	3094	98
73	3104	98
74	3114	98
75	3124	98
76	3134	98
77	3144	98
78	3154	98
79	3164	98
80	3174	98
81	3184	98
82	3194	98
0	2	2

Stop Event

1×	saturated
1×	node limit

Calls

Call 1

Inputs
0
1

Outputs
0
1

Call 2

Inputs
(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
(.f64 (/.f64 1 (sqrt.f64 n)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) k) (/.f64 (-.f64 1 n) 2)))

Outputs
(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2)))
(.f64 (/.f64 1 (sqrt.f64 n)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) k) (/.f64 (-.f64 1 n) 2)))
(.f64 (/.f64 1 (sqrt.f64 n)) (pow.f64 (.f64 k (*.f64 2 (PI.f64))) (/.f64 (-.f64 1 n) 2)))
(.f64 (/.f64 1 (sqrt.f64 n)) (pow.f64 (.f64 2 (*.f64 (PI.f64) k)) (/.f64 (-.f64 1 n) 2)))
(.f64 (/.f64 1 (sqrt.f64 n)) (pow.f64 (.f64 2 (*.f64 k (PI.f64))) (/.f64 (-.f64 1 n) 2)))

Compiler

Compiled 20 to 17 computations (15% saved)

simplify3.9s (25.9%)

Algorithm

1×	egg-herbie

Rules

26690×	`rational.json-simplify-41`
2366×	`rational.json-simplify-1`
1296×	`rational.json-simplify-35`
14×	`rational.json-simplify-2`
4×	`rational.json-simplify-43`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	49
1	27	49
2	37	49
3	51	49
4	69	49
5	115	49
6	242	49
7	630	49
8	799	49
9	805	49
10	811	49
11	817	49
12	823	49
13	829	49
14	835	49
15	841	49
16	847	49
17	853	49
18	859	49
19	865	49
20	871	49
21	877	49
22	883	49
23	2765	49
24	2771	49
25	2777	49
26	2783	49
27	2789	49
28	2795	49
29	3620	49
30	3626	49
31	3632	49
32	3638	49
33	3644	49
34	3650	49
35	3656	49
36	3662	49
37	3668	49
38	3674	49
39	3680	49
40	3686	49
41	3692	49
42	3698	49
43	3704	49
44	3710	49
45	3716	49
46	3722	49
47	3728	49
48	3734	49
49	3740	49
50	3746	49
51	3752	49
52	3758	49
53	3764	49
54	3770	49
55	3776	49
56	3782	49
57	3788	49
58	3794	49
59	3800	49
60	3806	49
61	3812	49
62	3818	49
63	3824	49
64	3830	49
65	3836	49
66	3842	49
67	3848	49
68	3854	49
69	3860	49
70	3866	49
71	3872	49
72	3878	49
73	3884	49
74	3890	49
75	3896	49
76	3902	49
77	3908	49
78	3914	49
79	3920	49
80	3926	49
81	3932	49
82	3938	49
83	3944	49
84	3950	49
85	3956	49
86	3962	49
87	3968	49
88	3974	49
89	3980	49
90	3986	49
91	3992	49
92	3998	49
93	4004	49
94	4010	49
95	4016	49
96	4022	49
97	4028	49
98	4034	49
99	4040	49
100	4046	49
101	4052	49
102	4058	49
103	4064	49
104	4070	49
105	4076	49
106	4082	49
107	4088	49
108	4094	49
109	4100	49
110	4106	49
111	4112	49
112	4118	49
113	4124	49
114	4130	49
115	4136	49
116	4142	49
117	4148	49
118	4154	49
119	4160	49
120	4166	49
121	4172	49
122	4178	49
123	4184	49
124	4190	49
125	4196	49
126	4202	49
127	4208	49
128	4214	49
129	4220	49
130	4226	49
131	4232	49
132	4238	49
133	4244	49
134	4250	49
135	4256	49
136	4262	49
137	4268	49
138	4274	49
139	4280	49
140	4286	49
141	4292	49
142	4298	49
143	4304	49
144	4310	49
145	4316	49
146	4322	49
147	4328	49
148	4334	49
149	4340	49
150	4346	49
151	4352	49
152	4358	49
153	4364	49
154	4370	49
155	4376	49
156	4382	49
157	4388	49
158	4394	49
159	4400	49
160	4406	49
161	4412	49
162	4418	49
163	4424	49
164	4430	49
165	4436	49
166	4442	49
167	4448	49
168	4454	49
169	4460	49
170	4466	49
171	4472	49
172	4478	49
173	4484	49
174	4490	49
175	4496	49
176	4502	49
177	4508	49
178	4514	49
179	4520	49
180	4526	49
181	4532	49
182	4538	49
183	4544	49
184	4550	49
185	4556	49
186	4562	49
187	4568	49
188	4574	49
189	4580	49
190	4586	49
191	4592	49
192	4598	49
193	4604	49
194	4610	49
195	4616	49
196	4622	49
197	4628	49
198	4634	49
199	4640	49
200	4646	49
201	4652	49
202	4658	49
203	4664	49
204	4670	49
205	4676	49
206	4682	49
207	4688	49
208	4694	49
209	4700	49
210	4706	49
211	4712	49
212	4718	49
213	4724	49
214	4730	49
215	4736	49
216	4742	49
217	4748	49
218	4754	49
219	4760	49
220	4766	49
221	4772	49
222	4778	49
223	4784	49
224	4790	49
225	4796	49
226	4802	49
227	4808	49
228	4814	49
229	4820	49
230	4826	49
231	4832	49
232	4838	49
233	4844	49
234	4850	49
235	4856	49
236	4862	49
237	4868	49
238	4874	49
239	4880	49
240	4886	49
241	4892	49
242	4898	49
243	4904	49
244	4910	49
245	4916	49
246	4922	49
247	4928	49
248	4934	49
249	4940	49
250	4946	49
251	4952	49
252	4958	49
253	4964	49
254	4970	49
255	4976	49
256	4982	49
257	4988	49
258	4994	49
259	5000	49
260	5006	49
261	5012	49
262	5018	49
263	5024	49
264	5030	49
265	5036	49
266	5042	49
267	5048	49
268	5054	49
269	5060	49
270	5066	49
271	5072	49
272	5078	49
273	5084	49
274	5090	49
275	5096	49
276	5102	49
277	5108	49
278	5114	49
279	5120	49
280	5126	49
281	5132	49
282	5138	49
283	5144	49
284	5150	49
285	5156	49
286	5162	49
287	5168	49
288	5174	49
289	5180	49
290	5186	49
291	5192	49
292	5198	49
293	5204	49
294	5210	49
295	5216	49
296	5222	49
297	5228	49
298	5234	49
299	5240	49
300	5246	49
301	5252	49
302	5258	49
303	5264	49
304	5270	49
305	5276	49
306	5282	49
307	5288	49
308	5294	49
309	5300	49
310	5306	49
311	5312	49
312	5318	49
313	5324	49
314	5330	49
315	5336	49
316	5342	49
317	5348	49
318	5354	49
319	5360	49
320	5366	49
321	5372	49
322	5378	49
323	5384	49

Stop Event

1×	node limit

Counts

1 → 2

Calls

Call 1

Inputs
(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))

Outputs
(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2)))

eval1.0ms (0%)

Compiler: Compiled 34 to 26 computations (23.5% saved)

prune1.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	2	3

Error

0.4b

Counts

3 → 1

Alt Table

Click to see full alt table

Status	Error	Program
▶	0.4b	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))

Compiler

Compiled 18 to 15 computations (16.7% saved)

localize26.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (.f64 2 (PI.f64)) n)
✓	0.3b	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
✓	0.3b	(pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))
✓	0.3b	(/.f64 1 (sqrt.f64 k))

Compiler

Compiled 56 to 38 computations (32.1% saved)

series99.0ms (0.7%)

Counts

4 → 48

Calls

18 calls:

Time	Variable		Point	Expression
47.0ms	n	@	0	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
23.0ms	n	@	0	(pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))
16.0ms	n	@	-inf	(pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))
6.0ms	n	@	inf	(pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))
1.0ms	k	@	0	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))

rewrite127.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

1588×	`bool.json-1`
1588×	`bool.json-2`
1542×	`rational.json-1`
1542×	`rational.json-2`
1542×	`rational.json-3`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	17	108
1	171	102
2	429	102
3	881	102
4	1945	102
5	5102	102

Stop Event

1×	node limit

Counts

4 → 99

Calls

Call 1

Inputs
(/.f64 1 (sqrt.f64 k))
(pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))
(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
(.f64 (.f64 2 (PI.f64)) n)

Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 1 (sqrt.f64 k)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 1 (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 1 (sqrt.f64 k)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (/.f64 1 (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 k) (/.f64 1 (.f64 (sqrt.f64 k) (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1 (sqrt.f64 k)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 2 (/.f64 1/2 (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 4 (/.f64 (/.f64 1 (sqrt.f64 k)) 4))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (sqrt.f64 k) 2) (/.f64 1/2 (.f64 (sqrt.f64 k) (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (sqrt.f64 k) 2) (/.f64 1 (.f64 2 (.f64 (sqrt.f64 k) (sqrt.f64 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 2 (sqrt.f64 k)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1/2 (/.f64 2 (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (/.f64 1 (sqrt.f64 k)) 4) 1/4)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1/4 (.f64 (/.f64 1 (sqrt.f64 k)) 4))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1/2 (sqrt.f64 k)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1 (.f64 (sqrt.f64 k) (sqrt.f64 k))) (sqrt.f64 k))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 2 (.f64 (sqrt.f64 k) (sqrt.f64 k))) (.f64 (sqrt.f64 k) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (sqrt.f64 k) 1/2) (/.f64 2 (.f64 (sqrt.f64 k) (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x not (not (/.f64 1 (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x and (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x or (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 2 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 4 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)) 4))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 2 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2))) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1/2 (.f64 2 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)) 4) 1/4)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)) 1/2) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 2 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)) 4) 4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 2 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)) 4)) 8)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (.f64 2 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)) 4)) (.f64 2 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)) 4))) 16)))) (#(struct:change #<rule egg-rr> (2) ((x not (not (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x and (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x or (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2)))))))
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((#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (PI.f64) (+.f64 n n)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (.f64 (PI.f64) (+.f64 n n)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (PI.f64) n) (.f64 (PI.f64) n))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (.f64 (PI.f64) (+.f64 n n)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (PI.f64) (+.f64 n n)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (PI.f64) (.f64 n 4)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 n (.f64 (PI.f64) 8)) 4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 2 (.f64 n (.f64 (PI.f64) 8))) 8)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (.f64 2 (.f64 n (.f64 (PI.f64) 8))) (.f64 2 (.f64 n (.f64 (PI.f64) 8)))) 16)))) (#(struct:change #<rule egg-rr> (2) ((x not (not (.f64 (PI.f64) (+.f64 n n))))))) (#(struct:change #<rule egg-rr> (2) ((x and (.f64 (PI.f64) (+.f64 n n)) (.f64 (PI.f64) (+.f64 n n)))))) (#(struct:change #<rule egg-rr> (2) ((x or (.f64 (PI.f64) (+.f64 n n)) (.f64 (PI.f64) (+.f64 n n)))))))

simplify193.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

2246×	`rational.json-simplify-35`
1104×	`rational.json-simplify-2`
658×	`rational.json-simplify-59`
642×	`rational.json-simplify-41`
498×	`rational.json-simplify-53`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	275	5829
1	730	5797
2	2299	5743
3	3975	5743
4	7408	5743

Stop Event

1×	node limit

Counts

147 → 150

Calls

Call 1

Inputs
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
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(/.f64 (+.f64 (.f64 2 (.f64 n (.f64 (PI.f64) 8))) (.f64 2 (.f64 n (.f64 (PI.f64) 8)))) 16)

Outputs
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(exp.f64 (.f64 (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))) (*.f64 1/2 (-.f64 1 k))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(exp.f64 (.f64 (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))) (*.f64 1/2 (-.f64 1 k))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(exp.f64 (.f64 (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))) (*.f64 1/2 (-.f64 1 k))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(exp.f64 (.f64 (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))) (*.f64 1/2 (-.f64 1 k))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (.f64 -1 (log.f64 (/.f64 1 n)))))))
(exp.f64 (.f64 (-.f64 1 k) (.f64 1/2 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (.f64 -1 (log.f64 (/.f64 1 n)))))))
(exp.f64 (.f64 (-.f64 1 k) (.f64 1/2 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (.f64 -1 (log.f64 (/.f64 1 n)))))))
(exp.f64 (.f64 (-.f64 1 k) (.f64 1/2 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))))))
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(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 (PI.f64) -2))))))
(exp.f64 (.f64 (-.f64 1 k) (.f64 1/2 (+.f64 (neg.f64 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 (PI.f64) -2))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (neg.f64 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 (PI.f64) -2))))))
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(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 (PI.f64) -2))))))
(exp.f64 (.f64 (-.f64 1 k) (.f64 1/2 (+.f64 (neg.f64 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 (PI.f64) -2))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (neg.f64 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 (PI.f64) -2))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 (PI.f64) -2))))))
(exp.f64 (.f64 (-.f64 1 k) (.f64 1/2 (+.f64 (neg.f64 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 (PI.f64) -2))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (neg.f64 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 (PI.f64) -2))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64)))))))
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(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2))) (.f64 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2))) (/.f64 (sqrt.f64 k) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2)))))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (.f64 (sqrt.f64 k) (/.f64 2 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)))) (.f64 (.f64 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2))) (/.f64 (sqrt.f64 k) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2)))) 2))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (.f64 2 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)) 4)) (*.f64 (sqrt.f64 k) 8))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (.f64 2 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)) 4)) (*.f64 8 (sqrt.f64 k)))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (.f64 2 (.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k)) 4)) 8)
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (.f64 2 (neg.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)))) (.f64 (sqrt.f64 k) -2))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2)) (/.f64 1/2 (sqrt.f64 k))) 1/2)
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)) 1/2) (.f64 (sqrt.f64 k) 1/2))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (neg.f64 (.f64 2 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)))) (.f64 (sqrt.f64 k) -2))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (neg.f64 (.f64 2 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)))) (neg.f64 (.f64 (sqrt.f64 k) 2)))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (neg.f64 (neg.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (+.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)) (/.f64 1/2 (sqrt.f64 k))) (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)) (/.f64 1/2 (sqrt.f64 k)))) 1)
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (+.f64 (.f64 2 (.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k)) 4)) (.f64 2 (.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k)) 4))) 16)
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (+.f64 (.f64 2 (neg.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)))) (.f64 2 (neg.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2))))) (.f64 2 (.f64 (sqrt.f64 k) -2)))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (+.f64 (neg.f64 (.f64 2 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)))) (neg.f64 (.f64 2 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2))))) (.f64 2 (neg.f64 (.f64 (sqrt.f64 k) 2))))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (+.f64 (neg.f64 (neg.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)))) (neg.f64 (neg.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2))))) (*.f64 (sqrt.f64 k) 2))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (/.f64 (neg.f64 (neg.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)))) 2) (*.f64 (sqrt.f64 k) 1/2))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (/.f64 (.f64 2 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)) 4)) (sqrt.f64 k)) 8)
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)) (neg.f64 (sqrt.f64 k))) -1)
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)) 1/2) (*.f64 (sqrt.f64 k) 2))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (/.f64 (neg.f64 (neg.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)))) 1/2) (*.f64 (sqrt.f64 k) 2))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)) (*.f64 (sqrt.f64 k) 4)) 1/4)
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (/.f64 (neg.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2))) (sqrt.f64 k)) -1)
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (/.f64 (neg.f64 (neg.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)))) (*.f64 (sqrt.f64 k) 4)) 1/4)
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (neg.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)) 4)) (neg.f64 (.f64 (sqrt.f64 k) 4)))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (neg.f64 (.f64 2 (neg.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2))))) (-.f64 0 (.f64 (sqrt.f64 k) -2)))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (neg.f64 (neg.f64 (.f64 2 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2))))) (.f64 (sqrt.f64 k) 2))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (neg.f64 (neg.f64 (.f64 2 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2))))) (-.f64 0 (neg.f64 (.f64 (sqrt.f64 k) 2))))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (neg.f64 (neg.f64 (neg.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2))))) (neg.f64 (sqrt.f64 k)))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(+.f64 (*.f64 (PI.f64) (+.f64 n n)) 0)
(.f64 n (.f64 2 (PI.f64)))
(+.f64 0 (*.f64 (PI.f64) (+.f64 n n)))
(.f64 n (.f64 2 (PI.f64)))
(+.f64 (.f64 (PI.f64) n) (.f64 (PI.f64) n))
(.f64 n (.f64 2 (PI.f64)))
(-.f64 (*.f64 (PI.f64) (+.f64 n n)) 0)
(.f64 n (.f64 2 (PI.f64)))
(/.f64 (*.f64 (PI.f64) (+.f64 n n)) 1)
(.f64 n (.f64 2 (PI.f64)))
(/.f64 (.f64 (PI.f64) (.f64 n 4)) 2)
(.f64 n (.f64 2 (PI.f64)))
(/.f64 (.f64 n (.f64 (PI.f64) 8)) 4)
(.f64 n (.f64 2 (PI.f64)))
(/.f64 (.f64 2 (.f64 n (*.f64 (PI.f64) 8))) 8)
(.f64 (.f64 n (*.f64 (PI.f64) 8)) 1/4)
(.f64 1/4 (.f64 (PI.f64) (*.f64 n 8)))
(.f64 1/4 (.f64 n (*.f64 (PI.f64) 8)))
(/.f64 (+.f64 (.f64 2 (.f64 n (.f64 (PI.f64) 8))) (.f64 2 (.f64 n (.f64 (PI.f64) 8)))) 16)
(.f64 (.f64 n (*.f64 (PI.f64) 8)) 1/4)
(.f64 1/4 (.f64 (PI.f64) (*.f64 n 8)))
(.f64 1/4 (.f64 n (*.f64 (PI.f64) 8)))

eval113.0ms (0.7%)

Compiler: Compiled 3470 to 2190 computations (36.9% saved)

prune35.0ms (0.2%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	139	11	150
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	139	12	151

Error

0.1b

Counts

151 → 12

Alt Table

Click to see full alt table

Status	Error	Program
▶	0.4b	(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k))
	33.2b	(/.f64 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2))) (.f64 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2))) (/.f64 (sqrt.f64 k) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2)))))
▶	0.5b	(/.f64 (/.f64 2 (sqrt.f64 k)) (/.f64 2 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2))))
	33.2b	(/.f64 (.f64 (sqrt.f64 k) (/.f64 2 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)))) (.f64 (.f64 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2))) (/.f64 (sqrt.f64 k) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2)))) 2))
	0.4b	(/.f64 2 (.f64 (sqrt.f64 k) (/.f64 2 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2)))))
▶	0.4b	(/.f64 1 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2))))
✓	0.4b	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
	24.0b	(.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 -1/2 (.f64 k (.f64 (sqrt.f64 2) (log.f64 (.f64 n (.f64 2 (PI.f64)))))))) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (.f64 1/8 (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 2) (pow.f64 (log.f64 (.f64 n (*.f64 2 (PI.f64)))) 2))))))))
▶	23.9b	(.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (.f64 -1/2 (.f64 k (.f64 (sqrt.f64 2) (log.f64 (.f64 n (.f64 2 (PI.f64))))))))))
	23.9b	(.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))))
▶	3.0b	(.f64 (/.f64 1 (sqrt.f64 k)) (exp.f64 (.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) (*.f64 1/2 (-.f64 1 k)))))
	0.5b	(.f64 (.f64 (/.f64 1 (.f64 (sqrt.f64 k) (sqrt.f64 k))) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))

Compiler

Compiled 632 to 459 computations (27.4% saved)

localize21.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k))
✓	0.2b	(*.f64 (PI.f64) (+.f64 n n))
✓	0.3b	(pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2))

Compiler

Compiled 50 to 25 computations (50% saved)

series3.0ms (0%)

Counts

3 → 48

Calls

15 calls:

Time	Variable		Point	Expression
0.0ms	k	@	-inf	(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k))
0.0ms	k	@	0	(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k))
0.0ms	k	@	inf	(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k))
0.0ms	k	@	0	(pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2))
0.0ms	n	@	0	(pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2))

rewrite110.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

1010×	`rational.json-simplify-50`
940×	`rational.json-simplify-53`
744×	`rational.json-simplify-35`
734×	`rational.json-simplify-1`
638×	`bool.json-1`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	91
1	159	91
2	413	91
3	862	91
4	1963	91
5	5731	91

Stop Event

1×	node limit

Counts

3 → 89

Calls

Call 1

Inputs
(pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2))
(*.f64 (PI.f64) (+.f64 n n))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k))

Outputs
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Outputs

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((#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (PI.f64) (+.f64 n n)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 (PI.f64) (+.f64 n n)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (PI.f64) n) (*.f64 (PI.f64) n))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (*.f64 (PI.f64) (+.f64 n n)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (PI.f64) (+.f64 n n)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (PI.f64) (*.f64 n 4)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (*.f64 (PI.f64) n) 8) 4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 (*.f64 (PI.f64) n) 8)) 8)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 2 (*.f64 (*.f64 (PI.f64) n) 8))) 16)))) (#(struct:change #<rule egg-rr> (2) ((x not (not (*.f64 (PI.f64) (+.f64 n n))))))) (#(struct:change #<rule egg-rr> (2) ((x and (*.f64 (PI.f64) (+.f64 n n)) (*.f64 (PI.f64) (+.f64 n n)))))) (#(struct:change #<rule egg-rr> (2) ((x or (*.f64 (PI.f64) (+.f64 n n)) (*.f64 (PI.f64) (+.f64 n n)))))))

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simplify260.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

1452×	`rational.json-simplify-51`
962×	`rational.json-simplify-44`
956×	`rational.json-simplify-2`
864×	`rational.json-simplify-1`
824×	`rational.json-simplify-46`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	247	5769
1	552	5737
2	1456	5683
3	4790	5647
4	7445	5647

Stop Event

1×	node limit

Counts

137 → 141

Calls

Call 1

Inputs
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))))))
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(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64)))))))
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(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (.f64 n (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (.f64 n (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (.f64 n (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (.f64 n (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (+.f64 1 (.f64 -1 k)) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (+.f64 1 (.f64 -1 k)) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))
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(.f64 2 (.f64 n (PI.f64)))
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(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))))
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(.f64 2 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)) 1/2))
(.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)) 4) 1/4)
(.f64 (neg.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2))) -1)
(.f64 -1 (neg.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2))))
(.f64 1/4 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)) 4))
(.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2)) 2) 2)
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)) 1)
(/.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2)) 2) 2)
(/.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2)) 4) 4)
(/.f64 (neg.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2))) -1)
(/.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2)) 8) 8)
(/.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2)) -2) -2)
(/.f64 (.f64 2 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)) 8)) 16)
(/.f64 (neg.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2)) 4)) -4)
(/.f64 (neg.f64 (neg.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2)) 4))) 4)
(neg.f64 (neg.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2))))
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(/.f64 (.f64 2 (.f64 2 (.f64 (.f64 (PI.f64) n) 8))) 16)
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(+.f64 -1 (-.f64 1 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)) (neg.f64 (sqrt.f64 k)))))
(+.f64 (/.f64 1/2 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)))) (/.f64 1/2 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)))))
(-.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k)) 0)
(-.f64 0 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)) (neg.f64 (sqrt.f64 k))))
(.f64 1 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k)))
(.f64 1/2 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)) (/.f64 2 (sqrt.f64 k))))
(.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2)) (/.f64 1 (sqrt.f64 k)))
(.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)) (.f64 (*.f64 2 (/.f64 1 (sqrt.f64 k))) 1/2))
(.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)) (.f64 (/.f64 2 (sqrt.f64 k)) 1/2))
(.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k)) 1)
(.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)) 2) (/.f64 1/2 (sqrt.f64 k)))
(.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)) 2) (*.f64 1/2 (/.f64 1 (sqrt.f64 k))))
(.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)) 2) (.f64 (.f64 1/2 (/.f64 1 (sqrt.f64 k))) 1))
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(.f64 2 (.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)) 2) (/.f64 1 (sqrt.f64 k))))
(.f64 2 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)) (/.f64 1/2 (sqrt.f64 k))))
(.f64 2 (.f64 (/.f64 1/2 (sqrt.f64 k)) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2))))
(.f64 2 (.f64 (.f64 1/2 (/.f64 1 (sqrt.f64 k))) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2))))
(.f64 2 (.f64 (/.f64 1/2 (.f64 (sqrt.f64 k) 2)) (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)) 2)))
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(.f64 4 (.f64 (.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2)) 2) 1) (/.f64 1/2 (sqrt.f64 k))))
(.f64 4 (.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2)) 1/2) (/.f64 1/2 (sqrt.f64 k))))
(.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)) (/.f64 2 (sqrt.f64 k))) 1/2)
(.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)) 4) (/.f64 1/2 (*.f64 (sqrt.f64 k) 2)))
(.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)) 4) (.f64 (/.f64 1/2 (.f64 (sqrt.f64 k) 2)) 1))
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(.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)) 4) (*.f64 1/2 (/.f64 1/2 (sqrt.f64 k))))
(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2)))
(.f64 (neg.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2))) (/.f64 -1 (sqrt.f64 k)))
(.f64 (neg.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2))) (.f64 (/.f64 -1 (sqrt.f64 k)) 1))
(.f64 -1 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2)) (neg.f64 (sqrt.f64 k))))
(.f64 -1 (.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)) (neg.f64 (sqrt.f64 k))) 1))
(.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)) 8) (*.f64 1/4 (/.f64 1/2 (sqrt.f64 k))))
(.f64 (/.f64 1/2 (sqrt.f64 k)) (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)) 2))
(.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)) -2) (*.f64 -1 (/.f64 1/2 (sqrt.f64 k))))
(.f64 -2 (.f64 (neg.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2))) (/.f64 1/2 (sqrt.f64 k))))
(.f64 (.f64 2 (/.f64 1 (sqrt.f64 k))) (.f64 1/2 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2))))
(.f64 (.f64 1/2 (/.f64 1 (sqrt.f64 k))) (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2)) 2))
(.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2)) (neg.f64 (sqrt.f64 k))) -1)
(.f64 (/.f64 1/2 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2)))) 2)
(.f64 (/.f64 1/2 (.f64 (sqrt.f64 k) 2)) (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2)) 4))
(.f64 (/.f64 -1 (sqrt.f64 k)) (neg.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2))))
(.f64 (+.f64 (.f64 1/2 (/.f64 1 (sqrt.f64 k))) (.f64 1/2 (/.f64 1 (sqrt.f64 k)))) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2)))
(.f64 (+.f64 (/.f64 1/2 (.f64 (sqrt.f64 k) 2)) (/.f64 1/2 (.f64 (sqrt.f64 k) 2))) (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)) 2))
(neg.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)) (neg.f64 (sqrt.f64 k))))
(neg.f64 (/.f64 (/.f64 (sqrt.f64 k) (neg.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)))) (.f64 (sqrt.f64 k) (/.f64 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2))) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2))))))
(neg.f64 (/.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)) -2) (.f64 (sqrt.f64 k) 2)))

Outputs
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(exp.f64 (.f64 (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))) (*.f64 1/2 (-.f64 1 k))))
(exp.f64 (.f64 (-.f64 1 k) (.f64 1/2 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(exp.f64 (.f64 (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))) (*.f64 1/2 (-.f64 1 k))))
(exp.f64 (.f64 (-.f64 1 k) (.f64 1/2 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(exp.f64 (.f64 (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))) (*.f64 1/2 (-.f64 1 k))))
(exp.f64 (.f64 (-.f64 1 k) (.f64 1/2 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(exp.f64 (.f64 (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))) (*.f64 1/2 (-.f64 1 k))))
(exp.f64 (.f64 (-.f64 1 k) (.f64 1/2 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))))))
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(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)) 2) (.f64 (.f64 1/2 (/.f64 1 (sqrt.f64 k))) 1))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(.f64 2 (/.f64 1/2 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2)))))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(.f64 2 (.f64 (/.f64 1/2 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)))) 1))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(.f64 2 (.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k)) 1/2))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(.f64 2 (.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)) 2) (/.f64 1 (sqrt.f64 k))))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(.f64 2 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)) (/.f64 1/2 (sqrt.f64 k))))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(.f64 2 (.f64 (/.f64 1/2 (sqrt.f64 k)) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2))))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(.f64 2 (.f64 (.f64 1/2 (/.f64 1 (sqrt.f64 k))) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2))))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(.f64 2 (.f64 (/.f64 1/2 (.f64 (sqrt.f64 k) 2)) (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)) 2)))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(.f64 4 (.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)) 2) (/.f64 1/2 (sqrt.f64 k))))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(.f64 4 (.f64 (.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2)) 2) 1) (/.f64 1/2 (sqrt.f64 k))))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(.f64 4 (.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2)) 1/2) (/.f64 1/2 (sqrt.f64 k))))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)) (/.f64 2 (sqrt.f64 k))) 1/2)
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)) 4) (/.f64 1/2 (*.f64 (sqrt.f64 k) 2)))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)) 4) (.f64 (/.f64 1/2 (.f64 (sqrt.f64 k) 2)) 1))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)) 4) (*.f64 1/4 (/.f64 1 (sqrt.f64 k))))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)) 4) (*.f64 1/2 (/.f64 1/2 (sqrt.f64 k))))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2)))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(.f64 (neg.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2))) (/.f64 -1 (sqrt.f64 k)))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(.f64 (neg.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2))) (.f64 (/.f64 -1 (sqrt.f64 k)) 1))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(.f64 -1 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2)) (neg.f64 (sqrt.f64 k))))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(.f64 -1 (.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)) (neg.f64 (sqrt.f64 k))) 1))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)) 8) (*.f64 1/4 (/.f64 1/2 (sqrt.f64 k))))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(.f64 (/.f64 1/2 (sqrt.f64 k)) (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)) 2))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)) -2) (*.f64 -1 (/.f64 1/2 (sqrt.f64 k))))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(.f64 -2 (.f64 (neg.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2))) (/.f64 1/2 (sqrt.f64 k))))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(.f64 (.f64 2 (/.f64 1 (sqrt.f64 k))) (.f64 1/2 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2))))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(.f64 (.f64 1/2 (/.f64 1 (sqrt.f64 k))) (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2)) 2))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2)) (neg.f64 (sqrt.f64 k))) -1)
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(.f64 (/.f64 1/2 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2)))) 2)
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(.f64 (/.f64 1/2 (.f64 (sqrt.f64 k) 2)) (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2)) 4))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(.f64 (/.f64 -1 (sqrt.f64 k)) (neg.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2))))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(.f64 (+.f64 (.f64 1/2 (/.f64 1 (sqrt.f64 k))) (.f64 1/2 (/.f64 1 (sqrt.f64 k)))) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2)))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(.f64 (+.f64 (/.f64 1/2 (.f64 (sqrt.f64 k) 2)) (/.f64 1/2 (.f64 (sqrt.f64 k) 2))) (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)) 2))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(neg.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)) (neg.f64 (sqrt.f64 k))))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(neg.f64 (/.f64 (/.f64 (sqrt.f64 k) (neg.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)))) (.f64 (sqrt.f64 k) (/.f64 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2))) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2))))))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(neg.f64 (/.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)) -2) (.f64 (sqrt.f64 k) 2)))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))

localize89.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 1 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2))))
✓	0.2b	(/.f64 (sqrt.f64 k) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)))
	0.2b	(*.f64 (PI.f64) (+.f64 n n))
	0.3b	(pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2))

Compiler

Compiled 66 to 33 computations (50% saved)

series9.0ms (0.1%)

Counts

2 → 24

Calls

12 calls:

Time	Variable		Point	Expression
3.0ms	k	@	0	(/.f64 (sqrt.f64 k) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)))
1.0ms	n	@	0	(/.f64 (sqrt.f64 k) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)))
1.0ms	k	@	-inf	(/.f64 (sqrt.f64 k) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)))
1.0ms	n	@	inf	(/.f64 (sqrt.f64 k) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)))
1.0ms	n	@	-inf	(/.f64 (sqrt.f64 k) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)))

rewrite98.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

2084×	`bool.json-1`
2084×	`bool.json-2`
1612×	`bool.json-3`
1002×	`rational.json-simplify-35`
812×	`rational.json-simplify-46`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	86
1	172	86
2	456	86
3	1008	86
4	2428	86
5	6464	86

Stop Event

1×	node limit

Counts

2 → 58

Calls

Call 1

Inputs
(/.f64 (sqrt.f64 k) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)))
(/.f64 1 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2))))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 -1 (-.f64 1 (/.f64 (sqrt.f64 k) (neg.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 0 (/.f64 (sqrt.f64 k) (neg.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 k) (/.f64 1 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2))))))) (#(struct:change 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simplify133.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

1818×	`rational.json-simplify-35`
1382×	`rational.json-simplify-2`
1100×	`rational.json-simplify-49`
906×	`rational.json-simplify-1`
780×	`rational.json-simplify-53`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	152	4126
1	286	4094
2	553	4046
3	1567	4046
4	3488	4046
5	5970	4046

Stop Event

1×	node limit

Counts

82 → 88

Calls

Call 1

Inputs
(.f64 (sqrt.f64 k) (/.f64 1 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))))))
(.f64 (sqrt.f64 k) (/.f64 1 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))))))
(.f64 (sqrt.f64 k) (/.f64 1 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))))))
(.f64 (sqrt.f64 k) (/.f64 1 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))))))
(.f64 (sqrt.f64 k) (/.f64 1 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))))))
(.f64 (sqrt.f64 k) (/.f64 1 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))))))
(.f64 (sqrt.f64 k) (/.f64 1 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))))))
(.f64 (sqrt.f64 k) (/.f64 1 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))))))
(.f64 (sqrt.f64 k) (/.f64 1 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))))))
(.f64 (sqrt.f64 k) (/.f64 1 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))))))
(.f64 (sqrt.f64 k) (/.f64 1 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))))))
(.f64 (sqrt.f64 k) (/.f64 1 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))))
(+.f64 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2))) 0)
(+.f64 0 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2))))
(+.f64 -1 (-.f64 1 (/.f64 (sqrt.f64 k) (neg.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2))))))
(-.f64 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2))) 0)
(-.f64 0 (/.f64 (sqrt.f64 k) (neg.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)))))
(.f64 (sqrt.f64 k) (/.f64 1 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2))))
(.f64 1 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2))))
(.f64 1/2 (.f64 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2))) 2))
(.f64 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2))) 1)
(.f64 2 (/.f64 (sqrt.f64 k) (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)) 2)))
(.f64 2 (.f64 (/.f64 1/2 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2))) (sqrt.f64 k)))
(.f64 (.f64 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2))) 2) 1/2)
(.f64 (.f64 (sqrt.f64 k) 2) (/.f64 1/2 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2))))
(.f64 (.f64 (sqrt.f64 k) 2) (.f64 1/2 (/.f64 1 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2)))))
(.f64 (.f64 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2))) 4) 1/4)
(.f64 (.f64 (sqrt.f64 k) 4) (/.f64 1 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2)) 4)))
(.f64 (/.f64 1 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2))) (sqrt.f64 k))
(.f64 (/.f64 1 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2))) (/.f64 -1 (/.f64 -1 (sqrt.f64 k))))
(.f64 -1 (/.f64 (sqrt.f64 k) (neg.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2)))))
(.f64 (/.f64 (sqrt.f64 k) (neg.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2)))) -1)
(.f64 (neg.f64 (sqrt.f64 k)) (/.f64 -1 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2))))
(.f64 (.f64 2 (/.f64 1 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)))) (/.f64 (sqrt.f64 k) 2))
(.f64 (/.f64 1/2 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2))) (.f64 (sqrt.f64 k) 2))
(.f64 (.f64 1/2 (/.f64 1 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)))) (*.f64 (sqrt.f64 k) 2))
(.f64 (/.f64 -1 (/.f64 -1 (sqrt.f64 k))) (/.f64 1 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2))))
(.f64 (/.f64 (sqrt.f64 k) (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)) 2)) 2)
(.f64 1/4 (.f64 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2))) 4))
(.f64 (/.f64 (sqrt.f64 k) 2) (.f64 2 (/.f64 1 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)))))
(.f64 (/.f64 1 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)) 4)) (*.f64 (sqrt.f64 k) 4))
(.f64 (/.f64 -1 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2))) (neg.f64 (sqrt.f64 k)))
(.f64 (+.f64 (/.f64 1/2 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2))) (/.f64 1/2 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2)))) (sqrt.f64 k))
(neg.f64 (/.f64 (sqrt.f64 k) (neg.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)))))
(+.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k)) 0)
(+.f64 0 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k)))
(-.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k)) 0)
(.f64 1 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k)))
(.f64 1/2 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)) (/.f64 2 (sqrt.f64 k))))
(.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2)) (/.f64 1 (sqrt.f64 k)))
(.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k)) 1)
(.f64 2 (/.f64 1/2 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2)))))
(.f64 2 (.f64 (/.f64 1/2 (sqrt.f64 k)) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2))))
(.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)) 2) (/.f64 1/2 (sqrt.f64 k)))
(.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)) 2) (*.f64 1/2 (/.f64 1 (sqrt.f64 k))))
(.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)) (/.f64 2 (sqrt.f64 k))) 1/2)
(.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)) 4) (/.f64 1 (*.f64 (sqrt.f64 k) 4)))
(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2)))
(.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (/.f64 1 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2)))))
(.f64 -1 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2)) (neg.f64 (sqrt.f64 k))))
(.f64 (neg.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2))) (/.f64 -1 (sqrt.f64 k)))
(.f64 (/.f64 1/2 (sqrt.f64 k)) (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)) 2))
(.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2)) (neg.f64 (sqrt.f64 k))) -1)
(.f64 (.f64 1/2 (/.f64 1 (sqrt.f64 k))) (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2)) 2))
(.f64 (/.f64 1 (/.f64 1 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2)))) (/.f64 1 (sqrt.f64 k)))
(.f64 (/.f64 1/2 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2)))) 2)
(.f64 (/.f64 1 (.f64 (sqrt.f64 k) 4)) (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2)) 4))
(.f64 (/.f64 -1 (sqrt.f64 k)) (neg.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2))))
(.f64 (+.f64 (/.f64 1/2 (sqrt.f64 k)) (/.f64 1/2 (sqrt.f64 k))) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2)))
(neg.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)) (neg.f64 (sqrt.f64 k))))

Outputs
(.f64 (sqrt.f64 k) (/.f64 1 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))))))
(.f64 (sqrt.f64 k) (exp.f64 (neg.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))))))
(.f64 (sqrt.f64 k) (exp.f64 (.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))) -1/2)))
(.f64 (sqrt.f64 k) (exp.f64 (.f64 (-.f64 1 k) (.f64 (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))) -1/2))))
(.f64 (sqrt.f64 k) (exp.f64 (.f64 1/2 (.f64 (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))) (-.f64 k 1)))))
(.f64 (sqrt.f64 k) (/.f64 1 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))))))
(.f64 (sqrt.f64 k) (exp.f64 (neg.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))))))
(.f64 (sqrt.f64 k) (exp.f64 (.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))) -1/2)))
(.f64 (sqrt.f64 k) (exp.f64 (.f64 (-.f64 1 k) (.f64 (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))) -1/2))))
(.f64 (sqrt.f64 k) (exp.f64 (.f64 1/2 (.f64 (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))) (-.f64 k 1)))))
(.f64 (sqrt.f64 k) (/.f64 1 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))))))
(.f64 (sqrt.f64 k) (exp.f64 (neg.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))))))
(.f64 (sqrt.f64 k) (exp.f64 (.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))) -1/2)))
(.f64 (sqrt.f64 k) (exp.f64 (.f64 (-.f64 1 k) (.f64 (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))) -1/2))))
(.f64 (sqrt.f64 k) (exp.f64 (.f64 1/2 (.f64 (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))) (-.f64 k 1)))))
(.f64 (sqrt.f64 k) (/.f64 1 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))))))
(.f64 (sqrt.f64 k) (exp.f64 (neg.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))))))
(.f64 (sqrt.f64 k) (exp.f64 (.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))) -1/2)))
(.f64 (sqrt.f64 k) (exp.f64 (.f64 (-.f64 1 k) (.f64 (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))) -1/2))))
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(.f64 (sqrt.f64 k) (/.f64 1 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))))))
(.f64 (sqrt.f64 k) (exp.f64 (neg.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (*.f64 -1 (log.f64 (/.f64 1 n)))))))))
(.f64 (sqrt.f64 k) (exp.f64 (neg.f64 (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n)))) (.f64 1/2 (-.f64 1 k))))))
(.f64 (sqrt.f64 k) (exp.f64 (.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n))))) -1/2)))
(/.f64 (sqrt.f64 k) (exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n)))) (*.f64 1/2 (-.f64 1 k)))))
(.f64 (sqrt.f64 k) (exp.f64 (.f64 (-.f64 1 k) (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n)))) -1/2))))
(.f64 (sqrt.f64 k) (exp.f64 (.f64 1/2 (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n)))) (-.f64 k 1)))))
(.f64 (sqrt.f64 k) (/.f64 1 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))))))
(.f64 (sqrt.f64 k) (exp.f64 (neg.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (*.f64 -1 (log.f64 (/.f64 1 n)))))))))
(.f64 (sqrt.f64 k) (exp.f64 (neg.f64 (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n)))) (.f64 1/2 (-.f64 1 k))))))
(.f64 (sqrt.f64 k) (exp.f64 (.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n))))) -1/2)))
(/.f64 (sqrt.f64 k) (exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n)))) (*.f64 1/2 (-.f64 1 k)))))
(.f64 (sqrt.f64 k) (exp.f64 (.f64 (-.f64 1 k) (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n)))) -1/2))))
(.f64 (sqrt.f64 k) (exp.f64 (.f64 1/2 (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n)))) (-.f64 k 1)))))
(.f64 (sqrt.f64 k) (/.f64 1 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))))))
(.f64 (sqrt.f64 k) (exp.f64 (neg.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (*.f64 -1 (log.f64 (/.f64 1 n)))))))))
(.f64 (sqrt.f64 k) (exp.f64 (neg.f64 (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n)))) (.f64 1/2 (-.f64 1 k))))))
(.f64 (sqrt.f64 k) (exp.f64 (.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n))))) -1/2)))
(/.f64 (sqrt.f64 k) (exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n)))) (*.f64 1/2 (-.f64 1 k)))))
(.f64 (sqrt.f64 k) (exp.f64 (.f64 (-.f64 1 k) (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n)))) -1/2))))
(.f64 (sqrt.f64 k) (exp.f64 (.f64 1/2 (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n)))) (-.f64 k 1)))))
(.f64 (sqrt.f64 k) (/.f64 1 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))))))
(.f64 (sqrt.f64 k) (exp.f64 (neg.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (*.f64 -1 (log.f64 (/.f64 1 n)))))))))
(.f64 (sqrt.f64 k) (exp.f64 (neg.f64 (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n)))) (.f64 1/2 (-.f64 1 k))))))
(.f64 (sqrt.f64 k) (exp.f64 (.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n))))) -1/2)))
(/.f64 (sqrt.f64 k) (exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n)))) (*.f64 1/2 (-.f64 1 k)))))
(.f64 (sqrt.f64 k) (exp.f64 (.f64 (-.f64 1 k) (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n)))) -1/2))))
(.f64 (sqrt.f64 k) (exp.f64 (.f64 1/2 (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n)))) (-.f64 k 1)))))
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(.f64 (sqrt.f64 k) (exp.f64 (.f64 (-.f64 1 k) (.f64 (+.f64 (neg.f64 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 (PI.f64) -2))) -1/2))))
(.f64 (sqrt.f64 k) (exp.f64 (.f64 1/2 (.f64 (+.f64 (neg.f64 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 (PI.f64) -2))) (-.f64 k 1)))))
(.f64 (sqrt.f64 k) (/.f64 1 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))))))
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(.f64 (sqrt.f64 k) (exp.f64 (neg.f64 (.f64 (+.f64 (neg.f64 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 (PI.f64) -2))) (.f64 1/2 (-.f64 1 k))))))
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(.f64 (sqrt.f64 k) (exp.f64 (.f64 (-.f64 1 k) (.f64 (+.f64 (neg.f64 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 (PI.f64) -2))) -1/2))))
(.f64 (sqrt.f64 k) (exp.f64 (.f64 1/2 (.f64 (+.f64 (neg.f64 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 (PI.f64) -2))) (-.f64 k 1)))))
(.f64 (sqrt.f64 k) (/.f64 1 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))))))
(.f64 (sqrt.f64 k) (exp.f64 (neg.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 (PI.f64) -2))))))))
(.f64 (sqrt.f64 k) (exp.f64 (neg.f64 (.f64 (+.f64 (neg.f64 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 (PI.f64) -2))) (.f64 1/2 (-.f64 1 k))))))
(.f64 (sqrt.f64 k) (exp.f64 (.f64 (.f64 (-.f64 1 k) (+.f64 (neg.f64 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 (PI.f64) -2)))) -1/2)))
(.f64 (sqrt.f64 k) (exp.f64 (.f64 (-.f64 1 k) (.f64 (+.f64 (neg.f64 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 (PI.f64) -2))) -1/2))))
(.f64 (sqrt.f64 k) (exp.f64 (.f64 1/2 (.f64 (+.f64 (neg.f64 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 (PI.f64) -2))) (-.f64 k 1)))))
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(.f64 (sqrt.f64 k) (exp.f64 (neg.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 (PI.f64) -2))))))))
(.f64 (sqrt.f64 k) (exp.f64 (neg.f64 (.f64 (+.f64 (neg.f64 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 (PI.f64) -2))) (.f64 1/2 (-.f64 1 k))))))
(.f64 (sqrt.f64 k) (exp.f64 (.f64 (.f64 (-.f64 1 k) (+.f64 (neg.f64 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 (PI.f64) -2)))) -1/2)))
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(.f64 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))))) (sqrt.f64 (/.f64 1 k)))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))))
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(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))))
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(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(.f64 (/.f64 1 (/.f64 1 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2)))) (/.f64 1 (sqrt.f64 k)))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(.f64 (/.f64 1/2 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2)))) 2)
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(.f64 (/.f64 1 (.f64 (sqrt.f64 k) 4)) (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2)) 4))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(.f64 (/.f64 -1 (sqrt.f64 k)) (neg.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2))))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(.f64 (+.f64 (/.f64 1/2 (sqrt.f64 k)) (/.f64 1/2 (sqrt.f64 k))) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2)))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(neg.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)) (neg.f64 (sqrt.f64 k))))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))

localize319.0ms (2.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 (/.f64 2 (sqrt.f64 k)) (/.f64 2 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2))))
	0.2b	(*.f64 (PI.f64) (+.f64 n n))
	0.3b	(pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2))
✓	0.3b	(/.f64 2 (sqrt.f64 k))

Compiler

Compiled 72 to 39 computations (45.8% saved)

series5.0ms (0%)

Counts

2 → 12

Calls

9 calls:

Time	Variable		Point	Expression
2.0ms	n	@	0	(/.f64 (/.f64 2 (sqrt.f64 k)) (/.f64 2 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2))))
0.0ms	k	@	0	(/.f64 (/.f64 2 (sqrt.f64 k)) (/.f64 2 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2))))
0.0ms	k	@	-inf	(/.f64 2 (sqrt.f64 k))
0.0ms	k	@	-inf	(/.f64 (/.f64 2 (sqrt.f64 k)) (/.f64 2 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2))))
0.0ms	k	@	0	(/.f64 2 (sqrt.f64 k))

rewrite78.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

1586×	`bool.json-1`
1586×	`bool.json-2`
1548×	`rational.json-1`
1548×	`rational.json-2`
1548×	`rational.json-3`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	19	66
1	197	54
2	573	54
3	1519	54
4	4899	54

Stop Event

1×	node limit

Counts

2 → 42

Calls

Call 1

Inputs
(/.f64 2 (sqrt.f64 k))
(/.f64 (/.f64 2 (sqrt.f64 k)) (/.f64 2 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2))))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 2 (sqrt.f64 k)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 2 (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 2 (sqrt.f64 k)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 0 (/.f64 -2 (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 2 (/.f64 1 (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 2 (sqrt.f64 k)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 2 (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/2 (/.f64 4 (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 4 (sqrt.f64 k)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 2 (/.f64 4 (sqrt.f64 k))) 1/4)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 -2 (sqrt.f64 k)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (sqrt.f64 k)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -1 (/.f64 -2 (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 -2 (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x not (not (/.f64 2 (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x and (/.f64 2 (sqrt.f64 k)) (/.f64 2 (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x or (/.f64 2 (sqrt.f64 k)) (/.f64 2 (sqrt.f64 k)))))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 2 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)) (*.f64 2 (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 2 (/.f64 (/.f64 2 (sqrt.f64 k)) (/.f64 4 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 2 (/.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 2 (sqrt.f64 k)) (*.f64 1/2 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/2 (*.f64 (/.f64 2 (sqrt.f64 k)) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)) (/.f64 1 (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 2 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2))) (/.f64 1/2 (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 2 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2))) (*.f64 (/.f64 1/2 (sqrt.f64 k)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 4 (sqrt.f64 k)) (/.f64 1 (/.f64 4 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 4 (sqrt.f64 k)) (*.f64 (/.f64 1 (/.f64 4 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 4 (sqrt.f64 k)) (*.f64 1/2 (*.f64 1/2 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)) 4) (/.f64 1 (*.f64 (sqrt.f64 k) 4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 2 (/.f64 4 (sqrt.f64 k))) (/.f64 1 (*.f64 2 (/.f64 4 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 -2 (sqrt.f64 k)) (/.f64 1 (/.f64 -2 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2))) (/.f64 1 (neg.f64 (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 1/2 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2))) (/.f64 2 (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -1 (/.f64 (/.f64 2 (sqrt.f64 k)) (/.f64 -2 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -1 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)) (neg.f64 (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (/.f64 2 (sqrt.f64 k)) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2))) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (/.f64 4 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)))) (/.f64 4 (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1/2 (sqrt.f64 k)) (*.f64 2 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x not (not (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x and (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k)) (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x or (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k)) (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k)))))))

simplify118.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

1282×	`rational.json-simplify-2`
886×	`rational.json-simplify-47`
838×	`rational.json-simplify-44`
794×	`rational.json-simplify-1`
754×	`rational.json-simplify-51`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	122	2154
1	252	2138
2	474	2138
3	1030	2138
4	4013	2138
5	6969	2138

Stop Event

1×	node limit

Counts

54 → 55

Calls

Call 1

Inputs
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))))
(+.f64 (/.f64 2 (sqrt.f64 k)) 0)
(+.f64 0 (/.f64 2 (sqrt.f64 k)))
(+.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))
(-.f64 (/.f64 2 (sqrt.f64 k)) 0)
(-.f64 0 (/.f64 -2 (sqrt.f64 k)))
(*.f64 2 (/.f64 1 (sqrt.f64 k)))
(*.f64 (/.f64 2 (sqrt.f64 k)) 1)
(*.f64 1 (/.f64 2 (sqrt.f64 k)))
(*.f64 1/2 (/.f64 4 (sqrt.f64 k)))
(*.f64 (/.f64 4 (sqrt.f64 k)) 1/2)
(.f64 (.f64 2 (/.f64 4 (sqrt.f64 k))) 1/4)
(*.f64 (/.f64 -2 (sqrt.f64 k)) -1)
(*.f64 (/.f64 1 (sqrt.f64 k)) 2)
(*.f64 -1 (/.f64 -2 (sqrt.f64 k)))
(neg.f64 (/.f64 -2 (sqrt.f64 k)))
(+.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k)) 0)
(+.f64 0 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k)))
(-.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k)) 0)
(.f64 2 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)) (*.f64 2 (sqrt.f64 k))))
(.f64 2 (/.f64 (/.f64 2 (sqrt.f64 k)) (/.f64 4 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)))))
(.f64 2 (/.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k)) 2))
(.f64 (/.f64 2 (sqrt.f64 k)) (.f64 1/2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2))))
(.f64 1 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k)))
(.f64 1/2 (.f64 (/.f64 2 (sqrt.f64 k)) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2))))
(.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)) (/.f64 1 (sqrt.f64 k)))
(.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k)) 1)
(.f64 (.f64 2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2))) (/.f64 1/2 (sqrt.f64 k)))
(.f64 (.f64 2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2))) (.f64 (/.f64 1/2 (sqrt.f64 k)) 1))
(.f64 (/.f64 4 (sqrt.f64 k)) (/.f64 1 (/.f64 4 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)))))
(.f64 (/.f64 4 (sqrt.f64 k)) (.f64 (/.f64 1 (/.f64 4 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)))) 1))
(.f64 (/.f64 4 (sqrt.f64 k)) (.f64 1/2 (.f64 1/2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)))))
(.f64 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)) 4) (/.f64 1 (.f64 (sqrt.f64 k) 4)))
(.f64 (.f64 2 (/.f64 4 (sqrt.f64 k))) (/.f64 1 (.f64 2 (/.f64 4 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2))))))
(.f64 (/.f64 -2 (sqrt.f64 k)) (/.f64 1 (/.f64 -2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)))))
(.f64 (neg.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2))) (/.f64 1 (neg.f64 (sqrt.f64 k))))
(.f64 (.f64 1/2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2))) (/.f64 2 (sqrt.f64 k)))
(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)))
(.f64 -1 (/.f64 (/.f64 2 (sqrt.f64 k)) (/.f64 -2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)))))
(.f64 -1 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)) (neg.f64 (sqrt.f64 k))))
(.f64 (.f64 (/.f64 2 (sqrt.f64 k)) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2))) 1/2)
(.f64 (/.f64 1 (/.f64 4 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)))) (/.f64 4 (sqrt.f64 k)))
(.f64 (/.f64 1/2 (sqrt.f64 k)) (.f64 2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2))))

Outputs
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)) (.f64 1/2 (-.f64 1 k)))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)) (.f64 1/2 (-.f64 1 k)))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)) (.f64 1/2 (-.f64 1 k)))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)) (.f64 1/2 (-.f64 1 k)))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (-.f64 1 k) (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (*.f64 -1 (log.f64 (/.f64 1 n)))) 1/2))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (-.f64 1 k) (.f64 1/2 (+.f64 (log.f64 (.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (-.f64 1 k) (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (*.f64 -1 (log.f64 (/.f64 1 n)))) 1/2))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (-.f64 1 k) (.f64 1/2 (+.f64 (log.f64 (.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (-.f64 1 k) (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (*.f64 -1 (log.f64 (/.f64 1 n)))) 1/2))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (-.f64 1 k) (.f64 1/2 (+.f64 (log.f64 (.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (-.f64 1 k) (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (*.f64 -1 (log.f64 (/.f64 1 n)))) 1/2))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (-.f64 1 k) (.f64 1/2 (+.f64 (log.f64 (.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 (PI.f64) -2)))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 (neg.f64 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 (PI.f64) -2))) (.f64 1/2 (-.f64 1 k)))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (neg.f64 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 (PI.f64) -2)))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 (PI.f64) -2)))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 (neg.f64 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 (PI.f64) -2))) (.f64 1/2 (-.f64 1 k)))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (neg.f64 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 (PI.f64) -2)))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 (PI.f64) -2)))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 (neg.f64 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 (PI.f64) -2))) (.f64 1/2 (-.f64 1 k)))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (neg.f64 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 (PI.f64) -2)))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 (PI.f64) -2)))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 (neg.f64 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 (PI.f64) -2))) (.f64 1/2 (-.f64 1 k)))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (neg.f64 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 (PI.f64) -2)))))))
(+.f64 (/.f64 2 (sqrt.f64 k)) 0)
(/.f64 2 (sqrt.f64 k))
(+.f64 0 (/.f64 2 (sqrt.f64 k)))
(/.f64 2 (sqrt.f64 k))
(+.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))
(/.f64 2 (sqrt.f64 k))
(-.f64 (/.f64 2 (sqrt.f64 k)) 0)
(/.f64 2 (sqrt.f64 k))
(-.f64 0 (/.f64 -2 (sqrt.f64 k)))
(/.f64 2 (sqrt.f64 k))
(*.f64 2 (/.f64 1 (sqrt.f64 k)))
(/.f64 2 (sqrt.f64 k))
(*.f64 (/.f64 2 (sqrt.f64 k)) 1)
(/.f64 2 (sqrt.f64 k))
(*.f64 1 (/.f64 2 (sqrt.f64 k)))
(/.f64 2 (sqrt.f64 k))
(*.f64 1/2 (/.f64 4 (sqrt.f64 k)))
(/.f64 2 (sqrt.f64 k))
(*.f64 (/.f64 4 (sqrt.f64 k)) 1/2)
(/.f64 2 (sqrt.f64 k))
(.f64 (.f64 2 (/.f64 4 (sqrt.f64 k))) 1/4)
(/.f64 2 (sqrt.f64 k))
(*.f64 (/.f64 -2 (sqrt.f64 k)) -1)
(/.f64 2 (sqrt.f64 k))
(*.f64 (/.f64 1 (sqrt.f64 k)) 2)
(/.f64 2 (sqrt.f64 k))
(*.f64 -1 (/.f64 -2 (sqrt.f64 k)))
(/.f64 2 (sqrt.f64 k))
(neg.f64 (/.f64 -2 (sqrt.f64 k)))
(/.f64 2 (sqrt.f64 k))
(+.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k)) 0)
(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(+.f64 0 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k)))
(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(-.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k)) 0)
(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(.f64 2 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)) (*.f64 2 (sqrt.f64 k))))
(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(.f64 2 (/.f64 (/.f64 2 (sqrt.f64 k)) (/.f64 4 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)))))
(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(.f64 2 (/.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k)) 2))
(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(.f64 (/.f64 2 (sqrt.f64 k)) (.f64 1/2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2))))
(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(.f64 1 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k)))
(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(.f64 1/2 (.f64 (/.f64 2 (sqrt.f64 k)) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2))))
(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)) (/.f64 1 (sqrt.f64 k)))
(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k)) 1)
(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(.f64 (.f64 2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2))) (/.f64 1/2 (sqrt.f64 k)))
(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(.f64 (.f64 2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2))) (.f64 (/.f64 1/2 (sqrt.f64 k)) 1))
(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(.f64 (/.f64 4 (sqrt.f64 k)) (/.f64 1 (/.f64 4 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)))))
(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(.f64 (/.f64 4 (sqrt.f64 k)) (.f64 (/.f64 1 (/.f64 4 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)))) 1))
(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(.f64 (/.f64 4 (sqrt.f64 k)) (.f64 1/2 (.f64 1/2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)))))
(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(.f64 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)) 4) (/.f64 1 (.f64 (sqrt.f64 k) 4)))
(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(.f64 (.f64 2 (/.f64 4 (sqrt.f64 k))) (/.f64 1 (.f64 2 (/.f64 4 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2))))))
(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(.f64 (/.f64 -2 (sqrt.f64 k)) (/.f64 1 (/.f64 -2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)))))
(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(.f64 (neg.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2))) (/.f64 1 (neg.f64 (sqrt.f64 k))))
(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(.f64 (.f64 1/2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2))) (/.f64 2 (sqrt.f64 k)))
(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)))
(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(.f64 -1 (/.f64 (/.f64 2 (sqrt.f64 k)) (/.f64 -2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)))))
(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(.f64 -1 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)) (neg.f64 (sqrt.f64 k))))
(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(.f64 (.f64 (/.f64 2 (sqrt.f64 k)) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2))) 1/2)
(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(.f64 (/.f64 1 (/.f64 4 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)))) (/.f64 4 (sqrt.f64 k)))
(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(.f64 (/.f64 1/2 (sqrt.f64 k)) (.f64 2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2))))
(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))

localize37.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 n (.f64 2 (PI.f64)))
✓	0.3b	(.f64 (/.f64 1 (sqrt.f64 k)) (exp.f64 (.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) (*.f64 1/2 (-.f64 1 k)))))
	0.3b	(/.f64 1 (sqrt.f64 k))
✓	3.1b	(exp.f64 (.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) (.f64 1/2 (-.f64 1 k))))

Compiler

Compiled 79 to 56 computations (29.1% saved)

series5.0ms (0%)

Counts

3 → 48

Calls

15 calls:

Time	Variable		Point	Expression
1.0ms	k	@	-inf	(.f64 (/.f64 1 (sqrt.f64 k)) (exp.f64 (.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) (*.f64 1/2 (-.f64 1 k)))))
1.0ms	n	@	0	(exp.f64 (.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) (.f64 1/2 (-.f64 1 k))))
1.0ms	n	@	-inf	(exp.f64 (.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) (.f64 1/2 (-.f64 1 k))))
1.0ms	n	@	inf	(exp.f64 (.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) (.f64 1/2 (-.f64 1 k))))
0.0ms	k	@	0	(.f64 (/.f64 1 (sqrt.f64 k)) (exp.f64 (.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) (*.f64 1/2 (-.f64 1 k)))))

rewrite90.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

1632×	`bool.json-1`
1632×	`bool.json-2`
1588×	`rational.json-1`
1588×	`rational.json-2`
1588×	`rational.json-3`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	20	113
1	200	107
2	494	107
3	1029	107
4	2174	107
5	5280	107

Stop Event

1×	node limit

Counts

3 → 85

Calls

Call 1

Inputs

(exp.f64 (*.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64)))) (*.f64 1/2 (-.f64 1 k))))

(*.f64 (/.f64 1 (sqrt.f64 k)) (exp.f64 (*.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64)))) (*.f64 1/2 (-.f64 1 k)))))

(*.f64 n (*.f64 2 (PI.f64)))

Outputs

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((#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 n (*.f64 2 (PI.f64))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 n (*.f64 2 (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 n (PI.f64)) (*.f64 n (PI.f64)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (*.f64 n (*.f64 2 (PI.f64))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 n (*.f64 2 (PI.f64))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 n (*.f64 (PI.f64) 4)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (*.f64 n (PI.f64)) 8) 4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 (*.f64 n (PI.f64)) 8)) 8)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (*.f64 2 (*.f64 (*.f64 n (PI.f64)) 8)) (*.f64 2 (*.f64 (*.f64 n (PI.f64)) 8))) 16)))) (#(struct:change #<rule egg-rr> (2) ((x not (not (*.f64 n (*.f64 2 (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x and (*.f64 n (*.f64 2 (PI.f64))) (*.f64 n (*.f64 2 (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x or (*.f64 n (*.f64 2 (PI.f64))) (*.f64 n (*.f64 2 (PI.f64))))))))

simplify244.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

2162×	`rational.json-simplify-35`
994×	`rational.json-simplify-43`
706×	`rational.json-simplify-2`
686×	`rational.json-simplify-41`
636×	`rational.json-simplify-53`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	257	6355
1	715	6323
2	2274	6269
3	4598	6269
4	7975	6269

Stop Event

1×	node limit

Counts

133 → 134

Calls

Call 1

Inputs
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(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))
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(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))))))
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(/.f64 (neg.f64 (.f64 2 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 n (.f64 2 (PI.f64))))))))) (neg.f64 (.f64 2 (sqrt.f64 k))))
(/.f64 (neg.f64 (neg.f64 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 n (.f64 2 (PI.f64))))))))) (sqrt.f64 k))
(/.f64 (+.f64 (/.f64 1/2 (/.f64 (sqrt.f64 k) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 n (.f64 2 (PI.f64))))))))) (/.f64 1/2 (/.f64 (sqrt.f64 k) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 n (.f64 2 (PI.f64)))))))))) 1)
(/.f64 (+.f64 (.f64 2 (.f64 (/.f64 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 n (.f64 2 (PI.f64))))))) (sqrt.f64 k)) 4)) (.f64 2 (.f64 (/.f64 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 n (.f64 2 (PI.f64))))))) (sqrt.f64 k)) 4))) 16)
(/.f64 (+.f64 (.f64 2 (neg.f64 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 n (.f64 2 (PI.f64))))))))) (.f64 2 (neg.f64 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 n (.f64 2 (PI.f64)))))))))) (.f64 2 (.f64 2 (neg.f64 (sqrt.f64 k)))))
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(/.f64 (+.f64 (neg.f64 (.f64 2 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 n (.f64 2 (PI.f64))))))))) (neg.f64 (.f64 2 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 n (.f64 2 (PI.f64)))))))))) (.f64 2 (neg.f64 (.f64 2 (sqrt.f64 k)))))
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(/.f64 (/.f64 (.f64 2 (.f64 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 n (.f64 2 (PI.f64))))))) 4)) (sqrt.f64 k)) 8)
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(/.f64 (/.f64 (neg.f64 (neg.f64 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 n (.f64 2 (PI.f64))))))))) 1/2) (*.f64 2 (sqrt.f64 k)))
(/.f64 (/.f64 (neg.f64 (neg.f64 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 n (.f64 2 (PI.f64))))))))) 2) (/.f64 (sqrt.f64 k) 2))
(/.f64 (/.f64 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 n (.f64 2 (PI.f64))))))) (*.f64 (sqrt.f64 k) 4)) 1/4)
(/.f64 (/.f64 (neg.f64 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 n (.f64 2 (PI.f64)))))))) (sqrt.f64 k)) -1)
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(/.f64 (neg.f64 (.f64 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 n (.f64 2 (PI.f64))))))) 4)) (neg.f64 (.f64 (sqrt.f64 k) 4)))
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(/.f64 (neg.f64 (neg.f64 (.f64 2 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 n (.f64 2 (PI.f64)))))))))) (.f64 2 (sqrt.f64 k)))
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(+.f64 0 (.f64 n (.f64 2 (PI.f64))))
(+.f64 (.f64 n (PI.f64)) (.f64 n (PI.f64)))
(-.f64 (.f64 n (.f64 2 (PI.f64))) 0)
(/.f64 (.f64 n (.f64 2 (PI.f64))) 1)
(/.f64 (.f64 n (.f64 (PI.f64) 4)) 2)
(/.f64 (.f64 (.f64 n (PI.f64)) 8) 4)
(/.f64 (.f64 2 (.f64 (*.f64 n (PI.f64)) 8)) 8)
(/.f64 (+.f64 (.f64 2 (.f64 (.f64 n (PI.f64)) 8)) (.f64 2 (.f64 (.f64 n (PI.f64)) 8))) 16)

Outputs
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))
(exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)) (*.f64 (-.f64 1 k) 1/2)))
(exp.f64 (.f64 (-.f64 1 k) (.f64 1/2 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))
(exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)) (*.f64 (-.f64 1 k) 1/2)))
(exp.f64 (.f64 (-.f64 1 k) (.f64 1/2 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))
(exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)) (*.f64 (-.f64 1 k) 1/2)))
(exp.f64 (.f64 (-.f64 1 k) (.f64 1/2 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))
(exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)) (*.f64 (-.f64 1 k) 1/2)))
(exp.f64 (.f64 (-.f64 1 k) (.f64 1/2 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (.f64 -1 (log.f64 (/.f64 1 n)))))))
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(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (.f64 -1 (log.f64 (/.f64 1 n)))))))
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(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (.f64 -1 (log.f64 (/.f64 1 n)))))))
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(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (neg.f64 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 (PI.f64) -2))))))
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(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64)))))))
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(exp.f64 (.f64 (+.f64 (neg.f64 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 (PI.f64) -2))) (*.f64 (-.f64 1 k) 1/2)))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (neg.f64 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 (PI.f64) -2))))))
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(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64)))))))
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(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))))
(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 (PI.f64) n)))
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(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (.f64 n (PI.f64)))))))
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(/.f64 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (.f64 (PI.f64) n)))))) (sqrt.f64 k))
(/.f64 (exp.f64 (.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) (.f64 (-.f64 1 k) 1/2))) (sqrt.f64 k))
(/.f64 (/.f64 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 n (.f64 2 (PI.f64))))))) (neg.f64 (sqrt.f64 k))) -1)
(/.f64 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (.f64 (PI.f64) n)))))) (sqrt.f64 k))
(/.f64 (exp.f64 (.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) (.f64 (-.f64 1 k) 1/2))) (sqrt.f64 k))
(/.f64 (/.f64 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 n (.f64 2 (PI.f64))))))) 1/2) (*.f64 2 (sqrt.f64 k)))
(/.f64 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (.f64 (PI.f64) n)))))) (sqrt.f64 k))
(/.f64 (exp.f64 (.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) (.f64 (-.f64 1 k) 1/2))) (sqrt.f64 k))
(/.f64 (/.f64 (neg.f64 (neg.f64 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 n (.f64 2 (PI.f64))))))))) 1/2) (*.f64 2 (sqrt.f64 k)))
(/.f64 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (.f64 (PI.f64) n)))))) (sqrt.f64 k))
(/.f64 (exp.f64 (.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) (.f64 (-.f64 1 k) 1/2))) (sqrt.f64 k))
(/.f64 (/.f64 (neg.f64 (neg.f64 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 n (.f64 2 (PI.f64))))))))) 2) (/.f64 (sqrt.f64 k) 2))
(/.f64 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (.f64 (PI.f64) n)))))) (sqrt.f64 k))
(/.f64 (exp.f64 (.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) (.f64 (-.f64 1 k) 1/2))) (sqrt.f64 k))
(/.f64 (/.f64 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 n (.f64 2 (PI.f64))))))) (*.f64 (sqrt.f64 k) 4)) 1/4)
(/.f64 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (.f64 (PI.f64) n)))))) (sqrt.f64 k))
(/.f64 (exp.f64 (.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) (.f64 (-.f64 1 k) 1/2))) (sqrt.f64 k))
(/.f64 (/.f64 (neg.f64 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 n (.f64 2 (PI.f64)))))))) (sqrt.f64 k)) -1)
(/.f64 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (.f64 (PI.f64) n)))))) (sqrt.f64 k))
(/.f64 (exp.f64 (.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) (.f64 (-.f64 1 k) 1/2))) (sqrt.f64 k))
(/.f64 (/.f64 (neg.f64 (neg.f64 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 n (.f64 2 (PI.f64))))))))) (*.f64 (sqrt.f64 k) 4)) 1/4)
(/.f64 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (.f64 (PI.f64) n)))))) (sqrt.f64 k))
(/.f64 (exp.f64 (.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) (.f64 (-.f64 1 k) 1/2))) (sqrt.f64 k))
(/.f64 (neg.f64 (.f64 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 n (.f64 2 (PI.f64))))))) 4)) (neg.f64 (.f64 (sqrt.f64 k) 4)))
(/.f64 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (.f64 (PI.f64) n)))))) (sqrt.f64 k))
(/.f64 (exp.f64 (.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) (.f64 (-.f64 1 k) 1/2))) (sqrt.f64 k))
(/.f64 (neg.f64 (.f64 2 (neg.f64 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 n (.f64 2 (PI.f64)))))))))) (-.f64 0 (.f64 2 (neg.f64 (sqrt.f64 k)))))
(/.f64 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (.f64 (PI.f64) n)))))) (sqrt.f64 k))
(/.f64 (exp.f64 (.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) (.f64 (-.f64 1 k) 1/2))) (sqrt.f64 k))
(/.f64 (neg.f64 (neg.f64 (.f64 2 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 n (.f64 2 (PI.f64)))))))))) (.f64 2 (sqrt.f64 k)))
(/.f64 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (.f64 (PI.f64) n)))))) (sqrt.f64 k))
(/.f64 (exp.f64 (.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) (.f64 (-.f64 1 k) 1/2))) (sqrt.f64 k))
(/.f64 (neg.f64 (neg.f64 (.f64 2 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 n (.f64 2 (PI.f64)))))))))) (-.f64 0 (neg.f64 (.f64 2 (sqrt.f64 k)))))
(/.f64 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (.f64 (PI.f64) n)))))) (sqrt.f64 k))
(/.f64 (exp.f64 (.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) (.f64 (-.f64 1 k) 1/2))) (sqrt.f64 k))
(/.f64 (neg.f64 (neg.f64 (neg.f64 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 n (.f64 2 (PI.f64)))))))))) (neg.f64 (sqrt.f64 k)))
(/.f64 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (.f64 (PI.f64) n)))))) (sqrt.f64 k))
(/.f64 (exp.f64 (.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) (.f64 (-.f64 1 k) 1/2))) (sqrt.f64 k))
(+.f64 (.f64 n (.f64 2 (PI.f64))) 0)
(.f64 2 (.f64 (PI.f64) n))
(+.f64 0 (.f64 n (.f64 2 (PI.f64))))
(.f64 2 (.f64 (PI.f64) n))
(+.f64 (.f64 n (PI.f64)) (.f64 n (PI.f64)))
(.f64 2 (.f64 (PI.f64) n))
(-.f64 (.f64 n (.f64 2 (PI.f64))) 0)
(.f64 2 (.f64 (PI.f64) n))
(/.f64 (.f64 n (.f64 2 (PI.f64))) 1)
(.f64 2 (.f64 (PI.f64) n))
(/.f64 (.f64 n (.f64 (PI.f64) 4)) 2)
(.f64 2 (.f64 (PI.f64) n))
(/.f64 (.f64 (.f64 n (PI.f64)) 8) 4)
(.f64 2 (.f64 (PI.f64) n))
(/.f64 (.f64 2 (.f64 (*.f64 n (PI.f64)) 8)) 8)
(.f64 2 (.f64 (PI.f64) n))
(/.f64 (+.f64 (.f64 2 (.f64 (.f64 n (PI.f64)) 8)) (.f64 2 (.f64 (.f64 n (PI.f64)) 8))) 16)
(.f64 2 (.f64 (PI.f64) n))

localize80.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.3b	(/.f64 1 (sqrt.f64 k))
✓	0.4b	(.f64 (sqrt.f64 (.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (.f64 -1/2 (.f64 k (.f64 (sqrt.f64 2) (log.f64 (.f64 n (*.f64 2 (PI.f64)))))))))
✓	0.4b	(.f64 (sqrt.f64 2) (log.f64 (.f64 n (*.f64 2 (PI.f64)))))
✓	7.1b	(.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (.f64 -1/2 (.f64 k (.f64 (sqrt.f64 2) (log.f64 (.f64 n (.f64 2 (PI.f64))))))))))

Compiler

Compiled 133 to 91 computations (31.6% saved)

series68.0ms (0.4%)

Counts

3 → 24

Calls

15 calls:

Time	Variable		Point	Expression
51.0ms	n	@	-inf	(.f64 (sqrt.f64 (.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (.f64 -1/2 (.f64 k (.f64 (sqrt.f64 2) (log.f64 (.f64 n (*.f64 2 (PI.f64)))))))))
4.0ms	k	@	0	(.f64 (sqrt.f64 (.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (.f64 -1/2 (.f64 k (.f64 (sqrt.f64 2) (log.f64 (.f64 n (*.f64 2 (PI.f64)))))))))
2.0ms	k	@	0	(.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (.f64 -1/2 (.f64 k (.f64 (sqrt.f64 2) (log.f64 (.f64 n (.f64 2 (PI.f64))))))))))
1.0ms	n	@	-inf	(.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (.f64 -1/2 (.f64 k (.f64 (sqrt.f64 2) (log.f64 (.f64 n (.f64 2 (PI.f64))))))))))
1.0ms	n	@	0	(.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (.f64 -1/2 (.f64 k (.f64 (sqrt.f64 2) (log.f64 (.f64 n (.f64 2 (PI.f64))))))))))

rewrite127.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

974×	`bool.json-1`
974×	`bool.json-2`
948×	`rational.json-simplify-35`
942×	`rational.json-1`
942×	`rational.json-2`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	24	183
1	243	177
2	597	169
3	1273	169
4	2923	169
5	7503	169

Stop Event

1×	node limit

Counts

3 → 80

Calls

Call 1

Inputs

(*.f64 (/.f64 1 (sqrt.f64 k)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (*.f64 -1/2 (*.f64 k (*.f64 (sqrt.f64 2) (log.f64 (*.f64 n (*.f64 2 (PI.f64))))))))))

(*.f64 (sqrt.f64 2) (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))

(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (*.f64 -1/2 (*.f64 k (*.f64 (sqrt.f64 2) (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))))))

Outputs

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((#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (+.f64 1 (*.f64 k (*.f64 -1/2 (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (+.f64 1 (*.f64 k (*.f64 -1/2 (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (+.f64 1 (*.f64 k (*.f64 -1/2 (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (+.f64 1 (*.f64 k (*.f64 -1/2 (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (+.f64 1 (*.f64 k (*.f64 -1/2 (log.f64 (*.f64 (PI.f64) (+.f64 n n))))))))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (*.f64 (sqrt.f64 2) (+.f64 1 (*.f64 k (*.f64 -1/2 (log.f64 (*.f64 (PI.f64) (+.f64 n n))))))) 4)) 4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (*.f64 (sqrt.f64 2) (+.f64 1 (*.f64 k (*.f64 -1/2 (log.f64 (*.f64 (PI.f64) (+.f64 n n))))))) 4))) 8)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (*.f64 2 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (*.f64 (sqrt.f64 2) (+.f64 1 (*.f64 k (*.f64 -1/2 (log.f64 (*.f64 (PI.f64) (+.f64 n n))))))) 4))) (*.f64 2 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (*.f64 (sqrt.f64 2) (+.f64 1 (*.f64 k (*.f64 -1/2 (log.f64 (*.f64 (PI.f64) (+.f64 n n))))))) 4)))) 16)))) (#(struct:change #<rule egg-rr> (2) ((x not (not (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (+.f64 1 (*.f64 k (*.f64 -1/2 (log.f64 (*.f64 (PI.f64) (+.f64 n n))))))))))))) (#(struct:change #<rule egg-rr> (2) ((x and (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (+.f64 1 (*.f64 k (*.f64 -1/2 (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (+.f64 1 (*.f64 k (*.f64 -1/2 (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))))))))) (#(struct:change #<rule egg-rr> (2) ((x or (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (+.f64 1 (*.f64 k (*.f64 -1/2 (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (+.f64 1 (*.f64 k (*.f64 -1/2 (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))))))))))

simplify227.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

1120×	`rational.json-simplify-53`
980×	`rational.json-simplify-43`
872×	`rational.json-simplify-39`
868×	`rational.json-simplify-1`
838×	`rational.json-simplify-2`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	222	6968
1	719	6952
2	2501	6790
3	4393	6790
4	7921	6790

Stop Event

1×	node limit

Counts

104 → 105

Calls

Call 1

Inputs
(.f64 (sqrt.f64 2) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)))
(.f64 (sqrt.f64 2) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)))
(.f64 (sqrt.f64 2) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)))
(.f64 (sqrt.f64 2) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)))
(.f64 (sqrt.f64 2) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))
(.f64 (sqrt.f64 2) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))
(.f64 (sqrt.f64 2) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))
(.f64 (sqrt.f64 2) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))
(.f64 (sqrt.f64 2) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))
(.f64 (sqrt.f64 2) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))
(.f64 (sqrt.f64 2) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))
(.f64 (sqrt.f64 2) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))
(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))))
(+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 (.f64 n (PI.f64))))) (.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))))
(+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 (.f64 n (PI.f64))))) (.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))))
(+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 (.f64 n (PI.f64))))) (.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))))
(.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 (*.f64 n (PI.f64)))))
(+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 (.f64 n (PI.f64))))) (.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))))
(+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 (.f64 n (PI.f64))))) (.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))))
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(.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 (*.f64 n (PI.f64)))))
(+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 (.f64 n (PI.f64))))) (.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))))
(+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 (.f64 n (PI.f64))))) (.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))))
(+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 (.f64 n (PI.f64))))) (.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))))
(+.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (+.f64 1 (.f64 k (.f64 -1/2 (log.f64 (.f64 (PI.f64) (+.f64 n n)))))) (/.f64 (sqrt.f64 2) (sqrt.f64 k)))) 0)
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(-.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (+.f64 1 (.f64 k (.f64 -1/2 (log.f64 (.f64 (PI.f64) (+.f64 n n)))))) (/.f64 (sqrt.f64 2) (sqrt.f64 k)))) 0)
(/.f64 1 (/.f64 (sqrt.f64 k) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (sqrt.f64 2) (+.f64 1 (.f64 k (.f64 -1/2 (log.f64 (.f64 (PI.f64) (+.f64 n n))))))))))
(/.f64 1 (.f64 (/.f64 (sqrt.f64 k) (.f64 2 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (sqrt.f64 2) (+.f64 1 (.f64 k (.f64 -1/2 (log.f64 (.f64 (PI.f64) (+.f64 n n)))))))))) 2))
(/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (/.f64 1 (sqrt.f64 (.f64 n (PI.f64)))) (.f64 (sqrt.f64 2) (+.f64 1 (.f64 k (.f64 -1/2 (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))))))
(/.f64 (sqrt.f64 (.f64 n (PI.f64))) (/.f64 (sqrt.f64 k) (.f64 (sqrt.f64 2) (+.f64 1 (.f64 k (.f64 -1/2 (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))))))
(/.f64 2 (/.f64 (/.f64 (sqrt.f64 k) (/.f64 (sqrt.f64 (.f64 n (PI.f64))) 2)) (.f64 (sqrt.f64 2) (+.f64 1 (.f64 k (.f64 -1/2 (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))))))
(/.f64 2 (/.f64 (.f64 (sqrt.f64 k) 2) (neg.f64 (neg.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (sqrt.f64 2) (+.f64 1 (.f64 k (.f64 -1/2 (log.f64 (*.f64 (PI.f64) (+.f64 n n))))))))))))
(/.f64 (.f64 (sqrt.f64 2) (+.f64 1 (.f64 k (.f64 -1/2 (log.f64 (.f64 (PI.f64) (+.f64 n n))))))) (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 n (PI.f64)))))
(/.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (sqrt.f64 2) (+.f64 1 (.f64 k (.f64 -1/2 (log.f64 (.f64 (PI.f64) (+.f64 n n)))))))) (sqrt.f64 k))
(/.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (sqrt.f64 2) (+.f64 1 (.f64 k (.f64 -1/2 (log.f64 (.f64 (PI.f64) (+.f64 n n)))))))) (*.f64 -1 (neg.f64 (sqrt.f64 k))))
(/.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (+.f64 1 (.f64 k (.f64 -1/2 (log.f64 (.f64 (PI.f64) (+.f64 n n)))))) (/.f64 (sqrt.f64 2) (sqrt.f64 k)))) 1)
(/.f64 (/.f64 (.f64 (sqrt.f64 2) (+.f64 1 (.f64 k (.f64 -1/2 (log.f64 (.f64 (PI.f64) (+.f64 n n))))))) (/.f64 (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 n (PI.f64)))) 2)) 2)
(/.f64 (.f64 2 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (sqrt.f64 2) (+.f64 1 (.f64 k (.f64 -1/2 (log.f64 (.f64 (PI.f64) (+.f64 n n))))))))) (.f64 (sqrt.f64 k) 2))
(/.f64 4 (.f64 2 (/.f64 (/.f64 (sqrt.f64 k) (/.f64 (sqrt.f64 (.f64 n (PI.f64))) 2)) (.f64 (sqrt.f64 2) (+.f64 1 (.f64 k (.f64 -1/2 (log.f64 (.f64 (PI.f64) (+.f64 n n))))))))))
(/.f64 4 (/.f64 (/.f64 (.f64 (sqrt.f64 k) 4) (sqrt.f64 (.f64 n (PI.f64)))) (.f64 (sqrt.f64 2) (+.f64 1 (.f64 k (.f64 -1/2 (log.f64 (.f64 (PI.f64) (+.f64 n n)))))))))
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(/.f64 4 (.f64 (.f64 2 (/.f64 (/.f64 (sqrt.f64 k) (/.f64 (sqrt.f64 (.f64 n (PI.f64))) 2)) (.f64 (sqrt.f64 2) (+.f64 1 (.f64 k (.f64 -1/2 (log.f64 (*.f64 (PI.f64) (+.f64 n n))))))))) 1))
(/.f64 4 (.f64 (/.f64 (/.f64 (.f64 (sqrt.f64 k) 4) (sqrt.f64 (.f64 n (PI.f64)))) (.f64 (sqrt.f64 2) (+.f64 1 (.f64 k (.f64 -1/2 (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))))) 1))
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(/.f64 (/.f64 2 (sqrt.f64 k)) (/.f64 2 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (sqrt.f64 2) (+.f64 1 (.f64 k (.f64 -1/2 (log.f64 (.f64 (PI.f64) (+.f64 n n))))))))))
(/.f64 1/2 (/.f64 (sqrt.f64 k) (.f64 2 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (sqrt.f64 2) (+.f64 1 (.f64 k (.f64 -1/2 (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))))))))
(/.f64 -1 (/.f64 (sqrt.f64 k) (neg.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (sqrt.f64 2) (+.f64 1 (.f64 k (.f64 -1/2 (log.f64 (.f64 (PI.f64) (+.f64 n n)))))))))))
(/.f64 -1 (-.f64 0 (/.f64 (sqrt.f64 k) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (sqrt.f64 2) (+.f64 1 (.f64 k (.f64 -1/2 (log.f64 (.f64 (PI.f64) (+.f64 n n)))))))))))
(/.f64 8 (+.f64 (/.f64 (/.f64 (.f64 (sqrt.f64 k) 4) (sqrt.f64 (.f64 n (PI.f64)))) (.f64 (sqrt.f64 2) (+.f64 1 (.f64 k (.f64 -1/2 (log.f64 (.f64 (PI.f64) (+.f64 n n)))))))) (/.f64 (/.f64 (.f64 (sqrt.f64 k) 4) (sqrt.f64 (.f64 n (PI.f64)))) (.f64 (sqrt.f64 2) (+.f64 1 (.f64 k (.f64 -1/2 (log.f64 (.f64 (PI.f64) (+.f64 n n))))))))))
(/.f64 8 (+.f64 (.f64 2 (/.f64 (/.f64 (sqrt.f64 k) (/.f64 (sqrt.f64 (.f64 n (PI.f64))) 2)) (.f64 (sqrt.f64 2) (+.f64 1 (.f64 k (.f64 -1/2 (log.f64 (.f64 (PI.f64) (+.f64 n n))))))))) (.f64 2 (/.f64 (/.f64 (sqrt.f64 k) (/.f64 (sqrt.f64 (.f64 n (PI.f64))) 2)) (.f64 (sqrt.f64 2) (+.f64 1 (.f64 k (.f64 -1/2 (log.f64 (.f64 (PI.f64) (+.f64 n n)))))))))))
(/.f64 8 (/.f64 (.f64 2 (.f64 (sqrt.f64 k) 4)) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (sqrt.f64 2) (+.f64 1 (.f64 k (.f64 -1/2 (log.f64 (.f64 (PI.f64) (+.f64 n n))))))))))
(/.f64 8 (/.f64 (.f64 2 (.f64 (sqrt.f64 k) 4)) (neg.f64 (neg.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (sqrt.f64 2) (+.f64 1 (.f64 k (.f64 -1/2 (log.f64 (.f64 (PI.f64) (+.f64 n n))))))))))))
(/.f64 -2 (-.f64 0 (/.f64 (/.f64 (sqrt.f64 k) (/.f64 (sqrt.f64 (.f64 n (PI.f64))) 2)) (.f64 (sqrt.f64 2) (+.f64 1 (.f64 k (.f64 -1/2 (log.f64 (*.f64 (PI.f64) (+.f64 n n))))))))))
(/.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (.f64 (sqrt.f64 2) (+.f64 1 (.f64 k (.f64 -1/2 (log.f64 (.f64 (PI.f64) (+.f64 n n))))))) 4)) (.f64 (sqrt.f64 k) 4))
(/.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (.f64 (+.f64 1 (.f64 k (.f64 -1/2 (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))) (/.f64 (sqrt.f64 2) (sqrt.f64 k))) 4)) 4)
(/.f64 (neg.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (sqrt.f64 2) (+.f64 1 (.f64 k (.f64 -1/2 (log.f64 (.f64 (PI.f64) (+.f64 n n))))))))) (neg.f64 (sqrt.f64 k)))
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Outputs
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(.f64 (sqrt.f64 2) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)))
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(.f64 (+.f64 1 (.f64 -1/2 (.f64 k (log.f64 (.f64 (PI.f64) (+.f64 n n)))))) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (/.f64 (sqrt.f64 2) (sqrt.f64 k))))
(.f64 (sqrt.f64 2) (/.f64 (+.f64 1 (.f64 -1/2 (.f64 k (log.f64 (.f64 (PI.f64) (+.f64 n n)))))) (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 (PI.f64) n)))))
(/.f64 (neg.f64 (neg.f64 (neg.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (sqrt.f64 2) (+.f64 1 (.f64 k (.f64 -1/2 (log.f64 (.f64 (PI.f64) (+.f64 n n))))))))))) (neg.f64 (sqrt.f64 k)))
(.f64 (sqrt.f64 (.f64 (PI.f64) n)) (.f64 (+.f64 1 (.f64 -1/2 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) k))) (/.f64 (sqrt.f64 2) (sqrt.f64 k))))
(.f64 (+.f64 1 (.f64 -1/2 (.f64 k (log.f64 (.f64 (PI.f64) (+.f64 n n)))))) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (/.f64 (sqrt.f64 2) (sqrt.f64 k))))
(.f64 (sqrt.f64 2) (/.f64 (+.f64 1 (.f64 -1/2 (.f64 k (log.f64 (.f64 (PI.f64) (+.f64 n n)))))) (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 (PI.f64) n)))))
(+.f64 (.f64 (sqrt.f64 2) (log.f64 (.f64 (PI.f64) (+.f64 n n)))) 0)
(.f64 (sqrt.f64 2) (log.f64 (.f64 (PI.f64) (+.f64 n n))))
(+.f64 0 (.f64 (sqrt.f64 2) (log.f64 (.f64 (PI.f64) (+.f64 n n)))))
(.f64 (sqrt.f64 2) (log.f64 (.f64 (PI.f64) (+.f64 n n))))
(-.f64 (.f64 (sqrt.f64 2) (log.f64 (.f64 (PI.f64) (+.f64 n n)))) 0)
(.f64 (sqrt.f64 2) (log.f64 (.f64 (PI.f64) (+.f64 n n))))
(/.f64 (.f64 (sqrt.f64 2) (log.f64 (.f64 (PI.f64) (+.f64 n n)))) 1)
(.f64 (sqrt.f64 2) (log.f64 (.f64 (PI.f64) (+.f64 n n))))
(/.f64 (.f64 2 (.f64 (sqrt.f64 2) (log.f64 (*.f64 (PI.f64) (+.f64 n n))))) 2)
(.f64 (sqrt.f64 2) (log.f64 (.f64 (PI.f64) (+.f64 n n))))
(/.f64 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (*.f64 (sqrt.f64 2) 4)) 4)
(.f64 (sqrt.f64 2) (log.f64 (.f64 (PI.f64) (+.f64 n n))))
(/.f64 (.f64 2 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (.f64 (sqrt.f64 2) 4))) 8)
(.f64 (sqrt.f64 2) (log.f64 (.f64 (PI.f64) (+.f64 n n))))
(/.f64 (+.f64 (.f64 2 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (.f64 (sqrt.f64 2) 4))) (.f64 2 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (.f64 (sqrt.f64 2) 4)))) 16)
(.f64 (sqrt.f64 2) (log.f64 (.f64 (PI.f64) (+.f64 n n))))
(+.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (sqrt.f64 2) (+.f64 1 (.f64 k (.f64 -1/2 (log.f64 (.f64 (PI.f64) (+.f64 n n)))))))) 0)
(.f64 (sqrt.f64 2) (.f64 (+.f64 1 (.f64 -1/2 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) k))) (sqrt.f64 (.f64 (PI.f64) n))))
(.f64 (sqrt.f64 2) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (+.f64 1 (.f64 -1/2 (.f64 k (log.f64 (.f64 (PI.f64) (+.f64 n n))))))))
(+.f64 0 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (sqrt.f64 2) (+.f64 1 (.f64 k (.f64 -1/2 (log.f64 (.f64 (PI.f64) (+.f64 n n)))))))))
(.f64 (sqrt.f64 2) (.f64 (+.f64 1 (.f64 -1/2 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) k))) (sqrt.f64 (.f64 (PI.f64) n))))
(.f64 (sqrt.f64 2) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (+.f64 1 (.f64 -1/2 (.f64 k (log.f64 (.f64 (PI.f64) (+.f64 n n))))))))
(-.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (sqrt.f64 2) (+.f64 1 (.f64 k (.f64 -1/2 (log.f64 (.f64 (PI.f64) (+.f64 n n)))))))) 0)
(.f64 (sqrt.f64 2) (.f64 (+.f64 1 (.f64 -1/2 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) k))) (sqrt.f64 (.f64 (PI.f64) n))))
(.f64 (sqrt.f64 2) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (+.f64 1 (.f64 -1/2 (.f64 k (log.f64 (.f64 (PI.f64) (+.f64 n n))))))))
(/.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (sqrt.f64 2) (+.f64 1 (.f64 k (.f64 -1/2 (log.f64 (.f64 (PI.f64) (+.f64 n n)))))))) 1)
(.f64 (sqrt.f64 2) (.f64 (+.f64 1 (.f64 -1/2 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) k))) (sqrt.f64 (.f64 (PI.f64) n))))
(.f64 (sqrt.f64 2) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (+.f64 1 (.f64 -1/2 (.f64 k (log.f64 (.f64 (PI.f64) (+.f64 n n))))))))
(/.f64 (.f64 2 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (sqrt.f64 2) (+.f64 1 (.f64 k (.f64 -1/2 (log.f64 (*.f64 (PI.f64) (+.f64 n n))))))))) 2)
(.f64 (sqrt.f64 2) (.f64 (+.f64 1 (.f64 -1/2 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) k))) (sqrt.f64 (.f64 (PI.f64) n))))
(.f64 (sqrt.f64 2) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (+.f64 1 (.f64 -1/2 (.f64 k (log.f64 (.f64 (PI.f64) (+.f64 n n))))))))
(/.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (.f64 (sqrt.f64 2) (+.f64 1 (.f64 k (.f64 -1/2 (log.f64 (*.f64 (PI.f64) (+.f64 n n))))))) 4)) 4)
(.f64 (sqrt.f64 2) (.f64 (+.f64 1 (.f64 -1/2 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) k))) (sqrt.f64 (.f64 (PI.f64) n))))
(.f64 (sqrt.f64 2) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (+.f64 1 (.f64 -1/2 (.f64 k (log.f64 (.f64 (PI.f64) (+.f64 n n))))))))
(/.f64 (.f64 2 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (.f64 (sqrt.f64 2) (+.f64 1 (.f64 k (.f64 -1/2 (log.f64 (.f64 (PI.f64) (+.f64 n n))))))) 4))) 8)
(.f64 (sqrt.f64 2) (.f64 (+.f64 1 (.f64 -1/2 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) k))) (sqrt.f64 (.f64 (PI.f64) n))))
(.f64 (sqrt.f64 2) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (+.f64 1 (.f64 -1/2 (.f64 k (log.f64 (.f64 (PI.f64) (+.f64 n n))))))))
(/.f64 (+.f64 (.f64 2 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (.f64 (sqrt.f64 2) (+.f64 1 (.f64 k (.f64 -1/2 (log.f64 (.f64 (PI.f64) (+.f64 n n))))))) 4))) (.f64 2 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (.f64 (sqrt.f64 2) (+.f64 1 (.f64 k (.f64 -1/2 (log.f64 (.f64 (PI.f64) (+.f64 n n))))))) 4)))) 16)
(.f64 (sqrt.f64 2) (.f64 (+.f64 1 (.f64 -1/2 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) k))) (sqrt.f64 (.f64 (PI.f64) n))))
(.f64 (sqrt.f64 2) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (+.f64 1 (.f64 -1/2 (.f64 k (log.f64 (.f64 (PI.f64) (+.f64 n n))))))))

eval271.0ms (1.8%)

Compiler: Compiled 17812 to 11388 computations (36.1% saved)

prune150.0ms (1%)

Pruning

21 alts after pruning (17 fresh and 4 done)

	Pruned	Kept	Total
New	703	14	717
Fresh	3	3	6
Picked	1	0	1
Done	1	4	5
Total	708	21	729

Error

0.1b

Counts

729 → 21

Alt Table

Click to see full alt table

Status	Error	Program
✓	0.4b	(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k))
▶	33.2b	(/.f64 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2))) (.f64 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2))) (/.f64 (sqrt.f64 k) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2)))))
✓	0.5b	(/.f64 (/.f64 2 (sqrt.f64 k)) (/.f64 2 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2))))
	23.9b	(/.f64 (+.f64 (.f64 -1/2 (.f64 (sqrt.f64 2) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 k (log.f64 (.f64 n (.f64 2 (PI.f64)))))))) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (.f64 1/8 (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 2) (pow.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) 2))))))) (sqrt.f64 k))
	23.9b	(/.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (+.f64 (.f64 1/8 (.f64 (pow.f64 k 2) (.f64 (sqrt.f64 2) (pow.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) 2)))) (+.f64 (sqrt.f64 2) (.f64 -1/2 (.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) (.f64 k (sqrt.f64 2))))))) (sqrt.f64 k))
	23.7b	(/.f64 (.f64 (sqrt.f64 2) (+.f64 1 (.f64 k (.f64 -1/2 (log.f64 (.f64 (PI.f64) (+.f64 n n))))))) (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 n (PI.f64)))))
	23.8b	(/.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (sqrt.f64 k))
▶	23.7b	(/.f64 (sqrt.f64 (.f64 n (PI.f64))) (/.f64 (sqrt.f64 k) (.f64 (sqrt.f64 2) (+.f64 1 (.f64 k (.f64 -1/2 (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))))))
▶	3.0b	(/.f64 (exp.f64 (.f64 (-.f64 1 k) (.f64 1/2 (log.f64 (.f64 (PI.f64) (.f64 2 n)))))) (sqrt.f64 k))
	23.8b	(/.f64 4 (/.f64 (/.f64 (.f64 (sqrt.f64 k) 4) (sqrt.f64 (.f64 n (PI.f64)))) (.f64 (sqrt.f64 2) (+.f64 1 (.f64 k (.f64 -1/2 (log.f64 (.f64 (PI.f64) (+.f64 n n)))))))))
▶	0.4b	(/.f64 2 (.f64 (sqrt.f64 k) (/.f64 2 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2)))))
✓	0.4b	(/.f64 1 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2))))
	23.9b	(/.f64 1 (/.f64 (sqrt.f64 k) (+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 -1/2 (.f64 (log.f64 (.f64 (PI.f64) (.f64 2 n))) (*.f64 (sqrt.f64 2) k)))))))
	0.5b	(/.f64 1 (.f64 (/.f64 1 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2))) (/.f64 -1 (/.f64 -1 (sqrt.f64 k)))))
▶	0.5b	(.f64 (/.f64 4 (sqrt.f64 k)) (/.f64 1 (/.f64 4 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)))))
✓	0.4b	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
	23.9b	(.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 (PI.f64) n))))
	23.7b	(.f64 (+.f64 1 (.f64 -1/2 (.f64 k (log.f64 (.f64 (PI.f64) (+.f64 n n)))))) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (/.f64 (sqrt.f64 2) (sqrt.f64 k))))
	0.5b	(.f64 (.f64 (/.f64 1 (.f64 (sqrt.f64 k) (sqrt.f64 k))) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
	23.8b	(.f64 (sqrt.f64 2) (/.f64 (+.f64 1 (.f64 -1/2 (.f64 k (log.f64 (.f64 (PI.f64) (+.f64 n n)))))) (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 (PI.f64) n)))))
	33.1b	(neg.f64 (/.f64 (/.f64 (sqrt.f64 k) (neg.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)))) (.f64 (sqrt.f64 k) (/.f64 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2))) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2))))))

Compiler

Compiled 1038 to 775 computations (25.3% saved)

localize33.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 2 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)))
✓	0.2b	(.f64 (sqrt.f64 k) (/.f64 2 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2))))
	0.2b	(*.f64 (PI.f64) (+.f64 n n))
	0.3b	(pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2))

Compiler

Compiled 84 to 45 computations (46.4% saved)

series9.0ms (0.1%)

Counts

2 → 36

Calls

12 calls:

Time	Variable		Point	Expression
2.0ms	k	@	0	(.f64 (sqrt.f64 k) (/.f64 2 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2))))
1.0ms	k	@	0	(/.f64 2 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)))
1.0ms	n	@	inf	(.f64 (sqrt.f64 k) (/.f64 2 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2))))
1.0ms	k	@	-inf	(.f64 (sqrt.f64 k) (/.f64 2 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2))))
1.0ms	k	@	inf	(.f64 (sqrt.f64 k) (/.f64 2 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2))))

rewrite83.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

1410×	`bool.json-1`
1410×	`bool.json-2`
1366×	`rational.json-1`
1366×	`rational.json-2`
1366×	`rational.json-4`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	88
1	178	88
2	438	88
3	873	88
4	1822	88
5	4511	88

Stop Event

1×	node limit

Counts

2 → 62

Calls

Call 1

Inputs
(.f64 (sqrt.f64 k) (/.f64 2 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2))))
(/.f64 2 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (sqrt.f64 k) (/.f64 2 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 (sqrt.f64 k) (/.f64 2 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2))) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (*.f64 (sqrt.f64 k) (/.f64 2 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 k) (*.f64 1/2 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 2 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 2 (+.f64 (*.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)) (/.f64 1/2 (sqrt.f64 k))) (*.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)) (/.f64 1/2 (sqrt.f64 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 2 (*.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (*.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)) (/.f64 1/2 (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (*.f64 (*.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)) (/.f64 1/2 (sqrt.f64 k))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (sqrt.f64 k) (/.f64 2 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 4 (*.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)) (/.f64 2 (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 4 (+.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k)) (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 4 (*.f64 (*.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)) (/.f64 2 (sqrt.f64 k))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (*.f64 (sqrt.f64 k) 4) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 8 (+.f64 (*.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)) (/.f64 2 (sqrt.f64 k))) (*.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)) (/.f64 2 (sqrt.f64 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 8 (/.f64 (*.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)) 4) (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 8 (/.f64 (*.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)) 8) (*.f64 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simplify107.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

1438×	`rational.json-simplify-53`
1212×	`rational.json-simplify-51`
1074×	`rational.json-simplify-35`
960×	`rational.json-simplify-49`
898×	`rational.json-simplify-43`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	252	5984
1	674	5874
2	1792	5824
3	4876	5726

Stop Event

1×	node limit

Counts

98 → 120

Calls

Call 1

Inputs
(.f64 2 (.f64 (sqrt.f64 k) (/.f64 1 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))))))))
(.f64 2 (.f64 (sqrt.f64 k) (/.f64 1 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))))))))
(.f64 2 (.f64 (sqrt.f64 k) (/.f64 1 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))))))))
(.f64 2 (.f64 (sqrt.f64 k) (/.f64 1 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))))))))
(.f64 2 (.f64 (sqrt.f64 k) (/.f64 1 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64))))))))))
(.f64 2 (.f64 (sqrt.f64 k) (/.f64 1 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64))))))))))
(.f64 2 (.f64 (sqrt.f64 k) (/.f64 1 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64))))))))))
(.f64 2 (.f64 (sqrt.f64 k) (/.f64 1 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64))))))))))
(.f64 2 (.f64 (sqrt.f64 k) (/.f64 1 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64))))))))))
(.f64 2 (.f64 (sqrt.f64 k) (/.f64 1 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64))))))))))
(.f64 2 (.f64 (sqrt.f64 k) (/.f64 1 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64))))))))))
(.f64 2 (.f64 (sqrt.f64 k) (/.f64 1 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64))))))))))
(/.f64 2 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))))))
(/.f64 2 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))))))
(/.f64 2 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))))))
(/.f64 2 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))))))
(/.f64 2 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64))))))))
(/.f64 2 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64))))))))
(/.f64 2 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64))))))))
(/.f64 2 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64))))))))
(/.f64 2 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64))))))))
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(/.f64 2 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (.f64 n (PI.f64))))))))
(/.f64 2 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (.f64 n (PI.f64))))))))
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(/.f64 2 (exp.f64 (.f64 1/2 (.f64 (+.f64 1 (.f64 -1 k)) (log.f64 (.f64 2 (*.f64 n (PI.f64))))))))
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(/.f64 2 (.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k)) 1))
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(/.f64 4 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)) (/.f64 2 (sqrt.f64 k))))
(/.f64 4 (+.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k)) (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k))))
(/.f64 4 (.f64 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)) (/.f64 2 (sqrt.f64 k))) 1))
(/.f64 (/.f64 (.f64 (sqrt.f64 k) 4) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2))) 2)
(/.f64 8 (+.f64 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)) (/.f64 2 (sqrt.f64 k))) (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)) (/.f64 2 (sqrt.f64 k)))))
(/.f64 8 (/.f64 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)) 4) (sqrt.f64 k)))
(/.f64 8 (/.f64 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)) 8) (*.f64 (sqrt.f64 k) 2)))
(/.f64 (.f64 (sqrt.f64 k) 2) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)))
(/.f64 (.f64 (sqrt.f64 k) 4) (.f64 2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2))))
(/.f64 (/.f64 8 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k))) 4)
(/.f64 (.f64 2 (.f64 (sqrt.f64 k) 4)) (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)) 4))
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(/.f64 (.f64 2 (/.f64 8 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k)))) 8)
(/.f64 (.f64 (sqrt.f64 k) 1/2) (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)) 1/4))
(/.f64 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2))) 1/2)
(/.f64 (neg.f64 (sqrt.f64 k)) (neg.f64 (.f64 1/2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)))))
(/.f64 (neg.f64 (sqrt.f64 k)) (.f64 (neg.f64 (.f64 1/2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)))) 1))
(/.f64 (+.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k)) (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k))) (.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k)) (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k))))
(/.f64 (+.f64 (.f64 2 (/.f64 8 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k)))) (.f64 2 (/.f64 8 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k))))) 16)
(/.f64 (+.f64 (neg.f64 (sqrt.f64 k)) (neg.f64 (sqrt.f64 k))) (+.f64 (neg.f64 (.f64 1/2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)))) (neg.f64 (.f64 1/2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2))))))
(/.f64 (/.f64 (.f64 2 (.f64 (sqrt.f64 k) 4)) (.f64 1/2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)))) 8)
(/.f64 (/.f64 (sqrt.f64 k) 1/2) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)))
(/.f64 (/.f64 (sqrt.f64 k) (.f64 2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)))) 1/4)
(/.f64 (/.f64 (.f64 (sqrt.f64 k) 2) 1/2) (.f64 2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2))))
(/.f64 (/.f64 (.f64 (sqrt.f64 k) 2) (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)) 4)) 1/4)
(/.f64 (neg.f64 (.f64 (sqrt.f64 k) 2)) (neg.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2))))
(/.f64 (neg.f64 (neg.f64 (sqrt.f64 k))) (.f64 1/2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2))))
(/.f64 (+.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k)) (.f64 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)) (/.f64 1/2 (sqrt.f64 k))) 2)) (.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k)) (.f64 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)) (/.f64 1/2 (sqrt.f64 k))) 2)))
(/.f64 (+.f64 (.f64 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)) (/.f64 1/2 (sqrt.f64 k))) 2) (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k))) (.f64 (.f64 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)) (/.f64 1/2 (sqrt.f64 k))) 2) (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k))))
(/.f64 (+.f64 (.f64 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)) (/.f64 1/2 (sqrt.f64 k))) 2) (.f64 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)) (/.f64 1/2 (sqrt.f64 k))) 2)) (.f64 (.f64 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)) (/.f64 1/2 (sqrt.f64 k))) 2) (.f64 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)) (/.f64 1/2 (sqrt.f64 k))) 2)))
(+.f64 (/.f64 2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2))) 0)
(+.f64 0 (/.f64 2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2))))
(+.f64 (/.f64 1 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2))) (/.f64 1 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2))))
(-.f64 (/.f64 2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2))) 0)
(.f64 2 (/.f64 1 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2))))
(.f64 1 (/.f64 2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2))))
(.f64 1/2 (/.f64 4 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2))))
(.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)) (/.f64 1 (.f64 (.f64 1/2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2))) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)))))
(.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)) (/.f64 1/2 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)) (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)) 1/4))))
(.f64 (/.f64 2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2))) 1)
(.f64 4 (/.f64 (/.f64 2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2))) 4))
(.f64 (.f64 2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2))) (/.f64 1/2 (.f64 (.f64 1/2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2))) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)))))
(.f64 (/.f64 4 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2))) 1/2)
(.f64 (.f64 1/2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2))) (/.f64 2 (.f64 (.f64 1/2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2))) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)))))
(.f64 (.f64 1/2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2))) (/.f64 1 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)) (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)) 1/4))))
(.f64 (.f64 2 (/.f64 4 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)))) 1/4)
(.f64 (/.f64 1 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2))) 2)
(.f64 1/4 (/.f64 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)) 4) (.f64 (.f64 1/2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2))) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)))))
(.f64 1/4 (/.f64 (.f64 2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2))) (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)) (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)) 1/4))))
(.f64 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)) 1/4) (/.f64 2 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)) (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)) 1/4))))
(neg.f64 (/.f64 -2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2))))

Outputs
(.f64 2 (.f64 (sqrt.f64 k) (/.f64 1 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))))))))
(.f64 2 (.f64 (sqrt.f64 k) (exp.f64 (neg.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))))))))
(.f64 (sqrt.f64 k) (.f64 2 (exp.f64 (neg.f64 (.f64 (-.f64 1 k) (.f64 1/2 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))))))))
(.f64 2 (.f64 (sqrt.f64 k) (exp.f64 (.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))) -1/2))))
(.f64 2 (/.f64 (sqrt.f64 k) (exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)) (.f64 1/2 (-.f64 1 k))))))
(.f64 2 (.f64 (sqrt.f64 k) (/.f64 1 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))))))))
(.f64 2 (.f64 (sqrt.f64 k) (exp.f64 (neg.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))))))))
(.f64 (sqrt.f64 k) (.f64 2 (exp.f64 (neg.f64 (.f64 (-.f64 1 k) (.f64 1/2 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))))))))
(.f64 2 (.f64 (sqrt.f64 k) (exp.f64 (.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))) -1/2))))
(.f64 2 (/.f64 (sqrt.f64 k) (exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)) (.f64 1/2 (-.f64 1 k))))))
(.f64 2 (.f64 (sqrt.f64 k) (/.f64 1 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))))))))
(.f64 2 (.f64 (sqrt.f64 k) (exp.f64 (neg.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))))))))
(.f64 (sqrt.f64 k) (.f64 2 (exp.f64 (neg.f64 (.f64 (-.f64 1 k) (.f64 1/2 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))))))))
(.f64 2 (.f64 (sqrt.f64 k) (exp.f64 (.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))) -1/2))))
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(/.f64 (/.f64 (sqrt.f64 k) 1/2) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)))
(.f64 (sqrt.f64 k) (/.f64 2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 1/2 (-.f64 1 k)))))
(/.f64 2 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k)))
(.f64 (sqrt.f64 k) (/.f64 2 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (.f64 1/2 (-.f64 1 k)))))
(/.f64 (.f64 2 (sqrt.f64 k)) (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (.f64 1/2 (-.f64 1 k))))
(/.f64 (/.f64 (sqrt.f64 k) (.f64 2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)))) 1/4)
(.f64 (sqrt.f64 k) (/.f64 2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 1/2 (-.f64 1 k)))))
(/.f64 2 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k)))
(.f64 (sqrt.f64 k) (/.f64 2 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (.f64 1/2 (-.f64 1 k)))))
(/.f64 (.f64 2 (sqrt.f64 k)) (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (.f64 1/2 (-.f64 1 k))))
(/.f64 (/.f64 (.f64 (sqrt.f64 k) 2) 1/2) (.f64 2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2))))
(.f64 (sqrt.f64 k) (/.f64 2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 1/2 (-.f64 1 k)))))
(/.f64 2 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k)))
(.f64 (sqrt.f64 k) (/.f64 2 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (.f64 1/2 (-.f64 1 k)))))
(/.f64 (.f64 2 (sqrt.f64 k)) (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (.f64 1/2 (-.f64 1 k))))
(/.f64 (/.f64 (.f64 (sqrt.f64 k) 2) (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)) 4)) 1/4)
(.f64 (sqrt.f64 k) (/.f64 2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 1/2 (-.f64 1 k)))))
(/.f64 2 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k)))
(.f64 (sqrt.f64 k) (/.f64 2 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (.f64 1/2 (-.f64 1 k)))))
(/.f64 (.f64 2 (sqrt.f64 k)) (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (.f64 1/2 (-.f64 1 k))))
(/.f64 (neg.f64 (.f64 (sqrt.f64 k) 2)) (neg.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2))))
(.f64 (sqrt.f64 k) (/.f64 2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 1/2 (-.f64 1 k)))))
(/.f64 2 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k)))
(.f64 (sqrt.f64 k) (/.f64 2 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (.f64 1/2 (-.f64 1 k)))))
(/.f64 (.f64 2 (sqrt.f64 k)) (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (.f64 1/2 (-.f64 1 k))))
(/.f64 (neg.f64 (neg.f64 (sqrt.f64 k))) (.f64 1/2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2))))
(.f64 (sqrt.f64 k) (/.f64 2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 1/2 (-.f64 1 k)))))
(/.f64 2 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k)))
(.f64 (sqrt.f64 k) (/.f64 2 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (.f64 1/2 (-.f64 1 k)))))
(/.f64 (.f64 2 (sqrt.f64 k)) (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (.f64 1/2 (-.f64 1 k))))
(/.f64 (+.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k)) (.f64 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)) (/.f64 1/2 (sqrt.f64 k))) 2)) (.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k)) (.f64 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)) (/.f64 1/2 (sqrt.f64 k))) 2)))
(.f64 (sqrt.f64 k) (/.f64 2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 1/2 (-.f64 1 k)))))
(/.f64 2 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k)))
(.f64 (sqrt.f64 k) (/.f64 2 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (.f64 1/2 (-.f64 1 k)))))
(/.f64 (.f64 2 (sqrt.f64 k)) (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (.f64 1/2 (-.f64 1 k))))
(/.f64 (+.f64 (.f64 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)) (/.f64 1/2 (sqrt.f64 k))) 2) (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k))) (.f64 (.f64 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)) (/.f64 1/2 (sqrt.f64 k))) 2) (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k))))
(.f64 (sqrt.f64 k) (/.f64 2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 1/2 (-.f64 1 k)))))
(/.f64 2 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k)))
(.f64 (sqrt.f64 k) (/.f64 2 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (.f64 1/2 (-.f64 1 k)))))
(/.f64 (.f64 2 (sqrt.f64 k)) (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (.f64 1/2 (-.f64 1 k))))
(/.f64 (+.f64 (.f64 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)) (/.f64 1/2 (sqrt.f64 k))) 2) (.f64 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)) (/.f64 1/2 (sqrt.f64 k))) 2)) (.f64 (.f64 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)) (/.f64 1/2 (sqrt.f64 k))) 2) (.f64 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)) (/.f64 1/2 (sqrt.f64 k))) 2)))
(.f64 (sqrt.f64 k) (/.f64 2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 1/2 (-.f64 1 k)))))
(/.f64 2 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k)))
(.f64 (sqrt.f64 k) (/.f64 2 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (.f64 1/2 (-.f64 1 k)))))
(/.f64 (.f64 2 (sqrt.f64 k)) (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (.f64 1/2 (-.f64 1 k))))
(+.f64 (/.f64 2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2))) 0)
(/.f64 2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 1/2 (-.f64 1 k))))
(/.f64 2 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (*.f64 1/2 (-.f64 1 k))))
(+.f64 0 (/.f64 2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2))))
(/.f64 2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 1/2 (-.f64 1 k))))
(/.f64 2 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (*.f64 1/2 (-.f64 1 k))))
(+.f64 (/.f64 1 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2))) (/.f64 1 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2))))
(/.f64 2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 1/2 (-.f64 1 k))))
(/.f64 2 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (*.f64 1/2 (-.f64 1 k))))
(-.f64 (/.f64 2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2))) 0)
(/.f64 2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 1/2 (-.f64 1 k))))
(/.f64 2 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (*.f64 1/2 (-.f64 1 k))))
(.f64 2 (/.f64 1 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2))))
(/.f64 2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 1/2 (-.f64 1 k))))
(/.f64 2 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (*.f64 1/2 (-.f64 1 k))))
(.f64 1 (/.f64 2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2))))
(/.f64 2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 1/2 (-.f64 1 k))))
(/.f64 2 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (*.f64 1/2 (-.f64 1 k))))
(.f64 1/2 (/.f64 4 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2))))
(/.f64 2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 1/2 (-.f64 1 k))))
(/.f64 2 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (*.f64 1/2 (-.f64 1 k))))
(.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)) (/.f64 1 (.f64 (.f64 1/2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2))) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)))))
(/.f64 2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 1/2 (-.f64 1 k))))
(/.f64 2 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (*.f64 1/2 (-.f64 1 k))))
(.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)) (/.f64 1/2 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)) (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)) 1/4))))
(/.f64 2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 1/2 (-.f64 1 k))))
(/.f64 2 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (*.f64 1/2 (-.f64 1 k))))
(.f64 (/.f64 2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2))) 1)
(/.f64 2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 1/2 (-.f64 1 k))))
(/.f64 2 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (*.f64 1/2 (-.f64 1 k))))
(.f64 4 (/.f64 (/.f64 2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2))) 4))
(/.f64 2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 1/2 (-.f64 1 k))))
(/.f64 2 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (*.f64 1/2 (-.f64 1 k))))
(.f64 (.f64 2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2))) (/.f64 1/2 (.f64 (.f64 1/2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2))) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)))))
(/.f64 2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 1/2 (-.f64 1 k))))
(/.f64 2 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (*.f64 1/2 (-.f64 1 k))))
(.f64 (/.f64 4 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2))) 1/2)
(/.f64 2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 1/2 (-.f64 1 k))))
(/.f64 2 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (*.f64 1/2 (-.f64 1 k))))
(.f64 (.f64 1/2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2))) (/.f64 2 (.f64 (.f64 1/2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2))) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)))))
(/.f64 2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 1/2 (-.f64 1 k))))
(/.f64 2 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (*.f64 1/2 (-.f64 1 k))))
(.f64 (.f64 1/2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2))) (/.f64 1 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)) (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)) 1/4))))
(/.f64 2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 1/2 (-.f64 1 k))))
(/.f64 2 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (*.f64 1/2 (-.f64 1 k))))
(.f64 (.f64 2 (/.f64 4 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)))) 1/4)
(/.f64 2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 1/2 (-.f64 1 k))))
(/.f64 2 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (*.f64 1/2 (-.f64 1 k))))
(.f64 (/.f64 1 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2))) 2)
(/.f64 2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 1/2 (-.f64 1 k))))
(/.f64 2 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (*.f64 1/2 (-.f64 1 k))))
(.f64 1/4 (/.f64 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)) 4) (.f64 (.f64 1/2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2))) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)))))
(/.f64 2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 1/2 (-.f64 1 k))))
(/.f64 2 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (*.f64 1/2 (-.f64 1 k))))
(.f64 1/4 (/.f64 (.f64 2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2))) (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)) (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)) 1/4))))
(/.f64 2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 1/2 (-.f64 1 k))))
(/.f64 2 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (*.f64 1/2 (-.f64 1 k))))
(.f64 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)) 1/4) (/.f64 2 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)) (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)) 1/4))))
(/.f64 2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 1/2 (-.f64 1 k))))
(/.f64 2 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (*.f64 1/2 (-.f64 1 k))))
(neg.f64 (/.f64 -2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2))))
(/.f64 2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 1/2 (-.f64 1 k))))
(/.f64 2 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (*.f64 1/2 (-.f64 1 k))))

localize39.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(*.f64 (PI.f64) n)
✓	0.3b	(.f64 (/.f64 4 (sqrt.f64 k)) (/.f64 1 (/.f64 4 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)))))
✓	0.3b	(pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2))
✓	0.3b	(/.f64 4 (sqrt.f64 k))

Compiler

Compiled 90 to 60 computations (33.3% saved)

series4.0ms (0%)

Counts

4 → 48

Calls

18 calls:

Time	Variable		Point	Expression
0.0ms	k	@	0	(.f64 (/.f64 4 (sqrt.f64 k)) (/.f64 1 (/.f64 4 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)))))
0.0ms	k	@	-inf	(/.f64 4 (sqrt.f64 k))
0.0ms	k	@	0	(/.f64 4 (sqrt.f64 k))
0.0ms	k	@	-inf	(.f64 (/.f64 4 (sqrt.f64 k)) (/.f64 1 (/.f64 4 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)))))
0.0ms	k	@	inf	(.f64 (/.f64 4 (sqrt.f64 k)) (/.f64 1 (/.f64 4 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)))))

rewrite98.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

1698×	`rational.json-simplify-35`
1268×	`bool.json-1`
1268×	`bool.json-2`
1222×	`rational.json-1`
1222×	`rational.json-2`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	21	108
1	214	108
2	550	108
3	1216	96
4	3704	96

Stop Event

1×	node limit

Counts

4 → 218

Calls

Call 1

Inputs
(/.f64 4 (sqrt.f64 k))
(pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2))
(.f64 (/.f64 4 (sqrt.f64 k)) (/.f64 1 (/.f64 4 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)))))
(*.f64 (PI.f64) n)

Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 4 (sqrt.f64 k)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 4 (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 4 (sqrt.f64 k)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 4 (sqrt.f64 k)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 2 (/.f64 (/.f64 4 (sqrt.f64 k)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (/.f64 4 (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1/2 (.f64 (/.f64 4 (sqrt.f64 k)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (/.f64 4 (sqrt.f64 k)) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (/.f64 4 (sqrt.f64 k)) 2) 2)))) (#(struct:change #<rule egg-rr> (2) ((x not (not (/.f64 4 (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x and (/.f64 4 (sqrt.f64 k)) (/.f64 4 (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x or (/.f64 4 (sqrt.f64 k)) (/.f64 4 (sqrt.f64 k)))))))
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((#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (PI.f64) n) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (.f64 (PI.f64) n))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (PI.f64) (.f64 n 1/2)) (.f64 (PI.f64) (.f64 n 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (.f64 (PI.f64) n) 0)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (PI.f64) n) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 2 (.f64 (PI.f64) n)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 n (.f64 4 (PI.f64))) 4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 2 (.f64 n (.f64 4 (PI.f64)))) 8)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 2 (.f64 2 (.f64 n (.f64 4 (PI.f64))))) 16)))) (#(struct:change #<rule egg-rr> (2) ((x not (not (.f64 (PI.f64) n)))))) (#(struct:change #<rule egg-rr> (2) ((x and (.f64 (PI.f64) n) (.f64 (PI.f64) n))))) (#(struct:change #<rule egg-rr> (2) ((x or (.f64 (PI.f64) n) (.f64 (PI.f64) n))))))

simplify149.0ms (1%)

Algorithm

1×	egg-herbie

Rules

1380×	`rational.json-simplify-35`
1280×	`rational.json-simplify-44`
1126×	`rational.json-simplify-47`
842×	`rational.json-simplify-51`
796×	`rational.json-simplify-55`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	512	11436
1	1473	11034
2	6284	10972

Stop Event

1×	node limit

Counts

266 → 269

Calls

Call 1

Inputs
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64)))))))
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(/.f64 (+.f64 (/.f64 (/.f64 4 (sqrt.f64 k)) (.f64 2 (/.f64 4 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2))))) (/.f64 (/.f64 4 (sqrt.f64 k)) (.f64 2 (/.f64 4 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)))))) 1)
(/.f64 (+.f64 (/.f64 (.f64 4 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2))) (.f64 (sqrt.f64 k) 1/4)) (/.f64 (.f64 4 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2))) (.f64 (sqrt.f64 k) 1/4))) 32)
(/.f64 (+.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)) (.f64 (sqrt.f64 k) 2)) (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)) (.f64 (sqrt.f64 k) 2))) 1)
(/.f64 (+.f64 (neg.f64 (.f64 (/.f64 4 (sqrt.f64 k)) 2)) (neg.f64 (.f64 (/.f64 4 (sqrt.f64 k)) 2))) (.f64 2 (neg.f64 (.f64 2 (/.f64 4 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)))))))
(/.f64 (+.f64 (neg.f64 (.f64 4 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)))) (neg.f64 (.f64 4 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2))))) (+.f64 (neg.f64 (.f64 4 (sqrt.f64 k))) (neg.f64 (.f64 4 (sqrt.f64 k)))))
(/.f64 (+.f64 (/.f64 2 (/.f64 4 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)))) (/.f64 2 (/.f64 4 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2))))) (sqrt.f64 k))
(/.f64 (+.f64 (.f64 2 (.f64 4 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k)))) (.f64 2 (.f64 4 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k))))) 16)
(/.f64 (+.f64 (.f64 2 (/.f64 16 (sqrt.f64 k))) (.f64 2 (/.f64 16 (sqrt.f64 k)))) (.f64 2 (.f64 2 (.f64 4 (/.f64 4 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)))))))
(/.f64 (+.f64 (.f64 2 (/.f64 8 (sqrt.f64 k))) (.f64 2 (/.f64 8 (sqrt.f64 k)))) (.f64 2 (.f64 4 (/.f64 4 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2))))))
(/.f64 (+.f64 (.f64 2 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)) (/.f64 8 (sqrt.f64 k)))) (.f64 2 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)) (/.f64 8 (sqrt.f64 k))))) 32)
(/.f64 (+.f64 (.f64 2 (/.f64 -4 (sqrt.f64 k))) (.f64 2 (/.f64 -4 (sqrt.f64 k)))) (.f64 2 (.f64 2 (neg.f64 (/.f64 4 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)))))))
(/.f64 (+.f64 (.f64 2 (neg.f64 (/.f64 4 (sqrt.f64 k)))) (.f64 2 (neg.f64 (/.f64 4 (sqrt.f64 k))))) (.f64 2 (.f64 2 (neg.f64 (/.f64 4 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)))))))
(/.f64 (+.f64 (/.f64 32 (/.f64 4 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)))) (/.f64 32 (/.f64 4 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2))))) (.f64 2 (.f64 2 (*.f64 4 (sqrt.f64 k)))))
(/.f64 (+.f64 (/.f64 (.f64 4 (/.f64 4 (sqrt.f64 k))) (/.f64 4 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)))) (/.f64 (.f64 4 (/.f64 4 (sqrt.f64 k))) (/.f64 4 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2))))) 8)
(/.f64 (+.f64 (/.f64 -8 (/.f64 4 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)))) (/.f64 -8 (/.f64 4 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2))))) (.f64 2 (.f64 2 (neg.f64 (sqrt.f64 k)))))
(/.f64 (+.f64 (/.f64 -8 (/.f64 4 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)))) (/.f64 -8 (/.f64 4 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2))))) (.f64 2 (neg.f64 (.f64 (sqrt.f64 k) 2))))
(/.f64 (+.f64 (/.f64 16 (.f64 (sqrt.f64 k) 1/2)) (/.f64 16 (.f64 (sqrt.f64 k) 1/2))) (.f64 2 (.f64 2 (.f64 4 (/.f64 4 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)))))))
(/.f64 (+.f64 (/.f64 (neg.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2))) (.f64 (sqrt.f64 k) 1/4)) (/.f64 (neg.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2))) (.f64 (sqrt.f64 k) 1/4))) -8)
(/.f64 (+.f64 (/.f64 -4 (.f64 (sqrt.f64 k) 1/2)) (/.f64 -4 (.f64 (sqrt.f64 k) 1/2))) (.f64 2 (.f64 2 (neg.f64 (/.f64 4 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)))))))
(/.f64 (+.f64 (/.f64 -4 (.f64 (sqrt.f64 k) 1/2)) (/.f64 -4 (.f64 (sqrt.f64 k) 1/2))) (.f64 2 (neg.f64 (.f64 2 (/.f64 4 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)))))))
(/.f64 (+.f64 (/.f64 (.f64 4 (/.f64 4 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)))) (sqrt.f64 k)) (/.f64 (.f64 4 (/.f64 4 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)))) (sqrt.f64 k))) (.f64 2 (.f64 (/.f64 4 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2))) (/.f64 4 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2))))))
(/.f64 (+.f64 (/.f64 (sqrt.f64 k) (.f64 4 (/.f64 4 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2))))) (/.f64 (sqrt.f64 k) (.f64 4 (/.f64 4 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)))))) (.f64 2 (.f64 (sqrt.f64 k) (.f64 1/4 (.f64 (sqrt.f64 k) 1/4)))))
(/.f64 (+.f64 (/.f64 (/.f64 16 (sqrt.f64 k)) 2) (/.f64 (/.f64 16 (sqrt.f64 k)) 2)) (.f64 4 (/.f64 4 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)))))
(/.f64 (+.f64 (/.f64 (/.f64 8 (sqrt.f64 k)) (/.f64 4 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)))) (/.f64 (/.f64 8 (sqrt.f64 k)) (/.f64 4 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2))))) 4)
(/.f64 (+.f64 (neg.f64 (/.f64 16 (sqrt.f64 k))) (neg.f64 (/.f64 16 (sqrt.f64 k)))) (+.f64 (neg.f64 (.f64 4 (/.f64 4 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2))))) (neg.f64 (.f64 4 (/.f64 4 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)))))))
(/.f64 (+.f64 (neg.f64 (/.f64 8 (sqrt.f64 k))) (neg.f64 (/.f64 8 (sqrt.f64 k)))) (.f64 2 (neg.f64 (.f64 2 (/.f64 4 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)))))))
(/.f64 (+.f64 (neg.f64 (/.f64 -4 (sqrt.f64 k))) (neg.f64 (/.f64 -4 (sqrt.f64 k)))) (.f64 2 (/.f64 4 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)))))
(/.f64 (+.f64 (neg.f64 (neg.f64 (/.f64 4 (sqrt.f64 k)))) (neg.f64 (neg.f64 (/.f64 4 (sqrt.f64 k))))) (.f64 2 (/.f64 4 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)))))
(+.f64 (*.f64 (PI.f64) n) 0)
(+.f64 0 (*.f64 (PI.f64) n))
(+.f64 (.f64 (PI.f64) (.f64 n 1/2)) (.f64 (PI.f64) (.f64 n 1/2)))
(-.f64 (*.f64 (PI.f64) n) 0)
(/.f64 (*.f64 (PI.f64) n) 1)
(/.f64 (.f64 2 (.f64 (PI.f64) n)) 2)
(/.f64 (.f64 n (.f64 4 (PI.f64))) 4)
(/.f64 (.f64 2 (.f64 n (*.f64 4 (PI.f64)))) 8)
(/.f64 (.f64 2 (.f64 2 (.f64 n (.f64 4 (PI.f64))))) 16)

Outputs
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(exp.f64 (.f64 (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))) (*.f64 1/2 (-.f64 1 k))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(exp.f64 (.f64 (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))) (*.f64 1/2 (-.f64 1 k))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(exp.f64 (.f64 (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))) (*.f64 1/2 (-.f64 1 k))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(exp.f64 (.f64 (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))) (*.f64 1/2 (-.f64 1 k))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (.f64 -1 (log.f64 (/.f64 1 n)))))))
(exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n)))) (*.f64 1/2 (-.f64 1 k))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (.f64 -1 (log.f64 (/.f64 1 n)))))))
(exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n)))) (*.f64 1/2 (-.f64 1 k))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (.f64 -1 (log.f64 (/.f64 1 n)))))))
(exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n)))) (*.f64 1/2 (-.f64 1 k))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (.f64 -1 (log.f64 (/.f64 1 n)))))))
(exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n)))) (*.f64 1/2 (-.f64 1 k))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 (PI.f64) -2))))))
(exp.f64 (.f64 (-.f64 1 k) (.f64 1/2 (+.f64 (neg.f64 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 (PI.f64) -2))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 (PI.f64) -2))))))
(exp.f64 (.f64 (-.f64 1 k) (.f64 1/2 (+.f64 (neg.f64 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 (PI.f64) -2))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 (PI.f64) -2))))))
(exp.f64 (.f64 (-.f64 1 k) (.f64 1/2 (+.f64 (neg.f64 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 (PI.f64) -2))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 (PI.f64) -2))))))
(exp.f64 (.f64 (-.f64 1 k) (.f64 1/2 (+.f64 (neg.f64 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 (PI.f64) -2))))))
(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))))
(+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 (.f64 n (PI.f64))))) (.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))))
(+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (.f64 (.f64 k (.f64 (log.f64 (.f64 (PI.f64) (.f64 n 2))) (sqrt.f64 2))) (.f64 (sqrt.f64 (*.f64 n (PI.f64))) -1/2)))
(+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 -1/2 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (.f64 (sqrt.f64 2) k)))))
(.f64 (sqrt.f64 (.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (.f64 -1/2 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (.f64 (sqrt.f64 2) k)))))
(+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 (.f64 n (PI.f64))))) (+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (.f64 1/8 (.f64 (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 2) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2))) (sqrt.f64 (.f64 n (PI.f64)))))))
(+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (+.f64 (.f64 (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 2) (pow.f64 (log.f64 (.f64 (PI.f64) (.f64 n 2))) 2))) (.f64 (sqrt.f64 (.f64 n (PI.f64))) 1/8)) (.f64 (.f64 k (.f64 (log.f64 (.f64 (PI.f64) (.f64 n 2))) (sqrt.f64 2))) (.f64 (sqrt.f64 (.f64 n (PI.f64))) -1/2))))
(+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (+.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 -1/2 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (.f64 (sqrt.f64 2) k)))) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (.f64 (pow.f64 k 2) (.f64 (sqrt.f64 2) (pow.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) 2))) 1/8))))
(+.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 -1/2 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (.f64 (sqrt.f64 2) k)))) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (.f64 (.f64 (pow.f64 k 2) (.f64 (sqrt.f64 2) (pow.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) 2))) 1/8))))
(+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 (.f64 n (PI.f64))))) (+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (+.f64 (.f64 1/8 (.f64 (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 2) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2))) (sqrt.f64 (.f64 n (PI.f64))))) (.f64 -1/48 (.f64 (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 3) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 3))) (sqrt.f64 (*.f64 n (PI.f64))))))))
(+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (+.f64 (+.f64 (.f64 (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 2) (pow.f64 (log.f64 (.f64 (PI.f64) (.f64 n 2))) 2))) (.f64 (sqrt.f64 (.f64 n (PI.f64))) 1/8)) (.f64 (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 3) (pow.f64 (log.f64 (.f64 (PI.f64) (.f64 n 2))) 3))) (.f64 (sqrt.f64 (.f64 n (PI.f64))) -1/48))) (.f64 (.f64 k (.f64 (log.f64 (.f64 (PI.f64) (.f64 n 2))) (sqrt.f64 2))) (.f64 (sqrt.f64 (*.f64 n (PI.f64))) -1/2))))
(+.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 -1/2 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (.f64 (sqrt.f64 2) k)))) (+.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (.f64 (pow.f64 k 2) (.f64 (sqrt.f64 2) (pow.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) 2))) 1/8)) (+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (.f64 (pow.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) 3) (.f64 (pow.f64 k 3) (sqrt.f64 2))) -1/48)))))
(+.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 -1/2 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (.f64 (sqrt.f64 2) k)))) (+.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (.f64 (pow.f64 k 2) (.f64 (sqrt.f64 2) (pow.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) 2))) 1/8)) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (.f64 (.f64 (pow.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) 3) (.f64 (pow.f64 k 3) (sqrt.f64 2))) -1/48)))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (.f64 n (PI.f64)))))))
(exp.f64 (.f64 (-.f64 1 k) (.f64 (log.f64 (.f64 (PI.f64) (.f64 n 2))) 1/2)))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (.f64 n (PI.f64)))))))
(exp.f64 (.f64 (-.f64 1 k) (.f64 (log.f64 (.f64 (PI.f64) (.f64 n 2))) 1/2)))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (.f64 n (PI.f64)))))))
(exp.f64 (.f64 (-.f64 1 k) (.f64 (log.f64 (.f64 (PI.f64) (.f64 n 2))) 1/2)))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (.f64 n (PI.f64)))))))
(exp.f64 (.f64 (-.f64 1 k) (.f64 (log.f64 (.f64 (PI.f64) (.f64 n 2))) 1/2)))
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(/.f64 (neg.f64 (.f64 4 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)))) (neg.f64 (*.f64 4 (sqrt.f64 k))))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (neg.f64 (/.f64 16 (sqrt.f64 k))) (neg.f64 (.f64 4 (/.f64 4 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2))))))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (neg.f64 (/.f64 8 (sqrt.f64 k))) (neg.f64 (.f64 2 (/.f64 4 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2))))))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (neg.f64 (/.f64 -4 (sqrt.f64 k))) (/.f64 4 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2))))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (neg.f64 (neg.f64 (/.f64 4 (sqrt.f64 k)))) (/.f64 4 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2))))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (+.f64 (/.f64 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)) 1/4) (sqrt.f64 k)) (/.f64 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)) 1/4) (sqrt.f64 k))) 1/2)
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (+.f64 (/.f64 (/.f64 4 (sqrt.f64 k)) (.f64 2 (/.f64 4 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2))))) (/.f64 (/.f64 4 (sqrt.f64 k)) (.f64 2 (/.f64 4 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)))))) 1)
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (+.f64 (/.f64 (.f64 4 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2))) (.f64 (sqrt.f64 k) 1/4)) (/.f64 (.f64 4 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2))) (.f64 (sqrt.f64 k) 1/4))) 32)
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (+.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)) (.f64 (sqrt.f64 k) 2)) (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)) (.f64 (sqrt.f64 k) 2))) 1)
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (+.f64 (neg.f64 (.f64 (/.f64 4 (sqrt.f64 k)) 2)) (neg.f64 (.f64 (/.f64 4 (sqrt.f64 k)) 2))) (.f64 2 (neg.f64 (.f64 2 (/.f64 4 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)))))))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (+.f64 (neg.f64 (.f64 4 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)))) (neg.f64 (.f64 4 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2))))) (+.f64 (neg.f64 (.f64 4 (sqrt.f64 k))) (neg.f64 (.f64 4 (sqrt.f64 k)))))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (+.f64 (/.f64 2 (/.f64 4 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)))) (/.f64 2 (/.f64 4 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2))))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (+.f64 (.f64 2 (.f64 4 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k)))) (.f64 2 (.f64 4 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k))))) 16)
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (+.f64 (.f64 2 (/.f64 16 (sqrt.f64 k))) (.f64 2 (/.f64 16 (sqrt.f64 k)))) (.f64 2 (.f64 2 (.f64 4 (/.f64 4 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)))))))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (+.f64 (.f64 2 (/.f64 8 (sqrt.f64 k))) (.f64 2 (/.f64 8 (sqrt.f64 k)))) (.f64 2 (.f64 4 (/.f64 4 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2))))))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (+.f64 (.f64 2 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)) (/.f64 8 (sqrt.f64 k)))) (.f64 2 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)) (/.f64 8 (sqrt.f64 k))))) 32)
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (+.f64 (.f64 2 (/.f64 -4 (sqrt.f64 k))) (.f64 2 (/.f64 -4 (sqrt.f64 k)))) (.f64 2 (.f64 2 (neg.f64 (/.f64 4 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)))))))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (+.f64 (.f64 2 (neg.f64 (/.f64 4 (sqrt.f64 k)))) (.f64 2 (neg.f64 (/.f64 4 (sqrt.f64 k))))) (.f64 2 (.f64 2 (neg.f64 (/.f64 4 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)))))))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (+.f64 (/.f64 32 (/.f64 4 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)))) (/.f64 32 (/.f64 4 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2))))) (.f64 2 (.f64 2 (*.f64 4 (sqrt.f64 k)))))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (+.f64 (/.f64 (.f64 4 (/.f64 4 (sqrt.f64 k))) (/.f64 4 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)))) (/.f64 (.f64 4 (/.f64 4 (sqrt.f64 k))) (/.f64 4 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2))))) 8)
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (+.f64 (/.f64 -8 (/.f64 4 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)))) (/.f64 -8 (/.f64 4 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2))))) (.f64 2 (.f64 2 (neg.f64 (sqrt.f64 k)))))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (+.f64 (/.f64 -8 (/.f64 4 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)))) (/.f64 -8 (/.f64 4 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2))))) (.f64 2 (neg.f64 (.f64 (sqrt.f64 k) 2))))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (+.f64 (/.f64 16 (.f64 (sqrt.f64 k) 1/2)) (/.f64 16 (.f64 (sqrt.f64 k) 1/2))) (.f64 2 (.f64 2 (.f64 4 (/.f64 4 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)))))))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (+.f64 (/.f64 (neg.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2))) (.f64 (sqrt.f64 k) 1/4)) (/.f64 (neg.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2))) (.f64 (sqrt.f64 k) 1/4))) -8)
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (+.f64 (/.f64 -4 (.f64 (sqrt.f64 k) 1/2)) (/.f64 -4 (.f64 (sqrt.f64 k) 1/2))) (.f64 2 (.f64 2 (neg.f64 (/.f64 4 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)))))))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (+.f64 (/.f64 -4 (.f64 (sqrt.f64 k) 1/2)) (/.f64 -4 (.f64 (sqrt.f64 k) 1/2))) (.f64 2 (neg.f64 (.f64 2 (/.f64 4 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)))))))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (+.f64 (/.f64 (.f64 4 (/.f64 4 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)))) (sqrt.f64 k)) (/.f64 (.f64 4 (/.f64 4 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)))) (sqrt.f64 k))) (.f64 2 (.f64 (/.f64 4 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2))) (/.f64 4 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2))))))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (+.f64 (/.f64 (sqrt.f64 k) (.f64 4 (/.f64 4 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2))))) (/.f64 (sqrt.f64 k) (.f64 4 (/.f64 4 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)))))) (.f64 2 (.f64 (sqrt.f64 k) (.f64 1/4 (.f64 (sqrt.f64 k) 1/4)))))
(/.f64 (sqrt.f64 k) (+.f64 (.f64 (.f64 2 (/.f64 4 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 1/2 (-.f64 1 k))))) (.f64 (sqrt.f64 k) (.f64 (sqrt.f64 k) 1/16))) (.f64 (.f64 2 (/.f64 4 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 1/2 (-.f64 1 k))))) (.f64 (sqrt.f64 k) (.f64 (sqrt.f64 k) 1/16)))))
(/.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 1/2 (-.f64 1 k))) (/.f64 16 (sqrt.f64 k))) (.f64 (sqrt.f64 k) (.f64 (sqrt.f64 k) 1/16)))
(/.f64 (+.f64 (/.f64 (/.f64 16 (sqrt.f64 k)) 2) (/.f64 (/.f64 16 (sqrt.f64 k)) 2)) (.f64 4 (/.f64 4 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)))))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (+.f64 (/.f64 (/.f64 8 (sqrt.f64 k)) (/.f64 4 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)))) (/.f64 (/.f64 8 (sqrt.f64 k)) (/.f64 4 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2))))) 4)
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (+.f64 (neg.f64 (/.f64 16 (sqrt.f64 k))) (neg.f64 (/.f64 16 (sqrt.f64 k)))) (+.f64 (neg.f64 (.f64 4 (/.f64 4 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2))))) (neg.f64 (.f64 4 (/.f64 4 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)))))))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (+.f64 (neg.f64 (/.f64 8 (sqrt.f64 k))) (neg.f64 (/.f64 8 (sqrt.f64 k)))) (.f64 2 (neg.f64 (.f64 2 (/.f64 4 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)))))))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (+.f64 (neg.f64 (/.f64 -4 (sqrt.f64 k))) (neg.f64 (/.f64 -4 (sqrt.f64 k)))) (.f64 2 (/.f64 4 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)))))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (+.f64 (neg.f64 (neg.f64 (/.f64 4 (sqrt.f64 k)))) (neg.f64 (neg.f64 (/.f64 4 (sqrt.f64 k))))) (.f64 2 (/.f64 4 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)))))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(+.f64 (*.f64 (PI.f64) n) 0)
(*.f64 n (PI.f64))
(+.f64 0 (*.f64 (PI.f64) n))
(*.f64 n (PI.f64))
(+.f64 (.f64 (PI.f64) (.f64 n 1/2)) (.f64 (PI.f64) (.f64 n 1/2)))
(+.f64 (.f64 n (.f64 1/2 (PI.f64))) (.f64 n (.f64 1/2 (PI.f64))))
(.f64 (.f64 1/2 n) (+.f64 (PI.f64) (PI.f64)))
(.f64 (PI.f64) (.f64 n 1))
(-.f64 (*.f64 (PI.f64) n) 0)
(*.f64 n (PI.f64))
(/.f64 (*.f64 (PI.f64) n) 1)
(*.f64 n (PI.f64))
(/.f64 (.f64 2 (.f64 (PI.f64) n)) 2)
(*.f64 n (PI.f64))
(/.f64 (.f64 n (.f64 4 (PI.f64))) 4)
(*.f64 n (PI.f64))
(/.f64 (.f64 2 (.f64 n (*.f64 4 (PI.f64)))) 8)
(*.f64 n (PI.f64))
(/.f64 (.f64 2 (.f64 2 (.f64 n (.f64 4 (PI.f64))))) 16)
(*.f64 n (PI.f64))

localize35.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (-.f64 1 k) (.f64 1/2 (log.f64 (.f64 (PI.f64) (.f64 2 n)))))
✓	0.2b	(/.f64 (exp.f64 (.f64 (-.f64 1 k) (.f64 1/2 (log.f64 (.f64 (PI.f64) (.f64 2 n)))))) (sqrt.f64 k))
✓	0.2b	(.f64 (PI.f64) (.f64 2 n))
✓	3.1b	(exp.f64 (.f64 (-.f64 1 k) (.f64 1/2 (log.f64 (.f64 (PI.f64) (.f64 2 n))))))

Compiler

Compiled 76 to 54 computations (28.9% saved)

series5.0ms (0%)

Counts

4 → 72

Calls

21 calls:

Time	Variable		Point	Expression
0.0ms	k	@	inf	(.f64 (-.f64 1 k) (.f64 1/2 (log.f64 (.f64 (PI.f64) (.f64 2 n)))))
0.0ms	k	@	0	(/.f64 (exp.f64 (.f64 (-.f64 1 k) (.f64 1/2 (log.f64 (.f64 (PI.f64) (.f64 2 n)))))) (sqrt.f64 k))
0.0ms	k	@	-inf	(/.f64 (exp.f64 (.f64 (-.f64 1 k) (.f64 1/2 (log.f64 (.f64 (PI.f64) (.f64 2 n)))))) (sqrt.f64 k))
0.0ms	k	@	0	(.f64 (-.f64 1 k) (.f64 1/2 (log.f64 (.f64 (PI.f64) (.f64 2 n)))))
0.0ms	k	@	-inf	(.f64 (-.f64 1 k) (.f64 1/2 (log.f64 (.f64 (PI.f64) (.f64 2 n)))))

rewrite113.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

1008×	`rational.json-simplify-50`
820×	`rational.json-simplify-35`
808×	`rational.json-simplify-1`
736×	`bool.json-1`
736×	`bool.json-2`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	144
1	191	144
2	493	144
3	1042	144
4	2261	144
5	6326	144

Stop Event

1×	node limit

Counts

4 → 75

Calls

Call 1

Inputs
(exp.f64 (.f64 (-.f64 1 k) (.f64 1/2 (log.f64 (.f64 (PI.f64) (.f64 2 n))))))
(.f64 (PI.f64) (.f64 2 n))
(/.f64 (exp.f64 (.f64 (-.f64 1 k) (.f64 1/2 (log.f64 (.f64 (PI.f64) (.f64 2 n)))))) (sqrt.f64 k))
(.f64 (-.f64 1 k) (.f64 1/2 (log.f64 (.f64 (PI.f64) (.f64 2 n)))))

Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (exp.f64 (.f64 1/2 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (exp.f64 (.f64 1/2 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 -1 (-.f64 (exp.f64 (.f64 1/2 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)))) -1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 (exp.f64 (.f64 1/2 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)))) 2) (/.f64 (exp.f64 (.f64 1/2 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 (exp.f64 (.f64 1/2 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)))) -1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (.f64 1/2 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 0 (neg.f64 (exp.f64 (.f64 1/2 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k))))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (exp.f64 (.f64 1/2 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1/2 (.f64 2 (exp.f64 (.f64 1/2 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k))))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 2 (/.f64 (exp.f64 (.f64 1/2 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (exp.f64 (.f64 1/2 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 2 (exp.f64 (.f64 1/2 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k))))) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (exp.f64 (.f64 1/2 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)))) 4) 1/4)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (neg.f64 (exp.f64 (.f64 1/2 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k))))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 -1 (neg.f64 (exp.f64 (.f64 1/2 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k))))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1/4 (.f64 (exp.f64 (.f64 1/2 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)))) 4))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (exp.f64 (.f64 1/2 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)))) 2) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (exp.f64 (.f64 1/2 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 2 (exp.f64 (.f64 1/2 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k))))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (exp.f64 (.f64 1/2 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)))) 4) 4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (exp.f64 (.f64 1/2 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k))))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 2 (.f64 (exp.f64 (.f64 1/2 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)))) 4)) 8)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (exp.f64 (.f64 1/2 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)))) -2) -2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 2 (.f64 2 (.f64 (exp.f64 (.f64 1/2 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)))) 4))) 16)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (.f64 (exp.f64 (.f64 1/2 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)))) 4)) -4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (neg.f64 (.f64 (exp.f64 (.f64 1/2 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)))) 4))) 4)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (neg.f64 (exp.f64 (.f64 1/2 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k))))))))) (#(struct:change #<rule egg-rr> (2) ((x not (not (exp.f64 (.f64 1/2 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k))))))))) (#(struct:change #<rule egg-rr> (2) ((x and (exp.f64 (.f64 1/2 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)))) (exp.f64 (.f64 1/2 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x or (exp.f64 (.f64 1/2 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)))) (exp.f64 (.f64 1/2 (.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)))))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (PI.f64) (+.f64 n n)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (.f64 (PI.f64) (+.f64 n n)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (PI.f64) n) (.f64 (PI.f64) n))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (.f64 (PI.f64) (+.f64 n n)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (PI.f64) (+.f64 n n)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (PI.f64) (.f64 n 4)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (PI.f64) (.f64 n 8)) 4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 2 (.f64 (PI.f64) (.f64 n 8))) 8)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 2 (.f64 2 (.f64 (PI.f64) (.f64 n 8)))) 16)))) (#(struct:change #<rule egg-rr> (2) ((x not (not (.f64 (PI.f64) (+.f64 n n))))))) (#(struct:change #<rule egg-rr> (2) ((x and (.f64 (PI.f64) (+.f64 n n)) (.f64 (PI.f64) (+.f64 n n)))))) (#(struct:change #<rule egg-rr> (2) ((x or (.f64 (PI.f64) (+.f64 n n)) (.f64 (PI.f64) (+.f64 n n)))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 (exp.f64 (.f64 1/2 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)))) (sqrt.f64 k)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 (exp.f64 (.f64 1/2 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)))) (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 -1 (-.f64 1 (/.f64 (exp.f64 (.f64 1/2 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)))) (neg.f64 (sqrt.f64 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 (exp.f64 (.f64 1/2 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)))) (.f64 2 (sqrt.f64 k))) (/.f64 (exp.f64 (.f64 1/2 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)))) (.f64 2 (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (exp.f64 (.f64 1/2 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)))) (sqrt.f64 k)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 0 (/.f64 (exp.f64 (.f64 1/2 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)))) (neg.f64 (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (/.f64 (exp.f64 (.f64 1/2 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)))) (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1/2 (.f64 2 (/.f64 (exp.f64 (.f64 1/2 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)))) (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 2 (/.f64 (exp.f64 (.f64 1/2 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)))) (.f64 2 (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 2 (.f64 (/.f64 1/2 (sqrt.f64 k)) (exp.f64 (.f64 1/2 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k))))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (exp.f64 (.f64 1/2 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)))) (/.f64 1 (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (exp.f64 (.f64 1/2 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)))) (sqrt.f64 k)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 2 (exp.f64 (.f64 1/2 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k))))) (/.f64 1/2 (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 2 (exp.f64 (.f64 1/2 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k))))) (.f64 1/2 (/.f64 1 (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 2 (/.f64 (exp.f64 (.f64 1/2 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)))) (sqrt.f64 k))) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (exp.f64 (.f64 1/2 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)))) 4) (/.f64 1 (.f64 (sqrt.f64 k) 4)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1 (sqrt.f64 k)) (exp.f64 (.f64 1/2 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (neg.f64 (exp.f64 (.f64 1/2 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k))))) (/.f64 -1 (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 -1 (/.f64 (exp.f64 (.f64 1/2 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)))) (neg.f64 (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1/2 (sqrt.f64 k)) (.f64 2 (exp.f64 (.f64 1/2 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k))))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 1/2 (/.f64 1 (sqrt.f64 k))) (.f64 2 (exp.f64 (.f64 1/2 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k))))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (exp.f64 (.f64 1/2 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)))) (neg.f64 (sqrt.f64 k))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (exp.f64 (.f64 1/2 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)))) (.f64 2 (sqrt.f64 k))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1 (.f64 (sqrt.f64 k) 4)) (.f64 (exp.f64 (.f64 1/2 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)))) 4))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 -1 (sqrt.f64 k)) (neg.f64 (exp.f64 (.f64 1/2 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k))))))))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (exp.f64 (.f64 1/2 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)))) (neg.f64 (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (/.f64 (sqrt.f64 k) (exp.f64 (.f64 1/2 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k))))) (neg.f64 (.f64 (/.f64 (sqrt.f64 k) (exp.f64 (.f64 1/2 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k))))) (/.f64 (sqrt.f64 k) (exp.f64 (.f64 1/2 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)))))))))))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (.f64 (exp.f64 (.f64 1/2 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)))) -2) (.f64 2 (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x not (not (/.f64 (exp.f64 (.f64 1/2 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)))) (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x and (/.f64 (exp.f64 (.f64 1/2 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)))) (sqrt.f64 k)) (/.f64 (exp.f64 (.f64 1/2 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)))) (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x or (/.f64 (exp.f64 (.f64 1/2 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)))) (sqrt.f64 k)) (/.f64 (exp.f64 (.f64 1/2 (.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)))) (sqrt.f64 k)))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 1/2 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (.f64 1/2 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 1/2 (.f64 1/2 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)))) (.f64 1/2 (.f64 1/2 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)) 4) (/.f64 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)) 4))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (.f64 1/2 (log.f64 (.f64 (PI.f64) (+.f64 n n)))) (.f64 1/2 (-.f64 1 k))) (.f64 (.f64 1/2 (log.f64 (.f64 (PI.f64) (+.f64 n n)))) (.f64 1/2 (-.f64 1 k))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (.f64 1/2 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 1/2 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (.f64 2 (-.f64 1 k))) 4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)) 4) 8)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 2 (.f64 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)) 4)) 16)))) (#(struct:change #<rule egg-rr> (2) ((x not (not (.f64 1/2 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x and (.f64 1/2 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k))) (.f64 1/2 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k))))))) (#(struct:change #<rule egg-rr> (2) ((x or (.f64 1/2 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k))) (.f64 1/2 (.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k))))))))

simplify155.0ms (1%)

Algorithm

1×	egg-herbie

Rules

1182×	`rational.json-simplify-43`
1166×	`rational.json-simplify-51`
940×	`rational.json-simplify-1`
812×	`rational.json-simplify-44`
684×	`rational.json-simplify-2`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	221	6947
1	480	6899
2	1226	6591
3	4326	6549
4	7284	6549

Stop Event

1×	node limit

Counts

147 → 154

Calls

Call 1

Inputs
(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))))
(+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 (.f64 n (PI.f64))))) (.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))))
(+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 (.f64 n (PI.f64))))) (+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (.f64 1/8 (.f64 (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 2) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2))) (sqrt.f64 (.f64 n (PI.f64)))))))
(+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 (.f64 n (PI.f64))))) (+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (+.f64 (.f64 1/8 (.f64 (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 2) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2))) (sqrt.f64 (.f64 n (PI.f64))))) (.f64 -1/48 (.f64 (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 3) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 3))) (sqrt.f64 (*.f64 n (PI.f64))))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (.f64 n (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (.f64 n (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (.f64 n (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (.f64 n (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (+.f64 1 (.f64 -1 k)) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (+.f64 1 (.f64 -1 k)) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (+.f64 1 (.f64 -1 k)) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (+.f64 1 (.f64 -1 k)) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))
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Outputs
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(/.f64 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (.f64 n (PI.f64))))))) (sqrt.f64 k))
(/.f64 (exp.f64 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (*.f64 1/2 (-.f64 1 k)))) (sqrt.f64 k))
(.f64 (.f64 (exp.f64 (.f64 1/2 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)))) 4) (/.f64 1 (.f64 (sqrt.f64 k) 4)))
(/.f64 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))) (sqrt.f64 k))
(/.f64 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (.f64 n (PI.f64))))))) (sqrt.f64 k))
(/.f64 (exp.f64 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (*.f64 1/2 (-.f64 1 k)))) (sqrt.f64 k))
(.f64 (/.f64 1 (sqrt.f64 k)) (exp.f64 (.f64 1/2 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)))))
(/.f64 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))) (sqrt.f64 k))
(/.f64 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (.f64 n (PI.f64))))))) (sqrt.f64 k))
(/.f64 (exp.f64 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (*.f64 1/2 (-.f64 1 k)))) (sqrt.f64 k))
(.f64 (neg.f64 (exp.f64 (.f64 1/2 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k))))) (/.f64 -1 (sqrt.f64 k)))
(/.f64 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))) (sqrt.f64 k))
(/.f64 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (.f64 n (PI.f64))))))) (sqrt.f64 k))
(/.f64 (exp.f64 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (*.f64 1/2 (-.f64 1 k)))) (sqrt.f64 k))
(.f64 -1 (/.f64 (exp.f64 (.f64 1/2 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)))) (neg.f64 (sqrt.f64 k))))
(/.f64 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))) (sqrt.f64 k))
(/.f64 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (.f64 n (PI.f64))))))) (sqrt.f64 k))
(/.f64 (exp.f64 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (*.f64 1/2 (-.f64 1 k)))) (sqrt.f64 k))
(.f64 (/.f64 1/2 (sqrt.f64 k)) (.f64 2 (exp.f64 (.f64 1/2 (.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k))))))
(/.f64 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))) (sqrt.f64 k))
(/.f64 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (.f64 n (PI.f64))))))) (sqrt.f64 k))
(/.f64 (exp.f64 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (*.f64 1/2 (-.f64 1 k)))) (sqrt.f64 k))
(.f64 (.f64 1/2 (/.f64 1 (sqrt.f64 k))) (.f64 2 (exp.f64 (.f64 1/2 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k))))))
(/.f64 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))) (sqrt.f64 k))
(/.f64 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (.f64 n (PI.f64))))))) (sqrt.f64 k))
(/.f64 (exp.f64 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (*.f64 1/2 (-.f64 1 k)))) (sqrt.f64 k))
(.f64 (/.f64 (exp.f64 (.f64 1/2 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)))) (neg.f64 (sqrt.f64 k))) -1)
(/.f64 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))) (sqrt.f64 k))
(/.f64 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (.f64 n (PI.f64))))))) (sqrt.f64 k))
(/.f64 (exp.f64 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (*.f64 1/2 (-.f64 1 k)))) (sqrt.f64 k))
(.f64 (/.f64 (exp.f64 (.f64 1/2 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)))) (*.f64 2 (sqrt.f64 k))) 2)
(/.f64 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))) (sqrt.f64 k))
(/.f64 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (.f64 n (PI.f64))))))) (sqrt.f64 k))
(/.f64 (exp.f64 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (*.f64 1/2 (-.f64 1 k)))) (sqrt.f64 k))
(.f64 (/.f64 1 (.f64 (sqrt.f64 k) 4)) (.f64 (exp.f64 (.f64 1/2 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)))) 4))
(/.f64 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))) (sqrt.f64 k))
(/.f64 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (.f64 n (PI.f64))))))) (sqrt.f64 k))
(/.f64 (exp.f64 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (*.f64 1/2 (-.f64 1 k)))) (sqrt.f64 k))
(.f64 (/.f64 -1 (sqrt.f64 k)) (neg.f64 (exp.f64 (.f64 1/2 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k))))))
(/.f64 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))) (sqrt.f64 k))
(/.f64 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (.f64 n (PI.f64))))))) (sqrt.f64 k))
(/.f64 (exp.f64 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (*.f64 1/2 (-.f64 1 k)))) (sqrt.f64 k))
(neg.f64 (/.f64 (exp.f64 (.f64 1/2 (.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)))) (neg.f64 (sqrt.f64 k))))
(/.f64 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))) (sqrt.f64 k))
(/.f64 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (.f64 n (PI.f64))))))) (sqrt.f64 k))
(/.f64 (exp.f64 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (*.f64 1/2 (-.f64 1 k)))) (sqrt.f64 k))
(neg.f64 (/.f64 (/.f64 (sqrt.f64 k) (exp.f64 (.f64 1/2 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k))))) (neg.f64 (.f64 (/.f64 (sqrt.f64 k) (exp.f64 (.f64 1/2 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k))))) (/.f64 (sqrt.f64 k) (exp.f64 (.f64 1/2 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)))))))))
(neg.f64 (/.f64 (/.f64 (sqrt.f64 k) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n))))))) (neg.f64 (.f64 (/.f64 (sqrt.f64 k) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n))))))) (/.f64 (sqrt.f64 k) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n)))))))))))
(/.f64 (neg.f64 (sqrt.f64 k)) (.f64 (.f64 (/.f64 (sqrt.f64 k) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n))))))) (/.f64 (sqrt.f64 k) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n)))))))) (neg.f64 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))))))
(/.f64 (sqrt.f64 k) (.f64 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (.f64 n (PI.f64))))))) (.f64 (/.f64 (sqrt.f64 k) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (.f64 n (PI.f64)))))))) (/.f64 (sqrt.f64 k) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (.f64 n (PI.f64)))))))))))
(/.f64 (/.f64 (sqrt.f64 k) (exp.f64 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (.f64 1/2 (-.f64 1 k))))) (.f64 (/.f64 (sqrt.f64 k) (exp.f64 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (.f64 1/2 (-.f64 1 k))))) (/.f64 (sqrt.f64 k) (exp.f64 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (.f64 1/2 (-.f64 1 k)))))))
(neg.f64 (/.f64 (.f64 (exp.f64 (.f64 1/2 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)))) -2) (*.f64 2 (sqrt.f64 k))))
(/.f64 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))) (sqrt.f64 k))
(/.f64 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (.f64 n (PI.f64))))))) (sqrt.f64 k))
(/.f64 (exp.f64 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (*.f64 1/2 (-.f64 1 k)))) (sqrt.f64 k))
(+.f64 (.f64 1/2 (.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k))) 0)
(.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))
(.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (.f64 n (PI.f64))))))
(.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (*.f64 1/2 (-.f64 1 k)))
(+.f64 0 (.f64 1/2 (.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k))))
(.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))
(.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (.f64 n (PI.f64))))))
(.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (*.f64 1/2 (-.f64 1 k)))
(+.f64 (.f64 1/2 (.f64 1/2 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)))) (.f64 1/2 (.f64 1/2 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)))))
(.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))
(.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (.f64 n (PI.f64))))))
(.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (*.f64 1/2 (-.f64 1 k)))
(+.f64 (/.f64 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)) 4) (/.f64 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)) 4))
(+.f64 (/.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n)))) 4) (/.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n)))) 4))
(+.f64 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (/.f64 (-.f64 1 k) 4)) (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (/.f64 (-.f64 1 k) 4)))
(.f64 (/.f64 (log.f64 (.f64 2 (*.f64 n (PI.f64)))) 4) (+.f64 (-.f64 1 k) (-.f64 1 k)))
(.f64 (/.f64 (-.f64 1 k) 4) (.f64 2 (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))
(+.f64 (.f64 (.f64 1/2 (log.f64 (.f64 (PI.f64) (+.f64 n n)))) (.f64 1/2 (-.f64 1 k))) (.f64 (.f64 1/2 (log.f64 (.f64 (PI.f64) (+.f64 n n)))) (.f64 1/2 (-.f64 1 k))))
(.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))
(.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (.f64 n (PI.f64))))))
(.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (*.f64 1/2 (-.f64 1 k)))
(-.f64 (.f64 1/2 (.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k))) 0)
(.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))
(.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (.f64 n (PI.f64))))))
(.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (*.f64 1/2 (-.f64 1 k)))
(/.f64 (.f64 1/2 (.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k))) 1)
(.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))
(.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (.f64 n (PI.f64))))))
(.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (*.f64 1/2 (-.f64 1 k)))
(/.f64 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)) 2)
(.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))
(.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (.f64 n (PI.f64))))))
(.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (*.f64 1/2 (-.f64 1 k)))
(/.f64 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (*.f64 2 (-.f64 1 k))) 4)
(.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))
(.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (.f64 n (PI.f64))))))
(.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (*.f64 1/2 (-.f64 1 k)))
(/.f64 (.f64 (.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)) 4) 8)
(.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))
(.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (.f64 n (PI.f64))))))
(.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (*.f64 1/2 (-.f64 1 k)))
(/.f64 (.f64 2 (.f64 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)) 4)) 16)
(.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))
(.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (.f64 n (PI.f64))))))
(.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (*.f64 1/2 (-.f64 1 k)))

localize38.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(*.f64 n (PI.f64))
✓	0.3b	(.f64 k (.f64 -1/2 (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))
✓	0.3b	(/.f64 (sqrt.f64 (.f64 n (PI.f64))) (/.f64 (sqrt.f64 k) (.f64 (sqrt.f64 2) (+.f64 1 (.f64 k (.f64 -1/2 (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))))))
✓	0.6b	(/.f64 (sqrt.f64 k) (.f64 (sqrt.f64 2) (+.f64 1 (.f64 k (.f64 -1/2 (log.f64 (.f64 (PI.f64) (+.f64 n n))))))))

Compiler

Compiled 119 to 51 computations (57.1% saved)

series53.0ms (0.3%)

Counts

4 → 36

Calls

21 calls:

Time	Variable		Point	Expression
35.0ms	k	@	0	(.f64 k (.f64 -1/2 (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))
3.0ms	k	@	inf	(/.f64 (sqrt.f64 k) (.f64 (sqrt.f64 2) (+.f64 1 (.f64 k (.f64 -1/2 (log.f64 (.f64 (PI.f64) (+.f64 n n))))))))
2.0ms	n	@	-inf	(/.f64 (sqrt.f64 k) (.f64 (sqrt.f64 2) (+.f64 1 (.f64 k (.f64 -1/2 (log.f64 (.f64 (PI.f64) (+.f64 n n))))))))
2.0ms	n	@	inf	(/.f64 (sqrt.f64 k) (.f64 (sqrt.f64 2) (+.f64 1 (.f64 k (.f64 -1/2 (log.f64 (.f64 (PI.f64) (+.f64 n n))))))))
2.0ms	k	@	-inf	(/.f64 (sqrt.f64 k) (.f64 (sqrt.f64 2) (+.f64 1 (.f64 k (.f64 -1/2 (log.f64 (.f64 (PI.f64) (+.f64 n n))))))))

rewrite116.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

1156×	`rational.json-simplify-51`
862×	`rational.json-simplify-35`
758×	`rational.json-simplify-61`
694×	`rational.json-simplify-49`
662×	`bool.json-1`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	172
1	236	172
2	657	172
3	1815	172
4	6538	172

Stop Event

1×	node limit

Counts

4 → 105

Calls

Call 1

Inputs
(/.f64 (sqrt.f64 k) (.f64 (sqrt.f64 2) (+.f64 1 (.f64 k (.f64 -1/2 (log.f64 (.f64 (PI.f64) (+.f64 n n))))))))
(/.f64 (sqrt.f64 (.f64 n (PI.f64))) (/.f64 (sqrt.f64 k) (.f64 (sqrt.f64 2) (+.f64 1 (.f64 k (.f64 -1/2 (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))))))
(.f64 k (.f64 -1/2 (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))
(*.f64 n (PI.f64))

Outputs
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((#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (PI.f64) n) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (.f64 (PI.f64) n))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (.f64 (PI.f64) n) 0)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 2 (.f64 (PI.f64) n)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (PI.f64) n) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (PI.f64) (.f64 n 4)) 4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (.f64 (PI.f64) n) 8) 8)))) (#(struct:change #<rule egg-rr> (2) ((x not (not (.f64 (PI.f64) n)))))) (#(struct:change #<rule egg-rr> (2) ((x and (.f64 (PI.f64) n) (.f64 (PI.f64) n))))) (#(struct:change #<rule egg-rr> (2) ((x or (.f64 (PI.f64) n) (*.f64 (PI.f64) n))))))

simplify141.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

1326×	`rational.json-simplify-51`
1268×	`rational.json-simplify-35`
1078×	`rational.json-simplify-44`
998×	`rational.json-simplify-61`
958×	`rational.json-simplify-2`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	279	8319
1	709	8269
2	1718	8265
3	6108	8189

Stop Event

1×	node limit

Counts

141 → 174

Calls

Call 1

Inputs
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(.f64 (sqrt.f64 k) (/.f64 1 (.f64 (sqrt.f64 2) (+.f64 1 (.f64 -1/2 (.f64 k (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))))))
(.f64 (sqrt.f64 k) (/.f64 1 (.f64 (sqrt.f64 2) (+.f64 1 (.f64 -1/2 (.f64 k (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))))))
(.f64 (sqrt.f64 k) (/.f64 1 (.f64 (sqrt.f64 2) (+.f64 1 (.f64 -1/2 (.f64 k (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64))))))))))
(.f64 (sqrt.f64 k) (/.f64 1 (.f64 (sqrt.f64 2) (+.f64 1 (.f64 -1/2 (.f64 k (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64))))))))))
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(.f64 (sqrt.f64 (.f64 (PI.f64) n)) (.f64 (+.f64 1 (.f64 k (.f64 -1/2 (log.f64 (.f64 2 (*.f64 (PI.f64) n)))))) (/.f64 (sqrt.f64 2) (sqrt.f64 k))))
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(.f64 1/2 (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (.f64 (sqrt.f64 2) (/.f64 (+.f64 (.f64 k (neg.f64 (log.f64 (.f64 2 (*.f64 (PI.f64) n))))) 2) (sqrt.f64 k)))))
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(/.f64 (.f64 k (.f64 -1/2 (log.f64 (.f64 2 (.f64 (PI.f64) n))))) 1)
(/.f64 (.f64 k (neg.f64 (log.f64 (.f64 2 (*.f64 (PI.f64) n))))) 2)
(/.f64 (.f64 k (.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) -2)) 4)
(/.f64 (.f64 2 (.f64 k (.f64 (log.f64 (.f64 2 (*.f64 (PI.f64) n))) -2))) 8)
(+.f64 (*.f64 (PI.f64) n) 0)
(+.f64 0 (*.f64 (PI.f64) n))
(-.f64 (*.f64 (PI.f64) n) 0)
(/.f64 (.f64 2 (.f64 (PI.f64) n)) 2)
(/.f64 (*.f64 (PI.f64) n) 1)
(/.f64 (.f64 (PI.f64) (.f64 n 4)) 4)
(/.f64 (.f64 (.f64 (PI.f64) n) 8) 8)

Outputs
(.f64 (sqrt.f64 k) (/.f64 1 (.f64 (sqrt.f64 2) (+.f64 1 (.f64 -1/2 (.f64 k (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))))))
(.f64 (sqrt.f64 k) (/.f64 1 (.f64 (sqrt.f64 2) (+.f64 1 (.f64 k (.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) -1/2))))))
(.f64 (sqrt.f64 k) (/.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 1 (.f64 k (.f64 -1/2 (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))))))
(.f64 (sqrt.f64 k) (/.f64 1 (.f64 (sqrt.f64 2) (+.f64 1 (.f64 k (.f64 -1/2 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))))))
(/.f64 (sqrt.f64 k) (.f64 (sqrt.f64 2) (+.f64 1 (.f64 (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))) (.f64 k -1/2)))))
(.f64 (sqrt.f64 k) (/.f64 1 (.f64 (sqrt.f64 2) (+.f64 1 (.f64 -1/2 (.f64 k (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))))))
(.f64 (sqrt.f64 k) (/.f64 1 (.f64 (sqrt.f64 2) (+.f64 1 (.f64 k (.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) -1/2))))))
(.f64 (sqrt.f64 k) (/.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 1 (.f64 k (.f64 -1/2 (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))))))
(.f64 (sqrt.f64 k) (/.f64 1 (.f64 (sqrt.f64 2) (+.f64 1 (.f64 k (.f64 -1/2 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))))))
(/.f64 (sqrt.f64 k) (.f64 (sqrt.f64 2) (+.f64 1 (.f64 (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))) (.f64 k -1/2)))))
(.f64 (sqrt.f64 k) (/.f64 1 (.f64 (sqrt.f64 2) (+.f64 1 (.f64 -1/2 (.f64 k (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))))))
(.f64 (sqrt.f64 k) (/.f64 1 (.f64 (sqrt.f64 2) (+.f64 1 (.f64 k (.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) -1/2))))))
(.f64 (sqrt.f64 k) (/.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 1 (.f64 k (.f64 -1/2 (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))))))
(.f64 (sqrt.f64 k) (/.f64 1 (.f64 (sqrt.f64 2) (+.f64 1 (.f64 k (.f64 -1/2 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))))))
(/.f64 (sqrt.f64 k) (.f64 (sqrt.f64 2) (+.f64 1 (.f64 (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))) (.f64 k -1/2)))))
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(.f64 (sqrt.f64 k) (/.f64 1 (.f64 (sqrt.f64 2) (+.f64 1 (.f64 k (.f64 -1/2 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))))))
(/.f64 (sqrt.f64 k) (.f64 (sqrt.f64 2) (+.f64 1 (.f64 (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))) (.f64 k -1/2)))))
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(.f64 (sqrt.f64 k) (/.f64 1 (.f64 (sqrt.f64 2) (+.f64 1 (.f64 k (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (.f64 -1 (log.f64 (/.f64 1 n)))) -1/2))))))
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(/.f64 (sqrt.f64 k) (.f64 (sqrt.f64 2) (+.f64 1 (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n)))) (.f64 k -1/2)))))
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(.f64 (sqrt.f64 k) (/.f64 1 (.f64 (sqrt.f64 2) (+.f64 1 (.f64 k (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (.f64 -1 (log.f64 (/.f64 1 n)))) -1/2))))))
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(.f64 (+.f64 1 (.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) (.f64 k -1/2))) (.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 (sqrt.f64 2) (sqrt.f64 k))))
(.f64 (.f64 (sqrt.f64 2) 1/2) (.f64 (+.f64 (.f64 k (neg.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))))) 2) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 k))))
(.f64 (+.f64 1 (.f64 k (.f64 -1/2 (log.f64 (.f64 2 (.f64 n (PI.f64))))))) (.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 k))))
(.f64 (+.f64 1 (.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) (.f64 -1/2 k))) (.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 k))))
(.f64 (+.f64 1 (.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) (.f64 k -1/2))) (.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 (sqrt.f64 2) (sqrt.f64 k))))
(.f64 (/.f64 (+.f64 (.f64 k (neg.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))))) 2) 4) (.f64 (.f64 2 (sqrt.f64 2)) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 k))))
(.f64 (+.f64 1 (.f64 k (.f64 -1/2 (log.f64 (.f64 2 (.f64 n (PI.f64))))))) (.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 k))))
(.f64 (+.f64 1 (.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) (.f64 -1/2 k))) (.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 k))))
(.f64 (+.f64 1 (.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) (.f64 k -1/2))) (.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 (sqrt.f64 2) (sqrt.f64 k))))
(.f64 (.f64 1/2 (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 k))) (.f64 (sqrt.f64 2) (+.f64 (.f64 k (neg.f64 (log.f64 (.f64 2 (*.f64 (PI.f64) n))))) 2)))
(.f64 (+.f64 1 (.f64 k (.f64 -1/2 (log.f64 (.f64 2 (.f64 n (PI.f64))))))) (.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 k))))
(.f64 (+.f64 1 (.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) (.f64 -1/2 k))) (.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 k))))
(.f64 (+.f64 1 (.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) (.f64 k -1/2))) (.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 (sqrt.f64 2) (sqrt.f64 k))))
(neg.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) (/.f64 (/.f64 (sqrt.f64 k) (-.f64 -1 (.f64 k (.f64 -1/2 (log.f64 (.f64 2 (*.f64 (PI.f64) n))))))) (sqrt.f64 2))))
(.f64 (+.f64 1 (.f64 k (.f64 -1/2 (log.f64 (.f64 2 (.f64 n (PI.f64))))))) (.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 k))))
(.f64 (+.f64 1 (.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) (.f64 -1/2 k))) (.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 k))))
(.f64 (+.f64 1 (.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) (.f64 k -1/2))) (.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 (sqrt.f64 2) (sqrt.f64 k))))
(+.f64 (.f64 k (.f64 -1/2 (log.f64 (.f64 2 (.f64 (PI.f64) n))))) 0)
(.f64 k (.f64 -1/2 (log.f64 (.f64 2 (.f64 n (PI.f64))))))
(.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) (.f64 -1/2 k))
(.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) (.f64 k -1/2))
(+.f64 0 (.f64 k (.f64 -1/2 (log.f64 (.f64 2 (.f64 (PI.f64) n))))))
(.f64 k (.f64 -1/2 (log.f64 (.f64 2 (.f64 n (PI.f64))))))
(.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) (.f64 -1/2 k))
(.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) (.f64 k -1/2))
(-.f64 (.f64 k (.f64 -1/2 (log.f64 (.f64 2 (.f64 (PI.f64) n))))) 0)
(.f64 k (.f64 -1/2 (log.f64 (.f64 2 (.f64 n (PI.f64))))))
(.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) (.f64 -1/2 k))
(.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) (.f64 k -1/2))
(/.f64 (.f64 k (.f64 -1/2 (log.f64 (.f64 2 (.f64 (PI.f64) n))))) 1)
(.f64 k (.f64 -1/2 (log.f64 (.f64 2 (.f64 n (PI.f64))))))
(.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) (.f64 -1/2 k))
(.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) (.f64 k -1/2))
(/.f64 (.f64 k (neg.f64 (log.f64 (.f64 2 (*.f64 (PI.f64) n))))) 2)
(.f64 k (.f64 -1/2 (log.f64 (.f64 2 (.f64 n (PI.f64))))))
(.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) (.f64 -1/2 k))
(.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) (.f64 k -1/2))
(/.f64 (.f64 k (.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) -2)) 4)
(.f64 k (.f64 -1/2 (log.f64 (.f64 2 (.f64 n (PI.f64))))))
(.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) (.f64 -1/2 k))
(.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) (.f64 k -1/2))
(/.f64 (.f64 2 (.f64 k (.f64 (log.f64 (.f64 2 (*.f64 (PI.f64) n))) -2))) 8)
(.f64 k (.f64 -1/2 (log.f64 (.f64 2 (.f64 n (PI.f64))))))
(.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) (.f64 -1/2 k))
(.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) (.f64 k -1/2))
(+.f64 (*.f64 (PI.f64) n) 0)
(*.f64 n (PI.f64))
(+.f64 0 (*.f64 (PI.f64) n))
(*.f64 n (PI.f64))
(-.f64 (*.f64 (PI.f64) n) 0)
(*.f64 n (PI.f64))
(/.f64 (.f64 2 (.f64 (PI.f64) n)) 2)
(*.f64 n (PI.f64))
(/.f64 (*.f64 (PI.f64) n) 1)
(*.f64 n (PI.f64))
(/.f64 (.f64 (PI.f64) (.f64 n 4)) 4)
(*.f64 n (PI.f64))
(/.f64 (.f64 (.f64 (PI.f64) n) 8) 8)
(*.f64 n (PI.f64))

localize46.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(/.f64 (sqrt.f64 k) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)))
	0.2b	(*.f64 (PI.f64) (+.f64 n n))
	0.3b	(pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2))
✓	9.9b	(/.f64 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2))) (.f64 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2))) (/.f64 (sqrt.f64 k) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2)))))

Compiler

Compiled 123 to 58 computations (52.8% saved)

series2.0ms (0%)

Counts

1 → 12

Calls

6 calls:

Time	Variable		Point	Expression
1.0ms	k	@	0	(/.f64 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2))) (.f64 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2))) (/.f64 (sqrt.f64 k) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2)))))
0.0ms	k	@	-inf	(/.f64 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2))) (.f64 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2))) (/.f64 (sqrt.f64 k) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2)))))
0.0ms	k	@	inf	(/.f64 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2))) (.f64 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2))) (/.f64 (sqrt.f64 k) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2)))))
0.0ms	n	@	-inf	(/.f64 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2))) (.f64 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2))) (/.f64 (sqrt.f64 k) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2)))))
0.0ms	n	@	inf	(/.f64 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2))) (.f64 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2))) (/.f64 (sqrt.f64 k) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2)))))

rewrite91.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

2074×	`bool.json-1`
2074×	`bool.json-2`
940×	`rational.json-simplify-35`
896×	`rational.json-simplify-46`
686×	`rational.json-1`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	18	139
1	187	139
2	572	43
3	1945	43
4	6769	43

Stop Event

1×	node limit

Counts

1 → 32

Calls

Call 1

Inputs

(/.f64 (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2))) (*.f64 (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2))) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2)))))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 k) (/.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k)) (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 k) (*.f64 (/.f64 1 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2))) (*.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k)) (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 k) (*.f64 (*.f64 (/.f64 (pow.f64 (*.f64 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k)) (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2))) (*.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k)) (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2))) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2)))) (*.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k)) (*.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k)) (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (*.f64 (sqrt.f64 k) 2) (pow.f64 (*.f64 (PI.f64) 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(pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k))) 2) (/.f64 1 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2)) 2) (/.f64 1/2 (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2)) 2) (*.f64 (/.f64 1/2 (sqrt.f64 k)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2)) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2)))) (/.f64 1 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fabs.f64 (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2)))) (*.f64 (/.f64 (fabs.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k))) (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k))) (*.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k)) (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k)) (sqrt.f64 k)) (sqrt.f64 k))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k)) (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k))) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2))) (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2)) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (*.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k)) (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k))) 2) (/.f64 (*.f64 (sqrt.f64 k) 2) (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1/2 (/.f64 (sqrt.f64 k) (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k)))) (*.f64 (sqrt.f64 k) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1/2 (sqrt.f64 k)) (*.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x not (not (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x and (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k)) (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x or (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k)) (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k)))))))

simplify144.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

1574×	`rational.json-simplify-35`
1130×	`rational.json-simplify-2`
1014×	`rational.json-simplify-1`
844×	`rational.json-simplify-39`
606×	`rational.json-simplify-43`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	112	3920
1	256	3904
2	590	3820
3	2146	3316
4	5497	3316
5	7594	3316

Stop Event

1×	node limit

Counts

44 → 64

Calls

Call 1

Inputs
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))))
(+.f64 0 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k)))
(+.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k)) 0)
(-.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k)) 0)
(.f64 (sqrt.f64 k) (/.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k)) (sqrt.f64 k)))
(.f64 (sqrt.f64 k) (.f64 (/.f64 1 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2))) (.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k)) (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k)))))
(.f64 (sqrt.f64 k) (.f64 (.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k)) (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k))) (/.f64 1 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2)))))
(.f64 1 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k)))
(.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2)) (/.f64 1 (sqrt.f64 k)))
(.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)) (.f64 (/.f64 1 (sqrt.f64 k)) 1))
(.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)) (.f64 (/.f64 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2))) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2))) (.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k)) (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k)))))
(.f64 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2))) (.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k)) (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k))))
(.f64 (.f64 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2))) (/.f64 (sqrt.f64 k) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)))) (.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k)) (.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k)) (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k)))))
(.f64 (/.f64 (.f64 (sqrt.f64 k) 2) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2))) (/.f64 (.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k)) (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k))) 2))
(.f64 (/.f64 (.f64 (sqrt.f64 k) 2) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2))) (.f64 (/.f64 (.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k)) (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k))) 2) 1))
(.f64 (/.f64 (.f64 (sqrt.f64 k) 2) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2))) (.f64 1/2 (.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k)) (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k)))))
(.f64 (.f64 (sqrt.f64 k) 2) (/.f64 1/2 (/.f64 (sqrt.f64 k) (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k)))))
(.f64 (.f64 (sqrt.f64 k) 2) (.f64 (/.f64 1/2 (/.f64 (sqrt.f64 k) (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k)))) 1))
(.f64 (.f64 (sqrt.f64 k) 2) (.f64 1/2 (/.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k)) (sqrt.f64 k))))
(.f64 (.f64 (sqrt.f64 k) 2) (.f64 (/.f64 1/2 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2))) (.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k)) (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k)))))
(.f64 (.f64 (sqrt.f64 k) 2) (.f64 (/.f64 (.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k)) (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k))) 2) (/.f64 1 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)))))
(.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)) 2) (/.f64 1/2 (sqrt.f64 k)))
(.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)) 2) (*.f64 (/.f64 1/2 (sqrt.f64 k)) 1))
(.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)) (/.f64 (sqrt.f64 k) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)))) (/.f64 1 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2))))
(.f64 (fabs.f64 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)))) (.f64 (/.f64 (fabs.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k))) (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k))) (.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k)) (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k)))))
(.f64 (/.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k)) (sqrt.f64 k)) (sqrt.f64 k))
(.f64 (.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k)) (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k))) (/.f64 (sqrt.f64 k) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2))))
(.f64 (/.f64 1 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2))) (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)) (/.f64 (sqrt.f64 k) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2)))))
(.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k)) 1)
(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2)))
(.f64 (/.f64 (.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k)) (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k))) 2) (/.f64 (.f64 (sqrt.f64 k) 2) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2))))
(.f64 (/.f64 1/2 (/.f64 (sqrt.f64 k) (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k)))) (.f64 (sqrt.f64 k) 2))
(.f64 (/.f64 1/2 (sqrt.f64 k)) (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)) 2))

Outputs
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)) (.f64 1/2 (-.f64 1 k)))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (-.f64 1 k) (.f64 1/2 (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)) (.f64 1/2 (-.f64 1 k)))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (-.f64 1 k) (.f64 1/2 (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)) (.f64 1/2 (-.f64 1 k)))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (-.f64 1 k) (.f64 1/2 (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)) (.f64 1/2 (-.f64 1 k)))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (-.f64 1 k) (.f64 1/2 (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (*.f64 -1 (log.f64 (/.f64 1 n))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (-.f64 1 k) (.f64 1/2 (+.f64 (log.f64 (.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (*.f64 -1 (log.f64 (/.f64 1 n))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (-.f64 1 k) (.f64 1/2 (+.f64 (log.f64 (.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n))))))))
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(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (*.f64 -1 (log.f64 (/.f64 1 n))))))))
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(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2)))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(.f64 (/.f64 (.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k)) (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k))) 2) (/.f64 (.f64 (sqrt.f64 k) 2) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2))))
(.f64 (sqrt.f64 k) (.f64 (/.f64 1 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 1/2 (-.f64 1 k)))) (.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 1/2 (-.f64 1 k))) (sqrt.f64 k)) (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k)))))
(.f64 (sqrt.f64 k) (.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 1/2 (-.f64 1 k))) (sqrt.f64 k)) (.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 1/2 (-.f64 1 k))) (sqrt.f64 k)) (/.f64 1 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (*.f64 1/2 (-.f64 1 k)))))))
(.f64 (/.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 1/2 (-.f64 1 k))) (sqrt.f64 k)) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 1/2 (-.f64 1 k)))) (.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 1/2 (-.f64 1 k))) (sqrt.f64 k)) (sqrt.f64 k)))
(+.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 1/2 (-.f64 1 k))) (sqrt.f64 k)) (/.f64 0 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 1/2 (-.f64 1 k))))))
(+.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 1/2 (-.f64 1 k))) (sqrt.f64 k)) (/.f64 0 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))))
(.f64 (/.f64 1/2 (/.f64 (sqrt.f64 k) (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k)))) (.f64 (sqrt.f64 k) 2))
(.f64 (sqrt.f64 k) (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 1/2 (-.f64 1 k))) (.f64 (sqrt.f64 k) (sqrt.f64 k))))
(.f64 (/.f64 1/2 (sqrt.f64 k)) (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)) 2))
(.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 1/2 (-.f64 1 k))) (.f64 2 (/.f64 1/2 (sqrt.f64 k))))
(.f64 2 (.f64 (/.f64 1/2 (sqrt.f64 k)) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 1/2 (-.f64 1 k)))))
(.f64 2 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 1/2 (-.f64 1 k))) (/.f64 1/2 (sqrt.f64 k))))
(.f64 2 (.f64 1/2 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))))

eval614.0ms (4%)

Compiler: Compiled 44210 to 26545 computations (40% saved)

prune294.0ms (1.9%)

Pruning

27 alts after pruning (19 fresh and 8 done)

	Pruned	Kept	Total
New	1222	12	1234
Fresh	5	7	12
Picked	1	0	1
Done	0	8	8
Total	1228	27	1255

Error

0.0b

Counts

1255 → 27

Alt Table

Click to see full alt table

Status	Error	Program
✓	0.4b	(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k))
▶	0.5b	(/.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 1/2 (-.f64 1 k))) (/.f64 16 (sqrt.f64 k))) (.f64 (sqrt.f64 k) (.f64 (sqrt.f64 k) 1/16)))
	23.2b	(/.f64 (/.f64 (.f64 4 (/.f64 4 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)))) (sqrt.f64 k)) (.f64 (/.f64 4 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2))) (/.f64 4 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)))))
	34.9b	(/.f64 (/.f64 (sqrt.f64 k) (exp.f64 (.f64 (-.f64 1 k) (.f64 1/2 (log.f64 (.f64 (PI.f64) (.f64 2 n))))))) (.f64 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2))) (/.f64 (sqrt.f64 k) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2)))))
✓	0.5b	(/.f64 (/.f64 2 (sqrt.f64 k)) (/.f64 2 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2))))
	23.9b	(/.f64 (+.f64 (.f64 -1/2 (.f64 (sqrt.f64 2) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 k (log.f64 (.f64 n (.f64 2 (PI.f64)))))))) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (.f64 1/8 (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 2) (pow.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) 2))))))) (sqrt.f64 k))
	23.9b	(/.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (+.f64 (.f64 1/8 (.f64 (pow.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) 2) (.f64 (sqrt.f64 2) (pow.f64 k 2)))) (+.f64 (sqrt.f64 2) (.f64 -1/2 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (.f64 (sqrt.f64 2) k)))))) (sqrt.f64 k))
	23.7b	(/.f64 (.f64 (sqrt.f64 2) (+.f64 1 (.f64 k (.f64 -1/2 (log.f64 (.f64 (PI.f64) (+.f64 n n))))))) (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 n (PI.f64)))))
	23.8b	(/.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (sqrt.f64 k))
	0.4b	(/.f64 (.f64 1/2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2))) (/.f64 2 (/.f64 4 (sqrt.f64 k))))
✓	23.7b	(/.f64 (sqrt.f64 (.f64 n (PI.f64))) (/.f64 (sqrt.f64 k) (.f64 (sqrt.f64 2) (+.f64 1 (.f64 k (.f64 -1/2 (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))))))
	3.0b	(/.f64 (exp.f64 (+.f64 (.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 1/2) (.f64 -1/2 (.f64 k (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))) (sqrt.f64 k))
✓	3.0b	(/.f64 (exp.f64 (.f64 (-.f64 1 k) (.f64 1/2 (log.f64 (.f64 (PI.f64) (.f64 2 n)))))) (sqrt.f64 k))
▶	0.4b	(/.f64 2 (/.f64 2 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k))))
✓	0.4b	(/.f64 2 (.f64 (sqrt.f64 k) (/.f64 2 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2)))))
	23.9b	(/.f64 2 (.f64 (sqrt.f64 k) (.f64 2 (.f64 (sqrt.f64 (/.f64 1 (.f64 (PI.f64) n))) (sqrt.f64 1/2)))))
✓	0.4b	(/.f64 1 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2))))
	23.9b	(/.f64 1 (/.f64 (sqrt.f64 k) (+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 -1/2 (.f64 (log.f64 (.f64 (PI.f64) (.f64 2 n))) (*.f64 (sqrt.f64 2) k)))))))
	0.5b	(/.f64 1 (.f64 (/.f64 1 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2))) (/.f64 -1 (/.f64 -1 (sqrt.f64 k)))))
▶	0.4b	(/.f64 1/4 (/.f64 (/.f64 1 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2))) (/.f64 4 (sqrt.f64 k))))
	4.8b	(.f64 (/.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k)) (sqrt.f64 k)) (sqrt.f64 k))
✓	0.5b	(.f64 (/.f64 4 (sqrt.f64 k)) (/.f64 1 (/.f64 4 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)))))
✓	0.4b	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
▶	23.9b	(.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 (PI.f64) n))))
▶	23.8b	(.f64 (-.f64 -1 (.f64 k (.f64 -1/2 (log.f64 (.f64 2 (.f64 (PI.f64) n)))))) (/.f64 1 (/.f64 (/.f64 (sqrt.f64 k) (sqrt.f64 2)) (neg.f64 (sqrt.f64 (.f64 (PI.f64) n))))))
	4.9b	(.f64 (sqrt.f64 k) (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 1/2 (-.f64 1 k))) (.f64 (sqrt.f64 k) (sqrt.f64 k))))
	23.8b	(.f64 (sqrt.f64 2) (/.f64 (+.f64 1 (.f64 -1/2 (.f64 k (log.f64 (.f64 (PI.f64) (+.f64 n n)))))) (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 (PI.f64) n)))))

Compiler

Compiled 1211 to 922 computations (23.9% saved)

localize34.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 2 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k)))
✓	0.2b	(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k))
	0.2b	(*.f64 (PI.f64) n)
	0.3b	(pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2))

Compiler

Compiled 85 to 53 computations (37.6% saved)

series3.0ms (0%)

Counts

2 → 24

Calls

12 calls:

Time	Variable		Point	Expression
1.0ms	k	@	0	(/.f64 2 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k)))
0.0ms	k	@	0	(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k))
0.0ms	k	@	-inf	(/.f64 2 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k)))
0.0ms	k	@	-inf	(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k))
0.0ms	k	@	inf	(/.f64 2 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k)))

rewrite113.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

1166×	`rational.json-simplify-35`
926×	`bool.json-1`
926×	`bool.json-2`
892×	`rational.json-1`
892×	`rational.json-2`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	92
1	185	92
2	502	92
3	1127	92
4	2852	92
5	7262	92

Stop Event

1×	node limit

Counts

2 → 61

Calls

Call 1

Inputs
(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k))
(/.f64 2 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k)))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)) (/.f64 1/2 (sqrt.f64 k))) (*.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)) (/.f64 1/2 (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 -1 (-.f64 1 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)) (neg.f64 (sqrt.f64 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 0 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)) (neg.f64 (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 2 (*.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)) (/.f64 1/2 (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/2 (*.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)) (/.f64 2 (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)) (/.f64 1 (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)) (+.f64 (/.f64 1/2 (sqrt.f64 k)) (*.f64 1/2 (/.f64 1 (sqrt.f64 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 2 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2))) (/.f64 1/2 (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 2 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2))) (*.f64 1/2 (/.f64 1 (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)) (/.f64 2 (sqrt.f64 k))) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 1/2 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2))) (*.f64 2 (/.f64 1 (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k)) 4) 1/4)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)) 4) (/.f64 1 (*.f64 (sqrt.f64 k) 4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)) (neg.f64 (sqrt.f64 k))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2))) (/.f64 -1 (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)) (/.f64 1/2 (sqrt.f64 k))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -1 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)) (neg.f64 (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 2 (/.f64 1 (sqrt.f64 k))) (*.f64 1/2 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1/2 (sqrt.f64 k)) (*.f64 2 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/4 (*.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k)) 4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 1/2 (/.f64 1 (sqrt.f64 k))) (*.f64 2 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (*.f64 (sqrt.f64 k) 4)) (*.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)) 4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 -1 (sqrt.f64 k)) (neg.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)) (neg.f64 (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (*.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)) -2) (*.f64 2 (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x not (not (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x and (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k)) (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x or (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k)) (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k)))))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 (sqrt.f64 k) (*.f64 1/2 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2))) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 -1 (-.f64 1 (/.f64 (neg.f64 (*.f64 2 (sqrt.f64 k))) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 (sqrt.f64 k) (*.f64 1/2 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 0 (/.f64 (neg.f64 (*.f64 2 (sqrt.f64 k))) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (sqrt.f64 k) (*.f64 1/2 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)))) 0)))) 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k) 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x or (/.f64 (sqrt.f64 k) (*.f64 1/2 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)))) (/.f64 (sqrt.f64 k) (*.f64 1/2 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)))))))))

simplify185.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

1934×	`rational.json-simplify-35`
1174×	`rational.json-simplify-2`
756×	`rational.json-simplify-41`
688×	`rational.json-simplify-38`
544×	`rational.json-simplify-51`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	162	4519
1	353	4487
2	739	4439
3	1920	4439
4	3418	4439
5	5666	4439
6	7040	4439

Stop Event

1×	node limit

Counts

85 → 105

Calls

Call 1

Inputs
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))))
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(.f64 2 (.f64 (sqrt.f64 k) (/.f64 1 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))))))))
(.f64 2 (.f64 (sqrt.f64 k) (/.f64 1 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))))))))
(.f64 2 (.f64 (sqrt.f64 k) (/.f64 1 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64))))))))))
(.f64 2 (.f64 (sqrt.f64 k) (/.f64 1 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64))))))))))
(.f64 2 (.f64 (sqrt.f64 k) (/.f64 1 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64))))))))))
(.f64 2 (.f64 (sqrt.f64 k) (/.f64 1 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64))))))))))
(.f64 2 (.f64 (sqrt.f64 k) (/.f64 1 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64))))))))))
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(.f64 1 (/.f64 (sqrt.f64 k) (.f64 1/2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)))))
(.f64 1/2 (.f64 (sqrt.f64 k) (/.f64 4 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)))))
(.f64 (sqrt.f64 k) (/.f64 2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2))))
(.f64 (.f64 2 (sqrt.f64 k)) (/.f64 1 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2))))
(.f64 (.f64 2 (sqrt.f64 k)) (.f64 1/2 (/.f64 2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)))))
(.f64 (.f64 (sqrt.f64 k) 4) (/.f64 1/2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2))))
(.f64 (/.f64 2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2))) (sqrt.f64 k))
(.f64 (/.f64 2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2))) (/.f64 1 (/.f64 1 (sqrt.f64 k))))
(.f64 (neg.f64 (sqrt.f64 k)) (/.f64 1 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)) -2)))
(.f64 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2))) 2)
(.f64 (.f64 (sqrt.f64 k) (/.f64 4 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)))) 1/2)
(.f64 (/.f64 1 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2))) (*.f64 2 (sqrt.f64 k)))
(.f64 (/.f64 (sqrt.f64 k) (.f64 1/2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)))) 1)
(.f64 (.f64 1/2 (/.f64 2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)))) (.f64 2 (sqrt.f64 k)))
(.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (/.f64 2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2))))
(.f64 (/.f64 1/2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2))) (*.f64 (sqrt.f64 k) 4))
(.f64 (/.f64 (neg.f64 (.f64 2 (sqrt.f64 k))) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2))) -1)
(.f64 (/.f64 1 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)) -2)) (neg.f64 (sqrt.f64 k)))
(neg.f64 (/.f64 (neg.f64 (.f64 2 (sqrt.f64 k))) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2))))
(neg.f64 (/.f64 -2 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k))))
(neg.f64 (/.f64 (.f64 2 (neg.f64 (sqrt.f64 k))) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2))))
(neg.f64 (/.f64 (neg.f64 (.f64 (sqrt.f64 k) 4)) (.f64 2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)))))
(neg.f64 (/.f64 (.f64 2 (sqrt.f64 k)) (neg.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)))))

Outputs
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (-.f64 1 k) (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)) 1/2))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)) (.f64 1/2 (-.f64 1 k)))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (-.f64 1 k) (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)) 1/2))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)) (.f64 1/2 (-.f64 1 k)))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (-.f64 1 k) (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)) 1/2))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)) (.f64 1/2 (-.f64 1 k)))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (-.f64 1 k) (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)) 1/2))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)) (.f64 1/2 (-.f64 1 k)))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (-.f64 1 k) (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (*.f64 -1 (log.f64 (/.f64 1 n)))) 1/2))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (-.f64 1 k) (.f64 1/2 (+.f64 (log.f64 (.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n)))) (.f64 1/2 (-.f64 1 k)))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (-.f64 1 k) (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (*.f64 -1 (log.f64 (/.f64 1 n)))) 1/2))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (-.f64 1 k) (.f64 1/2 (+.f64 (log.f64 (.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n)))) (.f64 1/2 (-.f64 1 k)))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (-.f64 1 k) (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (*.f64 -1 (log.f64 (/.f64 1 n)))) 1/2))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (-.f64 1 k) (.f64 1/2 (+.f64 (log.f64 (.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n)))) (.f64 1/2 (-.f64 1 k)))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (-.f64 1 k) (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (*.f64 -1 (log.f64 (/.f64 1 n)))) 1/2))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (-.f64 1 k) (.f64 1/2 (+.f64 (log.f64 (.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n)))) (.f64 1/2 (-.f64 1 k)))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 (PI.f64) -2)))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (neg.f64 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 (PI.f64) -2)))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (-.f64 1 k) (.f64 1/2 (+.f64 (neg.f64 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 (PI.f64) -2)))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 (PI.f64) -2)))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (neg.f64 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 (PI.f64) -2)))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (-.f64 1 k) (.f64 1/2 (+.f64 (neg.f64 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 (PI.f64) -2)))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 (PI.f64) -2)))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (neg.f64 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 (PI.f64) -2)))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (-.f64 1 k) (.f64 1/2 (+.f64 (neg.f64 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 (PI.f64) -2)))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 (PI.f64) -2)))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (neg.f64 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 (PI.f64) -2)))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (-.f64 1 k) (.f64 1/2 (+.f64 (neg.f64 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 (PI.f64) -2)))))))
(.f64 2 (.f64 (sqrt.f64 k) (/.f64 1 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))))))))
(.f64 2 (.f64 (sqrt.f64 k) (exp.f64 (neg.f64 (.f64 (-.f64 1 k) (.f64 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)) 1/2))))))
(.f64 2 (.f64 (sqrt.f64 k) (exp.f64 (neg.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))))))))
(.f64 (exp.f64 (.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))) -1/2)) (*.f64 2 (sqrt.f64 k)))
(/.f64 (.f64 2 (sqrt.f64 k)) (exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)) (.f64 1/2 (-.f64 1 k)))))
(/.f64 (.f64 2 (sqrt.f64 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))))
(.f64 2 (.f64 (sqrt.f64 k) (/.f64 1 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))))))))
(.f64 2 (.f64 (sqrt.f64 k) (exp.f64 (neg.f64 (.f64 (-.f64 1 k) (.f64 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)) 1/2))))))
(.f64 2 (.f64 (sqrt.f64 k) (exp.f64 (neg.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))))))))
(.f64 (exp.f64 (.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))) -1/2)) (*.f64 2 (sqrt.f64 k)))
(/.f64 (.f64 2 (sqrt.f64 k)) (exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)) (.f64 1/2 (-.f64 1 k)))))
(/.f64 (.f64 2 (sqrt.f64 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))))
(.f64 2 (.f64 (sqrt.f64 k) (/.f64 1 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))))))))
(.f64 2 (.f64 (sqrt.f64 k) (exp.f64 (neg.f64 (.f64 (-.f64 1 k) (.f64 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)) 1/2))))))
(.f64 2 (.f64 (sqrt.f64 k) (exp.f64 (neg.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))))))))
(.f64 (exp.f64 (.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))) -1/2)) (*.f64 2 (sqrt.f64 k)))
(/.f64 (.f64 2 (sqrt.f64 k)) (exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)) (.f64 1/2 (-.f64 1 k)))))
(/.f64 (.f64 2 (sqrt.f64 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))))
(.f64 2 (.f64 (sqrt.f64 k) (/.f64 1 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))))))))
(.f64 2 (.f64 (sqrt.f64 k) (exp.f64 (neg.f64 (.f64 (-.f64 1 k) (.f64 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)) 1/2))))))
(.f64 2 (.f64 (sqrt.f64 k) (exp.f64 (neg.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))))))))
(.f64 (exp.f64 (.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))) -1/2)) (*.f64 2 (sqrt.f64 k)))
(/.f64 (.f64 2 (sqrt.f64 k)) (exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)) (.f64 1/2 (-.f64 1 k)))))
(/.f64 (.f64 2 (sqrt.f64 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))))
(.f64 2 (.f64 (sqrt.f64 k) (/.f64 1 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64))))))))))
(.f64 (sqrt.f64 k) (.f64 (exp.f64 (neg.f64 (.f64 (-.f64 1 k) (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (.f64 -1 (log.f64 (/.f64 1 n)))) 1/2)))) 2))
(.f64 2 (.f64 (sqrt.f64 k) (exp.f64 (neg.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n))))))))))
(.f64 (sqrt.f64 k) (.f64 2 (exp.f64 (.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n))))) -1/2))))
(/.f64 (.f64 2 (sqrt.f64 k)) (exp.f64 (.f64 (-.f64 1 k) (.f64 1/2 (+.f64 (log.f64 (.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n))))))))
(/.f64 (.f64 2 (sqrt.f64 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n))))))))
(.f64 2 (.f64 (sqrt.f64 k) (exp.f64 (.f64 (.f64 1/2 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n))))) (-.f64 k 1)))))
(.f64 (exp.f64 (.f64 (.f64 1/2 (+.f64 (log.f64 (.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n))))) (+.f64 k -1))) (*.f64 2 (sqrt.f64 k)))
(.f64 2 (.f64 (sqrt.f64 k) (/.f64 1 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64))))))))))
(.f64 (sqrt.f64 k) (.f64 (exp.f64 (neg.f64 (.f64 (-.f64 1 k) (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (.f64 -1 (log.f64 (/.f64 1 n)))) 1/2)))) 2))
(.f64 2 (.f64 (sqrt.f64 k) (exp.f64 (neg.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n))))))))))
(.f64 (sqrt.f64 k) (.f64 2 (exp.f64 (.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n))))) -1/2))))
(/.f64 (.f64 2 (sqrt.f64 k)) (exp.f64 (.f64 (-.f64 1 k) (.f64 1/2 (+.f64 (log.f64 (.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n))))))))
(/.f64 (.f64 2 (sqrt.f64 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n))))))))
(.f64 2 (.f64 (sqrt.f64 k) (exp.f64 (.f64 (.f64 1/2 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n))))) (-.f64 k 1)))))
(.f64 (exp.f64 (.f64 (.f64 1/2 (+.f64 (log.f64 (.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n))))) (+.f64 k -1))) (*.f64 2 (sqrt.f64 k)))
(.f64 2 (.f64 (sqrt.f64 k) (/.f64 1 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64))))))))))
(.f64 (sqrt.f64 k) (.f64 (exp.f64 (neg.f64 (.f64 (-.f64 1 k) (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (.f64 -1 (log.f64 (/.f64 1 n)))) 1/2)))) 2))
(.f64 2 (.f64 (sqrt.f64 k) (exp.f64 (neg.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n))))))))))
(.f64 (sqrt.f64 k) (.f64 2 (exp.f64 (.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n))))) -1/2))))
(/.f64 (.f64 2 (sqrt.f64 k)) (exp.f64 (.f64 (-.f64 1 k) (.f64 1/2 (+.f64 (log.f64 (.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n))))))))
(/.f64 (.f64 2 (sqrt.f64 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n))))))))
(.f64 2 (.f64 (sqrt.f64 k) (exp.f64 (.f64 (.f64 1/2 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n))))) (-.f64 k 1)))))
(.f64 (exp.f64 (.f64 (.f64 1/2 (+.f64 (log.f64 (.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n))))) (+.f64 k -1))) (*.f64 2 (sqrt.f64 k)))
(.f64 2 (.f64 (sqrt.f64 k) (/.f64 1 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64))))))))))
(.f64 (sqrt.f64 k) (.f64 (exp.f64 (neg.f64 (.f64 (-.f64 1 k) (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (.f64 -1 (log.f64 (/.f64 1 n)))) 1/2)))) 2))
(.f64 2 (.f64 (sqrt.f64 k) (exp.f64 (neg.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n))))))))))
(.f64 (sqrt.f64 k) (.f64 2 (exp.f64 (.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n))))) -1/2))))
(/.f64 (.f64 2 (sqrt.f64 k)) (exp.f64 (.f64 (-.f64 1 k) (.f64 1/2 (+.f64 (log.f64 (.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n))))))))
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(/.f64 (/.f64 (sqrt.f64 k) 1/2) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 1/2 (-.f64 1 k))))
(/.f64 (sqrt.f64 k) (.f64 1/2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 1/2 (-.f64 1 k)))))
(.f64 2 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (.f64 1/2 (-.f64 1 k)))))
(.f64 2 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 1/2 (-.f64 1 k)))))
(/.f64 (sqrt.f64 k) (.f64 1/2 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (.f64 1/2 (-.f64 1 k)))))
(neg.f64 (/.f64 (.f64 2 (sqrt.f64 k)) (neg.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)))))
(/.f64 (/.f64 (sqrt.f64 k) 1/2) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 1/2 (-.f64 1 k))))
(/.f64 (sqrt.f64 k) (.f64 1/2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 1/2 (-.f64 1 k)))))
(.f64 2 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (.f64 1/2 (-.f64 1 k)))))
(.f64 2 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 1/2 (-.f64 1 k)))))
(/.f64 (sqrt.f64 k) (.f64 1/2 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (.f64 1/2 (-.f64 1 k)))))

localize105.0ms (0.7%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 (/.f64 1 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2))) (/.f64 4 (sqrt.f64 k)))
	0.2b	(*.f64 (PI.f64) n)
	0.3b	(pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2))
	0.3b	(/.f64 4 (sqrt.f64 k))

Compiler

Compiled 94 to 62 computations (34% saved)

series4.0ms (0%)

Counts

1 → 12

Calls

6 calls:

Time	Variable		Point	Expression
1.0ms	k	@	0	(/.f64 (/.f64 1 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2))) (/.f64 4 (sqrt.f64 k)))
1.0ms	k	@	-inf	(/.f64 (/.f64 1 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2))) (/.f64 4 (sqrt.f64 k)))
1.0ms	k	@	inf	(/.f64 (/.f64 1 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2))) (/.f64 4 (sqrt.f64 k)))
0.0ms	n	@	0	(/.f64 (/.f64 1 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2))) (/.f64 4 (sqrt.f64 k)))
0.0ms	n	@	inf	(/.f64 (/.f64 1 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2))) (/.f64 4 (sqrt.f64 k)))

rewrite162.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

1808×	`bool.json-1`
1808×	`bool.json-2`
1760×	`rational.json-1`
1496×	`bool.json-3`
692×	`rational.json-simplify-35`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	20	55
1	210	49
2	603	49
3	1612	49
4	5307	49

Stop Event

1×	node limit

Counts

1 → 49

Calls

Call 1

Inputs
(/.f64 (/.f64 1 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2))) (/.f64 4 (sqrt.f64 k)))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (sqrt.f64 k) (/.f64 1/4 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 (sqrt.f64 k) (/.f64 1/4 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (*.f64 (sqrt.f64 k) (/.f64 1/4 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (*.f64 (sqrt.f64 k) (/.f64 1/4 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 2 (/.f64 (/.f64 1 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2))) (*.f64 2 (/.f64 4 (sqrt.f64 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 2 (/.f64 (sqrt.f64 k) (*.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)) 8)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 2 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)) (*.f64 2 (*.f64 (/.f64 4 (sqrt.f64 k)) (*.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 2 (/.f64 (/.f64 1 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2))) (/.f64 8 (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 2 (/.f64 (*.f64 (sqrt.f64 k) (/.f64 1/4 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/2 (/.f64 (*.f64 1/2 (sqrt.f64 k)) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)) (/.f64 2 (*.f64 2 (*.f64 (/.f64 4 (sqrt.f64 k)) (*.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2))) (*.f64 (sqrt.f64 k) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2))) (/.f64 2 (/.f64 8 (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 k) (/.f64 1/4 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (sqrt.f64 k) (/.f64 1/4 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 2 (sqrt.f64 k)) (/.f64 1/8 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 2 (sqrt.f64 k)) (*.f64 1/8 (/.f64 1 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 2 (sqrt.f64 k)) (*.f64 (/.f64 1/8 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 2 (sqrt.f64 k)) (/.f64 2 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)) 1/16)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 2 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2))) (/.f64 1 (*.f64 2 (*.f64 (/.f64 4 (sqrt.f64 k)) (*.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 2 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2))) (/.f64 1/2 (/.f64 4 (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 2 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2))) (*.f64 (/.f64 1/2 (/.f64 4 (sqrt.f64 k))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 2 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2))) (*.f64 1/2 (*.f64 (sqrt.f64 k) 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 2 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2))) (/.f64 1 (/.f64 8 (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (sqrt.f64 k) 1/4) (/.f64 1 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (*.f64 1/2 (sqrt.f64 k)) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2))) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 2 (/.f64 2 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)))) (/.f64 1 (*.f64 (/.f64 4 (sqrt.f64 k)) 4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 1/2 (sqrt.f64 k)) (/.f64 1 (*.f64 2 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (sqrt.f64 k) 4) (/.f64 1 (*.f64 2 (*.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)) 8))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (sqrt.f64 k) 4) (/.f64 1 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)) 1/16)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -1 (/.f64 (/.f64 1 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2))) (neg.f64 (/.f64 4 (sqrt.f64 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -1 (/.f64 (/.f64 1 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2))) (/.f64 -4 (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -1 (/.f64 (*.f64 (sqrt.f64 k) 1/4) (neg.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 -1 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2))) (/.f64 (sqrt.f64 k) -4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 -1 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2))) (/.f64 1 (/.f64 -4 (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 k) -4) (/.f64 -1 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (sqrt.f64 k)) (/.f64 1 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)) -1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (sqrt.f64 k)) (/.f64 1 (neg.f64 (*.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)) 4))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/4 (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/4 (/.f64 (/.f64 1 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2))) (/.f64 1 (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1/4 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2))) (sqrt.f64 k))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1/4 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2))) (/.f64 1 (/.f64 1 (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1/2 (/.f64 4 (sqrt.f64 k))) (/.f64 2 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/8 (*.f64 (sqrt.f64 k) (/.f64 2 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (/.f64 1 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2))) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2))) (*.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)) (*.f64 (sqrt.f64 k) 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (/.f64 1 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2))) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2))) (/.f64 (*.f64 2 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2))) (/.f64 8 (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (/.f64 2 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2))) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2))) (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)) (*.f64 2 (/.f64 4 (sqrt.f64 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (/.f64 2 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2))) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2))) (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)) (/.f64 8 (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1/8 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2))) (*.f64 2 (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x not (not (*.f64 (sqrt.f64 k) (/.f64 1/4 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2))))))))) (#(struct:change #<rule egg-rr> (2) ((x and (*.f64 (sqrt.f64 k) (/.f64 1/4 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)))) (*.f64 (sqrt.f64 k) (/.f64 1/4 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x or (*.f64 (sqrt.f64 k) (/.f64 1/4 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)))) (*.f64 (sqrt.f64 k) (/.f64 1/4 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)))))))))

simplify137.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

1188×	`rational.json-simplify-55`
1058×	`rational.json-simplify-2`
758×	`rational.json-simplify-41`
708×	`rational.json-simplify-35`
606×	`rational.json-simplify-47`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	173	3277
1	456	3261
2	984	3213
3	3178	3213
4	5256	3213
5	7523	3213

Stop Event

1×	node limit

Counts

61 → 62

Calls

Call 1

Inputs
(.f64 1/4 (.f64 (sqrt.f64 k) (/.f64 1 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))))))))
(.f64 1/4 (.f64 (sqrt.f64 k) (/.f64 1 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))))))))
(.f64 1/4 (.f64 (sqrt.f64 k) (/.f64 1 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))))))))
(.f64 1/4 (.f64 (sqrt.f64 k) (/.f64 1 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))))))))
(.f64 1/4 (.f64 (sqrt.f64 k) (/.f64 1 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64))))))))))
(.f64 1/4 (.f64 (sqrt.f64 k) (/.f64 1 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64))))))))))
(.f64 1/4 (.f64 (sqrt.f64 k) (/.f64 1 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64))))))))))
(.f64 1/4 (.f64 (sqrt.f64 k) (/.f64 1 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64))))))))))
(.f64 1/4 (.f64 (sqrt.f64 k) (/.f64 1 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64))))))))))
(.f64 1/4 (.f64 (sqrt.f64 k) (/.f64 1 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64))))))))))
(.f64 1/4 (.f64 (sqrt.f64 k) (/.f64 1 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64))))))))))
(.f64 1/4 (.f64 (sqrt.f64 k) (/.f64 1 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64))))))))))
(+.f64 (.f64 (sqrt.f64 k) (/.f64 1/4 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)))) 0)
(+.f64 0 (.f64 (sqrt.f64 k) (/.f64 1/4 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)))))
(-.f64 (.f64 (sqrt.f64 k) (/.f64 1/4 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)))) 0)
(.f64 1 (.f64 (sqrt.f64 k) (/.f64 1/4 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)))))
(.f64 2 (/.f64 (/.f64 1 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2))) (*.f64 2 (/.f64 4 (sqrt.f64 k)))))
(.f64 2 (/.f64 (sqrt.f64 k) (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)) 8)))
(.f64 2 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)) (.f64 2 (.f64 (/.f64 4 (sqrt.f64 k)) (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)))))))
(.f64 2 (/.f64 (/.f64 1 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2))) (/.f64 8 (sqrt.f64 k))))
(.f64 2 (/.f64 (.f64 (sqrt.f64 k) (/.f64 1/4 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)))) 2))
(.f64 1/2 (/.f64 (.f64 1/2 (sqrt.f64 k)) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2))))
(.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)) (/.f64 2 (.f64 2 (.f64 (/.f64 4 (sqrt.f64 k)) (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)))))))
(.f64 (/.f64 1 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2))) (*.f64 (sqrt.f64 k) 1/4))
(.f64 (/.f64 1 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2))) (/.f64 2 (/.f64 8 (sqrt.f64 k))))
(.f64 (sqrt.f64 k) (/.f64 1/4 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2))))
(.f64 (.f64 (sqrt.f64 k) (/.f64 1/4 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)))) 1)
(.f64 (.f64 2 (sqrt.f64 k)) (/.f64 1/8 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2))))
(.f64 (.f64 2 (sqrt.f64 k)) (.f64 1/8 (/.f64 1 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)))))
(.f64 (.f64 2 (sqrt.f64 k)) (.f64 (/.f64 1/8 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2))) 1))
(.f64 (.f64 2 (sqrt.f64 k)) (/.f64 2 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)) 1/16)))
(.f64 (.f64 2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2))) (/.f64 1 (.f64 2 (.f64 (/.f64 4 (sqrt.f64 k)) (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)))))))
(.f64 (/.f64 2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2))) (/.f64 1/2 (/.f64 4 (sqrt.f64 k))))
(.f64 (/.f64 2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2))) (*.f64 (/.f64 1/2 (/.f64 4 (sqrt.f64 k))) 1))
(.f64 (/.f64 2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2))) (.f64 1/2 (.f64 (sqrt.f64 k) 1/4)))
(.f64 (/.f64 2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2))) (/.f64 1 (/.f64 8 (sqrt.f64 k))))
(.f64 (.f64 (sqrt.f64 k) 1/4) (/.f64 1 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2))))
(.f64 (/.f64 (.f64 1/2 (sqrt.f64 k)) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2))) 1/2)
(.f64 (.f64 2 (/.f64 2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)))) (/.f64 1 (.f64 (/.f64 4 (sqrt.f64 k)) 4)))
(.f64 (.f64 1/2 (sqrt.f64 k)) (/.f64 1 (.f64 2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)))))
(.f64 (.f64 (sqrt.f64 k) 4) (/.f64 1 (.f64 2 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)) 8))))
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(.f64 -1 (/.f64 (/.f64 1 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2))) (neg.f64 (/.f64 4 (sqrt.f64 k)))))
(.f64 -1 (/.f64 (/.f64 1 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2))) (/.f64 -4 (sqrt.f64 k))))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 k) 1/4) (neg.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)))))
(.f64 (/.f64 -1 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2))) (/.f64 (sqrt.f64 k) -4))
(.f64 (/.f64 -1 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2))) (/.f64 1 (/.f64 -4 (sqrt.f64 k))))
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(.f64 (neg.f64 (sqrt.f64 k)) (/.f64 1 (neg.f64 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)) 4))))
(.f64 1/4 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2))))
(.f64 1/4 (/.f64 (/.f64 1 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2))) (/.f64 1 (sqrt.f64 k))))
(.f64 (/.f64 1/4 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2))) (sqrt.f64 k))
(.f64 (/.f64 1/4 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2))) (/.f64 1 (/.f64 1 (sqrt.f64 k))))
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(.f64 1/8 (.f64 (sqrt.f64 k) (/.f64 2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)))))
(.f64 (/.f64 (/.f64 1 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2))) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2))) (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)) (.f64 (sqrt.f64 k) 1/4)))
(.f64 (/.f64 (/.f64 1 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2))) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2))) (/.f64 (.f64 2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2))) (/.f64 8 (sqrt.f64 k))))
(.f64 (/.f64 (/.f64 2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2))) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2))) (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)) (*.f64 2 (/.f64 4 (sqrt.f64 k)))))
(.f64 (/.f64 (/.f64 2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2))) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2))) (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)) (/.f64 8 (sqrt.f64 k))))
(.f64 (/.f64 1/8 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2))) (*.f64 2 (sqrt.f64 k)))

Outputs
(.f64 1/4 (.f64 (sqrt.f64 k) (/.f64 1 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))))))))
(.f64 1/4 (.f64 (sqrt.f64 k) (exp.f64 (neg.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))))))))
(.f64 1/4 (.f64 (sqrt.f64 k) (exp.f64 (.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))) -1/2))))
(.f64 1/4 (.f64 (sqrt.f64 k) (/.f64 1 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))))))))
(.f64 1/4 (.f64 (sqrt.f64 k) (exp.f64 (neg.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))))))))
(.f64 1/4 (.f64 (sqrt.f64 k) (exp.f64 (.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))) -1/2))))
(.f64 1/4 (.f64 (sqrt.f64 k) (/.f64 1 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))))))))
(.f64 1/4 (.f64 (sqrt.f64 k) (exp.f64 (neg.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))))))))
(.f64 1/4 (.f64 (sqrt.f64 k) (exp.f64 (.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))) -1/2))))
(.f64 1/4 (.f64 (sqrt.f64 k) (/.f64 1 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))))))))
(.f64 1/4 (.f64 (sqrt.f64 k) (exp.f64 (neg.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))))))))
(.f64 1/4 (.f64 (sqrt.f64 k) (exp.f64 (.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))) -1/2))))
(.f64 1/4 (.f64 (sqrt.f64 k) (/.f64 1 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64))))))))))
(.f64 1/4 (.f64 (sqrt.f64 k) (exp.f64 (neg.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (.f64 -1 (log.f64 (/.f64 1 n))))))))))
(.f64 1/4 (.f64 (sqrt.f64 k) (exp.f64 (neg.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n))))))))))
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(.f64 1/4 (.f64 (sqrt.f64 k) (exp.f64 (neg.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n))))))))))
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(.f64 1/4 (.f64 (sqrt.f64 k) (exp.f64 (neg.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n))))))))))
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(.f64 1/4 (.f64 (sqrt.f64 k) (/.f64 1 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64))))))))))
(.f64 1/4 (.f64 (sqrt.f64 k) (exp.f64 (neg.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (.f64 -1 (log.f64 (/.f64 1 n))))))))))
(.f64 1/4 (.f64 (sqrt.f64 k) (exp.f64 (neg.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n))))))))))
(.f64 1/4 (.f64 (sqrt.f64 k) (exp.f64 (.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n))))) -1/2))))
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(.f64 1/4 (.f64 (sqrt.f64 k) (exp.f64 (neg.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 (PI.f64) -2)))))))))
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(+.f64 0 (.f64 (sqrt.f64 k) (/.f64 1/4 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)))))
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(.f64 1/4 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 1/2 (-.f64 1 k)))))
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(.f64 (sqrt.f64 k) (/.f64 1/4 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 1/2 (-.f64 1 k)))))
(.f64 1/4 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 1/2 (-.f64 1 k)))))
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(.f64 (sqrt.f64 k) (/.f64 1/4 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 1/2 (-.f64 1 k)))))
(.f64 1/4 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 1/2 (-.f64 1 k)))))
(.f64 2 (/.f64 (sqrt.f64 k) (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)) 8)))
(.f64 (sqrt.f64 k) (/.f64 1/4 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 1/2 (-.f64 1 k)))))
(.f64 1/4 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 1/2 (-.f64 1 k)))))
(.f64 2 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)) (.f64 2 (.f64 (/.f64 4 (sqrt.f64 k)) (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)))))))
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(.f64 1/2 (/.f64 (.f64 1/2 (sqrt.f64 k)) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2))))
(.f64 (sqrt.f64 k) (/.f64 1/4 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 1/2 (-.f64 1 k)))))
(.f64 1/4 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 1/2 (-.f64 1 k)))))
(.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)) (/.f64 2 (.f64 2 (.f64 (/.f64 4 (sqrt.f64 k)) (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)))))))
(.f64 (sqrt.f64 k) (/.f64 1/4 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 1/2 (-.f64 1 k)))))
(.f64 1/4 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 1/2 (-.f64 1 k)))))
(.f64 (/.f64 1 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2))) (*.f64 (sqrt.f64 k) 1/4))
(.f64 (sqrt.f64 k) (/.f64 1/4 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 1/2 (-.f64 1 k)))))
(.f64 1/4 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 1/2 (-.f64 1 k)))))
(.f64 (/.f64 1 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2))) (/.f64 2 (/.f64 8 (sqrt.f64 k))))
(.f64 (sqrt.f64 k) (/.f64 1/4 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 1/2 (-.f64 1 k)))))
(.f64 1/4 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 1/2 (-.f64 1 k)))))
(.f64 (sqrt.f64 k) (/.f64 1/4 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2))))
(.f64 (sqrt.f64 k) (/.f64 1/4 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 1/2 (-.f64 1 k)))))
(.f64 1/4 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 1/2 (-.f64 1 k)))))
(.f64 (.f64 (sqrt.f64 k) (/.f64 1/4 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)))) 1)
(.f64 (sqrt.f64 k) (/.f64 1/4 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 1/2 (-.f64 1 k)))))
(.f64 1/4 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 1/2 (-.f64 1 k)))))
(.f64 (.f64 2 (sqrt.f64 k)) (/.f64 1/8 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2))))
(.f64 (sqrt.f64 k) (/.f64 1/4 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 1/2 (-.f64 1 k)))))
(.f64 1/4 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 1/2 (-.f64 1 k)))))
(.f64 (.f64 2 (sqrt.f64 k)) (.f64 1/8 (/.f64 1 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)))))
(.f64 (sqrt.f64 k) (/.f64 1/4 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 1/2 (-.f64 1 k)))))
(.f64 1/4 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 1/2 (-.f64 1 k)))))
(.f64 (.f64 2 (sqrt.f64 k)) (.f64 (/.f64 1/8 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2))) 1))
(.f64 (sqrt.f64 k) (/.f64 1/4 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 1/2 (-.f64 1 k)))))
(.f64 1/4 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 1/2 (-.f64 1 k)))))
(.f64 (.f64 2 (sqrt.f64 k)) (/.f64 2 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)) 1/16)))
(.f64 (sqrt.f64 k) (/.f64 1/4 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 1/2 (-.f64 1 k)))))
(.f64 1/4 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 1/2 (-.f64 1 k)))))
(.f64 (.f64 2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2))) (/.f64 1 (.f64 2 (.f64 (/.f64 4 (sqrt.f64 k)) (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)))))))
(.f64 (sqrt.f64 k) (/.f64 1/4 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 1/2 (-.f64 1 k)))))
(.f64 1/4 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 1/2 (-.f64 1 k)))))
(.f64 (/.f64 2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2))) (/.f64 1/2 (/.f64 4 (sqrt.f64 k))))
(.f64 (sqrt.f64 k) (/.f64 1/4 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 1/2 (-.f64 1 k)))))
(.f64 1/4 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 1/2 (-.f64 1 k)))))
(.f64 (/.f64 2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2))) (*.f64 (/.f64 1/2 (/.f64 4 (sqrt.f64 k))) 1))
(.f64 (sqrt.f64 k) (/.f64 1/4 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 1/2 (-.f64 1 k)))))
(.f64 1/4 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 1/2 (-.f64 1 k)))))
(.f64 (/.f64 2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2))) (.f64 1/2 (.f64 (sqrt.f64 k) 1/4)))
(.f64 (sqrt.f64 k) (/.f64 1/4 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 1/2 (-.f64 1 k)))))
(.f64 1/4 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 1/2 (-.f64 1 k)))))
(.f64 (/.f64 2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2))) (/.f64 1 (/.f64 8 (sqrt.f64 k))))
(.f64 (sqrt.f64 k) (/.f64 1/4 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 1/2 (-.f64 1 k)))))
(.f64 1/4 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 1/2 (-.f64 1 k)))))
(.f64 (.f64 (sqrt.f64 k) 1/4) (/.f64 1 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2))))
(.f64 (sqrt.f64 k) (/.f64 1/4 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 1/2 (-.f64 1 k)))))
(.f64 1/4 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 1/2 (-.f64 1 k)))))
(.f64 (/.f64 (.f64 1/2 (sqrt.f64 k)) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2))) 1/2)
(.f64 (sqrt.f64 k) (/.f64 1/4 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 1/2 (-.f64 1 k)))))
(.f64 1/4 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 1/2 (-.f64 1 k)))))
(.f64 (.f64 2 (/.f64 2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)))) (/.f64 1 (.f64 (/.f64 4 (sqrt.f64 k)) 4)))
(.f64 (sqrt.f64 k) (/.f64 1/4 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 1/2 (-.f64 1 k)))))
(.f64 1/4 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 1/2 (-.f64 1 k)))))
(.f64 (.f64 1/2 (sqrt.f64 k)) (/.f64 1 (.f64 2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)))))
(.f64 (sqrt.f64 k) (/.f64 1/4 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 1/2 (-.f64 1 k)))))
(.f64 1/4 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 1/2 (-.f64 1 k)))))
(.f64 (.f64 (sqrt.f64 k) 4) (/.f64 1 (.f64 2 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)) 8))))
(.f64 (sqrt.f64 k) (/.f64 1/4 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 1/2 (-.f64 1 k)))))
(.f64 1/4 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 1/2 (-.f64 1 k)))))
(.f64 (.f64 (sqrt.f64 k) 4) (/.f64 1 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)) 1/16)))
(.f64 (sqrt.f64 k) (/.f64 1/4 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 1/2 (-.f64 1 k)))))
(.f64 1/4 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 1/2 (-.f64 1 k)))))
(.f64 -1 (/.f64 (/.f64 1 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2))) (neg.f64 (/.f64 4 (sqrt.f64 k)))))
(.f64 (sqrt.f64 k) (/.f64 1/4 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 1/2 (-.f64 1 k)))))
(.f64 1/4 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 1/2 (-.f64 1 k)))))
(.f64 -1 (/.f64 (/.f64 1 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2))) (/.f64 -4 (sqrt.f64 k))))
(.f64 (sqrt.f64 k) (/.f64 1/4 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 1/2 (-.f64 1 k)))))
(.f64 1/4 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 1/2 (-.f64 1 k)))))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 k) 1/4) (neg.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)))))
(.f64 (sqrt.f64 k) (/.f64 1/4 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 1/2 (-.f64 1 k)))))
(.f64 1/4 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 1/2 (-.f64 1 k)))))
(.f64 (/.f64 -1 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2))) (/.f64 (sqrt.f64 k) -4))
(.f64 (sqrt.f64 k) (/.f64 1/4 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 1/2 (-.f64 1 k)))))
(.f64 1/4 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 1/2 (-.f64 1 k)))))
(.f64 (/.f64 -1 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2))) (/.f64 1 (/.f64 -4 (sqrt.f64 k))))
(.f64 (sqrt.f64 k) (/.f64 1/4 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 1/2 (-.f64 1 k)))))
(.f64 1/4 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 1/2 (-.f64 1 k)))))
(.f64 (/.f64 (sqrt.f64 k) -4) (/.f64 -1 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2))))
(.f64 (sqrt.f64 k) (/.f64 1/4 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 1/2 (-.f64 1 k)))))
(.f64 1/4 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 1/2 (-.f64 1 k)))))
(.f64 (neg.f64 (sqrt.f64 k)) (/.f64 1 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)) -1/4)))
(.f64 (sqrt.f64 k) (/.f64 1/4 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 1/2 (-.f64 1 k)))))
(.f64 1/4 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 1/2 (-.f64 1 k)))))
(.f64 (neg.f64 (sqrt.f64 k)) (/.f64 1 (neg.f64 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)) 4))))
(.f64 (sqrt.f64 k) (/.f64 1/4 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 1/2 (-.f64 1 k)))))
(.f64 1/4 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 1/2 (-.f64 1 k)))))
(.f64 1/4 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2))))
(.f64 (sqrt.f64 k) (/.f64 1/4 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 1/2 (-.f64 1 k)))))
(.f64 1/4 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 1/2 (-.f64 1 k)))))
(.f64 1/4 (/.f64 (/.f64 1 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2))) (/.f64 1 (sqrt.f64 k))))
(.f64 (sqrt.f64 k) (/.f64 1/4 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 1/2 (-.f64 1 k)))))
(.f64 1/4 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 1/2 (-.f64 1 k)))))
(.f64 (/.f64 1/4 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2))) (sqrt.f64 k))
(.f64 (sqrt.f64 k) (/.f64 1/4 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 1/2 (-.f64 1 k)))))
(.f64 1/4 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 1/2 (-.f64 1 k)))))
(.f64 (/.f64 1/4 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2))) (/.f64 1 (/.f64 1 (sqrt.f64 k))))
(.f64 (sqrt.f64 k) (/.f64 1/4 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 1/2 (-.f64 1 k)))))
(.f64 1/4 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 1/2 (-.f64 1 k)))))
(.f64 (/.f64 1/2 (/.f64 4 (sqrt.f64 k))) (/.f64 2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2))))
(.f64 (sqrt.f64 k) (/.f64 1/4 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 1/2 (-.f64 1 k)))))
(.f64 1/4 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 1/2 (-.f64 1 k)))))
(.f64 1/8 (.f64 (sqrt.f64 k) (/.f64 2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)))))
(.f64 (sqrt.f64 k) (/.f64 1/4 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 1/2 (-.f64 1 k)))))
(.f64 1/4 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 1/2 (-.f64 1 k)))))
(.f64 (/.f64 (/.f64 1 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2))) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2))) (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)) (.f64 (sqrt.f64 k) 1/4)))
(.f64 (sqrt.f64 k) (/.f64 1/4 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 1/2 (-.f64 1 k)))))
(.f64 1/4 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 1/2 (-.f64 1 k)))))
(.f64 (/.f64 (/.f64 1 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2))) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2))) (/.f64 (.f64 2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2))) (/.f64 8 (sqrt.f64 k))))
(.f64 (sqrt.f64 k) (/.f64 1/4 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 1/2 (-.f64 1 k)))))
(.f64 1/4 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 1/2 (-.f64 1 k)))))
(.f64 (/.f64 (/.f64 2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2))) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2))) (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)) (*.f64 2 (/.f64 4 (sqrt.f64 k)))))
(.f64 (sqrt.f64 k) (/.f64 1/4 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 1/2 (-.f64 1 k)))))
(.f64 1/4 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 1/2 (-.f64 1 k)))))
(.f64 (/.f64 (/.f64 2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2))) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2))) (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)) (/.f64 8 (sqrt.f64 k))))
(.f64 (sqrt.f64 k) (/.f64 1/4 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 1/2 (-.f64 1 k)))))
(.f64 1/4 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 1/2 (-.f64 1 k)))))
(.f64 (/.f64 1/8 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2))) (*.f64 2 (sqrt.f64 k)))
(.f64 (sqrt.f64 k) (/.f64 1/4 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 1/2 (-.f64 1 k)))))
(.f64 1/4 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 1/2 (-.f64 1 k)))))

localize22.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(*.f64 (PI.f64) n)
	0.3b	(/.f64 1 (sqrt.f64 k))
✓	0.4b	(.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 (PI.f64) n))))
✓	0.5b	(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 (PI.f64) n)))

Compiler

Compiled 41 to 21 computations (48.8% saved)

series5.0ms (0%)

Counts

2 → 0

Calls

9 calls:

Time	Variable		Point	Expression
1.0ms	k	@	-inf	(.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 (PI.f64) n))))
1.0ms	n	@	-inf	(.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 (PI.f64) n))))
1.0ms	n	@	-inf	(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 (PI.f64) n)))
0.0ms	n	@	0	(.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 (PI.f64) n))))
0.0ms	k	@	0	(.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 (PI.f64) n))))

rewrite83.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

1758×	`bool.json-1`
1758×	`bool.json-2`
1722×	`rational.json-1`
1378×	`bool.json-3`
710×	`rational.json-simplify-35`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	16	62
1	161	56
2	407	56
3	840	56
4	1854	56
5	5450	56

Stop Event

1×	node limit

Counts

2 → 66

Calls

Call 1

Inputs
(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 (PI.f64) n)))
(.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 (PI.f64) n))))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 (PI.f64) n))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 (PI.f64) n))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 (PI.f64) n))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 (PI.f64) n))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 (PI.f64) n)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) 4)) 4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) 4))) 8)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (*.f64 2 (*.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) 4))) (*.f64 2 (*.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) 4)))) 16)))) (#(struct:change #<rule egg-rr> (2) ((x not (not (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 (PI.f64) n)))))))) (#(struct:change #<rule egg-rr> (2) ((x and (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 (PI.f64) n))) (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 (PI.f64) n))))))) (#(struct:change #<rule egg-rr> (2) ((x or (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 (PI.f64) n))) (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 (PI.f64) n))))))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 k))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (*.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 k))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 2 (/.f64 (sqrt.f64 k) (*.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 2 (/.f64 (*.f64 2 (sqrt.f64 k)) (neg.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (neg.f64 (sqrt.f64 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 (PI.f64) n))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 (sqrt.f64 k) (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 (PI.f64) n))) (sqrt.f64 k))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (sqrt.f64 k) (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 (PI.f64) n)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (*.f64 (*.f64 1/2 (/.f64 (sqrt.f64 k) (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 (PI.f64) n))))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 (PI.f64) n)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 k))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 4 (/.f64 (*.f64 (sqrt.f64 k) 4) (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 (PI.f64) n)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 4 (*.f64 (/.f64 (sqrt.f64 k) (*.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) 1/2))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 4 (*.f64 (/.f64 (*.f64 (sqrt.f64 k) 4) (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 (PI.f64) n)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x 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(#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (sqrt.f64 k) (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 (PI.f64) n)))) (*.f64 (/.f64 (sqrt.f64 k) (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 (PI.f64) n)))) (/.f64 (sqrt.f64 k) (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 (PI.f64) n))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (sqrt.f64 k) (*.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) 1/2))) (*.f64 (*.f64 (/.f64 (sqrt.f64 k) (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 (PI.f64) n)))) (/.f64 (sqrt.f64 k) (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 (PI.f64) n))))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 k)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) 4))) 8)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (neg.f64 (sqrt.f64 2)))) (*.f64 (sqrt.f64 k) -2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) 4))) (*.f64 (sqrt.f64 k) 8))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) 4))) (*.f64 8 (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 (sqrt.f64 2) (/.f64 1/2 (sqrt.f64 k)))) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) 1/2)) (*.f64 (sqrt.f64 k) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (*.f64 2 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 (PI.f64) n))))) (*.f64 (sqrt.f64 k) -2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (*.f64 2 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 (PI.f64) n))))) (neg.f64 (*.f64 2 (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (neg.f64 (sqrt.f64 2)))) (sqrt.f64 k))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 (sqrt.f64 2) (/.f64 1/2 (sqrt.f64 k)))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 (sqrt.f64 2) (/.f64 1/2 (sqrt.f64 k))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (neg.f64 (*.f64 2 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 (PI.f64) n))))) (neg.f64 (*.f64 2 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 (PI.f64) n)))))) (*.f64 2 (neg.f64 (*.f64 2 (sqrt.f64 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (*.f64 2 (*.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 k)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) 4))) (*.f64 2 (*.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 k)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) 4)))) 16)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (*.f64 2 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (neg.f64 (sqrt.f64 2)))) (*.f64 2 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (neg.f64 (sqrt.f64 2))))) (*.f64 2 (*.f64 (sqrt.f64 k) -2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (neg.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (neg.f64 (sqrt.f64 2)))) (neg.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (neg.f64 (sqrt.f64 2))))) (*.f64 2 (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (neg.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (neg.f64 (sqrt.f64 2)))) 2) (*.f64 (sqrt.f64 k) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 (PI.f64) n))) 1/2) (*.f64 2 (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (neg.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (neg.f64 (sqrt.f64 2)))) 1/2) (*.f64 2 (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (*.f64 2 (*.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) 4))) (sqrt.f64 k)) 8)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 (PI.f64) n))) (neg.f64 (sqrt.f64 k))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 (PI.f64) n))) (*.f64 (sqrt.f64 k) 4)) 1/4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (neg.f64 (sqrt.f64 2))) (sqrt.f64 k)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (neg.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (neg.f64 (sqrt.f64 2)))) (*.f64 (sqrt.f64 k) 4)) 1/4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (*.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) 4))) (neg.f64 (*.f64 (sqrt.f64 k) 4)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (neg.f64 (*.f64 2 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 (PI.f64) n)))))) (*.f64 2 (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (neg.f64 (*.f64 2 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 (PI.f64) n)))))) (-.f64 0 (neg.f64 (*.f64 2 (sqrt.f64 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (*.f64 2 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (neg.f64 (sqrt.f64 2))))) (-.f64 0 (*.f64 (sqrt.f64 k) -2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (neg.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (neg.f64 (sqrt.f64 2))))) (neg.f64 (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x not (not (*.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x and (*.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 k))) (*.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x or (*.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 k))) (*.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 k))))))))

simplify76.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

1514×	`rational.json-simplify-35`
1248×	`rational.json-simplify-46`
1030×	`rational.json-simplify-53`
834×	`rational.json-simplify-43`
766×	`rational.json-simplify-50`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	163	2098
1	557	2098
2	1918	2098
3	4983	2098

Stop Event

1×	node limit

Counts

66 → 68

Calls

Call 1

Inputs
(+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 (PI.f64) n))) 0)
(+.f64 0 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 (PI.f64) n))))
(-.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 (PI.f64) n))) 0)
(/.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 (PI.f64) n))) 1)
(/.f64 (.f64 2 (.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 (PI.f64) n)))) 2)
(/.f64 (.f64 (sqrt.f64 2) (.f64 (sqrt.f64 (*.f64 (PI.f64) n)) 4)) 4)
(/.f64 (.f64 2 (.f64 (sqrt.f64 2) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) 4))) 8)
(/.f64 (+.f64 (.f64 2 (.f64 (sqrt.f64 2) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) 4))) (.f64 2 (.f64 (sqrt.f64 2) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) 4)))) 16)
(+.f64 (.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 k))) 0)
(+.f64 0 (.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 k))))
(-.f64 (.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 k))) 0)
(/.f64 2 (/.f64 (sqrt.f64 k) (.f64 (sqrt.f64 2) (.f64 (sqrt.f64 (*.f64 (PI.f64) n)) 1/2))))
(/.f64 2 (/.f64 (.f64 2 (sqrt.f64 k)) (neg.f64 (.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (neg.f64 (sqrt.f64 2))))))
(/.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 (PI.f64) n))))
(/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 (sqrt.f64 k) (sqrt.f64 2)))
(/.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 (PI.f64) n))) (sqrt.f64 k))
(/.f64 1 (/.f64 (sqrt.f64 k) (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 (PI.f64) n)))))
(/.f64 1 (.f64 (.f64 1/2 (/.f64 (sqrt.f64 k) (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 (PI.f64) n))))) 2))
(/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 (PI.f64) n)))))
(/.f64 (.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 k))) 1)
(/.f64 4 (/.f64 (.f64 (sqrt.f64 k) 4) (.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 (PI.f64) n)))))
(/.f64 4 (.f64 (/.f64 (sqrt.f64 k) (.f64 (sqrt.f64 2) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) 1/2))) 2))
(/.f64 4 (.f64 (/.f64 (.f64 (sqrt.f64 k) 4) (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 (PI.f64) n)))) 1))
(/.f64 4 (/.f64 (.f64 (sqrt.f64 k) 4) (neg.f64 (.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (neg.f64 (sqrt.f64 2))))))
(/.f64 (/.f64 2 (sqrt.f64 k)) (/.f64 2 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 (PI.f64) n)))))
(/.f64 (.f64 2 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 (PI.f64) n)))) (.f64 2 (sqrt.f64 k)))
(/.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (*.f64 2 (/.f64 (sqrt.f64 2) (sqrt.f64 k)))) 2)
(/.f64 1/2 (.f64 1/2 (/.f64 (sqrt.f64 k) (.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 (PI.f64) n))))))
(/.f64 -1 (/.f64 (sqrt.f64 k) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (neg.f64 (sqrt.f64 2)))))
(/.f64 -1 (-.f64 0 (/.f64 (sqrt.f64 k) (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 (PI.f64) n))))))
(/.f64 8 (+.f64 (/.f64 (.f64 (sqrt.f64 k) 4) (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 (PI.f64) n)))) (/.f64 (.f64 (sqrt.f64 k) 4) (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 (PI.f64) n))))))
(/.f64 8 (/.f64 (.f64 (sqrt.f64 k) 8) (.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 (PI.f64) n)))))
(/.f64 8 (/.f64 (.f64 (sqrt.f64 k) 8) (neg.f64 (.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (neg.f64 (sqrt.f64 2))))))
(/.f64 (.f64 (sqrt.f64 2) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) 4)) (.f64 (sqrt.f64 k) 4))
(/.f64 -2 (-.f64 0 (/.f64 (sqrt.f64 k) (.f64 (sqrt.f64 2) (.f64 (sqrt.f64 (*.f64 (PI.f64) n)) 1/2)))))
(/.f64 (.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 k)) (.f64 (sqrt.f64 (*.f64 (PI.f64) n)) 4)) 4)
(/.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (neg.f64 (sqrt.f64 2))) (neg.f64 (sqrt.f64 k)))
(/.f64 (/.f64 (sqrt.f64 k) (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 (PI.f64) n)))) (.f64 (/.f64 (sqrt.f64 k) (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 (PI.f64) n)))) (/.f64 (sqrt.f64 k) (.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 (PI.f64) n))))))
(/.f64 (/.f64 (sqrt.f64 k) (.f64 (sqrt.f64 2) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) 1/2))) (.f64 (.f64 (/.f64 (sqrt.f64 k) (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 (PI.f64) n)))) (/.f64 (sqrt.f64 k) (.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 (PI.f64) n))))) 2))
(/.f64 (.f64 2 (.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 k)) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) 4))) 8)
(/.f64 (.f64 2 (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (neg.f64 (sqrt.f64 2)))) (.f64 (sqrt.f64 k) -2))
(/.f64 (.f64 2 (.f64 (sqrt.f64 2) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) 4))) (*.f64 (sqrt.f64 k) 8))
(/.f64 (.f64 2 (.f64 (sqrt.f64 2) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) 4))) (*.f64 8 (sqrt.f64 k)))
(/.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (*.f64 (sqrt.f64 2) (/.f64 1/2 (sqrt.f64 k)))) 1/2)
(/.f64 (.f64 (sqrt.f64 2) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) 1/2)) (.f64 (sqrt.f64 k) 1/2))
(/.f64 (neg.f64 (.f64 2 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 (PI.f64) n))))) (.f64 (sqrt.f64 k) -2))
(/.f64 (neg.f64 (.f64 2 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 (PI.f64) n))))) (neg.f64 (.f64 2 (sqrt.f64 k))))
(/.f64 (neg.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (neg.f64 (sqrt.f64 2)))) (sqrt.f64 k))
(/.f64 (+.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (.f64 (sqrt.f64 2) (/.f64 1/2 (sqrt.f64 k)))) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (.f64 (sqrt.f64 2) (/.f64 1/2 (sqrt.f64 k))))) 1)
(/.f64 (+.f64 (neg.f64 (.f64 2 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 (PI.f64) n))))) (neg.f64 (.f64 2 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 (PI.f64) n)))))) (.f64 2 (neg.f64 (.f64 2 (sqrt.f64 k)))))
(/.f64 (+.f64 (.f64 2 (.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 k)) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) 4))) (.f64 2 (.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 k)) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) 4)))) 16)
(/.f64 (+.f64 (.f64 2 (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (neg.f64 (sqrt.f64 2)))) (.f64 2 (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (neg.f64 (sqrt.f64 2))))) (.f64 2 (.f64 (sqrt.f64 k) -2)))
(/.f64 (+.f64 (neg.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (neg.f64 (sqrt.f64 2)))) (neg.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (neg.f64 (sqrt.f64 2))))) (*.f64 2 (sqrt.f64 k)))
(/.f64 (/.f64 (neg.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (neg.f64 (sqrt.f64 2)))) 2) (*.f64 (sqrt.f64 k) 1/2))
(/.f64 (/.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 (PI.f64) n))) 1/2) (*.f64 2 (sqrt.f64 k)))
(/.f64 (/.f64 (neg.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (neg.f64 (sqrt.f64 2)))) 1/2) (*.f64 2 (sqrt.f64 k)))
(/.f64 (/.f64 (.f64 2 (.f64 (sqrt.f64 2) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) 4))) (sqrt.f64 k)) 8)
(/.f64 (/.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 (PI.f64) n))) (neg.f64 (sqrt.f64 k))) -1)
(/.f64 (/.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 (PI.f64) n))) (*.f64 (sqrt.f64 k) 4)) 1/4)
(/.f64 (/.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (neg.f64 (sqrt.f64 2))) (sqrt.f64 k)) -1)
(/.f64 (/.f64 (neg.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (neg.f64 (sqrt.f64 2)))) (*.f64 (sqrt.f64 k) 4)) 1/4)
(/.f64 (neg.f64 (.f64 (sqrt.f64 2) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) 4))) (neg.f64 (.f64 (sqrt.f64 k) 4)))
(/.f64 (neg.f64 (neg.f64 (.f64 2 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 (PI.f64) n)))))) (.f64 2 (sqrt.f64 k)))
(/.f64 (neg.f64 (neg.f64 (.f64 2 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 (PI.f64) n)))))) (-.f64 0 (neg.f64 (.f64 2 (sqrt.f64 k)))))
(/.f64 (neg.f64 (.f64 2 (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (neg.f64 (sqrt.f64 2))))) (-.f64 0 (.f64 (sqrt.f64 k) -2)))
(/.f64 (neg.f64 (neg.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (neg.f64 (sqrt.f64 2))))) (neg.f64 (sqrt.f64 k)))

Outputs
(+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 (PI.f64) n))) 0)
(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 (PI.f64) n)))
(+.f64 0 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 (PI.f64) n))))
(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 (PI.f64) n)))
(-.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 (PI.f64) n))) 0)
(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 (PI.f64) n)))
(/.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 (PI.f64) n))) 1)
(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 (PI.f64) n)))
(/.f64 (.f64 2 (.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 (PI.f64) n)))) 2)
(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 (PI.f64) n)))
(/.f64 (.f64 (sqrt.f64 2) (.f64 (sqrt.f64 (*.f64 (PI.f64) n)) 4)) 4)
(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 (PI.f64) n)))
(/.f64 (.f64 2 (.f64 (sqrt.f64 2) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) 4))) 8)
(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 (PI.f64) n)))
(/.f64 (+.f64 (.f64 2 (.f64 (sqrt.f64 2) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) 4))) (.f64 2 (.f64 (sqrt.f64 2) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) 4)))) 16)
(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 (PI.f64) n)))
(+.f64 (.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 k))) 0)
(.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 k)))
(+.f64 0 (.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 k))))
(.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 k)))
(-.f64 (.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 k))) 0)
(.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 k)))
(/.f64 2 (/.f64 (sqrt.f64 k) (.f64 (sqrt.f64 2) (.f64 (sqrt.f64 (*.f64 (PI.f64) n)) 1/2))))
(.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 k)))
(/.f64 2 (/.f64 (.f64 2 (sqrt.f64 k)) (neg.f64 (.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (neg.f64 (sqrt.f64 2))))))
(.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 k)))
(/.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 (PI.f64) n))))
(.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 k)))
(/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 (sqrt.f64 k) (sqrt.f64 2)))
(.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 k)))
(/.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 (PI.f64) n))) (sqrt.f64 k))
(.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 k)))
(/.f64 1 (/.f64 (sqrt.f64 k) (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 (PI.f64) n)))))
(.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 k)))
(/.f64 1 (.f64 (.f64 1/2 (/.f64 (sqrt.f64 k) (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 (PI.f64) n))))) 2))
(.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 k)))
(/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 (PI.f64) n)))))
(.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 k)))
(/.f64 (.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 k))) 1)
(.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 k)))
(/.f64 4 (/.f64 (.f64 (sqrt.f64 k) 4) (.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 (PI.f64) n)))))
(.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 k)))
(/.f64 4 (.f64 (/.f64 (sqrt.f64 k) (.f64 (sqrt.f64 2) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) 1/2))) 2))
(.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 k)))
(/.f64 4 (.f64 (/.f64 (.f64 (sqrt.f64 k) 4) (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 (PI.f64) n)))) 1))
(.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 k)))
(/.f64 4 (/.f64 (.f64 (sqrt.f64 k) 4) (neg.f64 (.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (neg.f64 (sqrt.f64 2))))))
(.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 k)))
(/.f64 (/.f64 2 (sqrt.f64 k)) (/.f64 2 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 (PI.f64) n)))))
(.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 k)))
(/.f64 (.f64 2 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 (PI.f64) n)))) (.f64 2 (sqrt.f64 k)))
(.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 k)))
(/.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (*.f64 2 (/.f64 (sqrt.f64 2) (sqrt.f64 k)))) 2)
(.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 k)))
(/.f64 1/2 (.f64 1/2 (/.f64 (sqrt.f64 k) (.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 (PI.f64) n))))))
(.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 k)))
(/.f64 -1 (/.f64 (sqrt.f64 k) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (neg.f64 (sqrt.f64 2)))))
(.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 k)))
(/.f64 -1 (-.f64 0 (/.f64 (sqrt.f64 k) (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 (PI.f64) n))))))
(.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 k)))
(/.f64 8 (+.f64 (/.f64 (.f64 (sqrt.f64 k) 4) (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 (PI.f64) n)))) (/.f64 (.f64 (sqrt.f64 k) 4) (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 (PI.f64) n))))))
(.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 k)))
(/.f64 8 (/.f64 (.f64 (sqrt.f64 k) 8) (.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 (PI.f64) n)))))
(.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 k)))
(/.f64 8 (/.f64 (.f64 (sqrt.f64 k) 8) (neg.f64 (.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (neg.f64 (sqrt.f64 2))))))
(.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 k)))
(/.f64 (.f64 (sqrt.f64 2) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) 4)) (.f64 (sqrt.f64 k) 4))
(.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 k)))
(/.f64 -2 (-.f64 0 (/.f64 (sqrt.f64 k) (.f64 (sqrt.f64 2) (.f64 (sqrt.f64 (*.f64 (PI.f64) n)) 1/2)))))
(.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 k)))
(/.f64 (.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 k)) (.f64 (sqrt.f64 (*.f64 (PI.f64) n)) 4)) 4)
(.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 k)))
(/.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (neg.f64 (sqrt.f64 2))) (neg.f64 (sqrt.f64 k)))
(.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 k)))
(/.f64 (/.f64 (sqrt.f64 k) (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 (PI.f64) n)))) (.f64 (/.f64 (sqrt.f64 k) (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 (PI.f64) n)))) (/.f64 (sqrt.f64 k) (.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 (PI.f64) n))))))
(.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 k)))
(/.f64 (/.f64 (sqrt.f64 k) (.f64 (sqrt.f64 2) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) 1/2))) (.f64 (.f64 (/.f64 (sqrt.f64 k) (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 (PI.f64) n)))) (/.f64 (sqrt.f64 k) (.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 (PI.f64) n))))) 2))
(.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 k)))
(/.f64 (.f64 2 (.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 k)) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) 4))) 8)
(.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 k)))
(/.f64 (.f64 2 (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (neg.f64 (sqrt.f64 2)))) (.f64 (sqrt.f64 k) -2))
(.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 k)))
(/.f64 (.f64 2 (.f64 (sqrt.f64 2) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) 4))) (*.f64 (sqrt.f64 k) 8))
(.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 k)))
(/.f64 (.f64 2 (.f64 (sqrt.f64 2) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) 4))) (*.f64 8 (sqrt.f64 k)))
(.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 k)))
(/.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (*.f64 (sqrt.f64 2) (/.f64 1/2 (sqrt.f64 k)))) 1/2)
(.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 k)))
(/.f64 (.f64 (sqrt.f64 2) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) 1/2)) (.f64 (sqrt.f64 k) 1/2))
(.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 k)))
(/.f64 (neg.f64 (.f64 2 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 (PI.f64) n))))) (.f64 (sqrt.f64 k) -2))
(.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 k)))
(/.f64 (neg.f64 (.f64 2 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 (PI.f64) n))))) (neg.f64 (.f64 2 (sqrt.f64 k))))
(.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 k)))
(/.f64 (neg.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (neg.f64 (sqrt.f64 2)))) (sqrt.f64 k))
(.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 k)))
(/.f64 (+.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (.f64 (sqrt.f64 2) (/.f64 1/2 (sqrt.f64 k)))) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (.f64 (sqrt.f64 2) (/.f64 1/2 (sqrt.f64 k))))) 1)
(.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 k)))
(/.f64 (+.f64 (neg.f64 (.f64 2 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 (PI.f64) n))))) (neg.f64 (.f64 2 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 (PI.f64) n)))))) (.f64 2 (neg.f64 (.f64 2 (sqrt.f64 k)))))
(.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 k)))
(/.f64 (+.f64 (.f64 2 (.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 k)) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) 4))) (.f64 2 (.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 k)) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) 4)))) 16)
(.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 k)))
(/.f64 (+.f64 (.f64 2 (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (neg.f64 (sqrt.f64 2)))) (.f64 2 (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (neg.f64 (sqrt.f64 2))))) (.f64 2 (.f64 (sqrt.f64 k) -2)))
(.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 k)))
(/.f64 (+.f64 (neg.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (neg.f64 (sqrt.f64 2)))) (neg.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (neg.f64 (sqrt.f64 2))))) (*.f64 2 (sqrt.f64 k)))
(.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 k)))
(/.f64 (/.f64 (neg.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (neg.f64 (sqrt.f64 2)))) 2) (*.f64 (sqrt.f64 k) 1/2))
(.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 k)))
(/.f64 (/.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 (PI.f64) n))) 1/2) (*.f64 2 (sqrt.f64 k)))
(.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 k)))
(/.f64 (/.f64 (neg.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (neg.f64 (sqrt.f64 2)))) 1/2) (*.f64 2 (sqrt.f64 k)))
(.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 k)))
(/.f64 (/.f64 (.f64 2 (.f64 (sqrt.f64 2) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) 4))) (sqrt.f64 k)) 8)
(.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 k)))
(/.f64 (/.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 (PI.f64) n))) (neg.f64 (sqrt.f64 k))) -1)
(.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 k)))
(/.f64 (/.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 (PI.f64) n))) (*.f64 (sqrt.f64 k) 4)) 1/4)
(.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 k)))
(/.f64 (/.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (neg.f64 (sqrt.f64 2))) (sqrt.f64 k)) -1)
(.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 k)))
(/.f64 (/.f64 (neg.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (neg.f64 (sqrt.f64 2)))) (*.f64 (sqrt.f64 k) 4)) 1/4)
(.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 k)))
(/.f64 (neg.f64 (.f64 (sqrt.f64 2) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) 4))) (neg.f64 (.f64 (sqrt.f64 k) 4)))
(.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 k)))
(/.f64 (neg.f64 (neg.f64 (.f64 2 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 (PI.f64) n)))))) (.f64 2 (sqrt.f64 k)))
(.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 k)))
(/.f64 (neg.f64 (neg.f64 (.f64 2 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 (PI.f64) n)))))) (-.f64 0 (neg.f64 (.f64 2 (sqrt.f64 k)))))
(.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 k)))
(/.f64 (neg.f64 (.f64 2 (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (neg.f64 (sqrt.f64 2))))) (-.f64 0 (.f64 (sqrt.f64 k) -2)))
(.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 k)))
(/.f64 (neg.f64 (neg.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (neg.f64 (sqrt.f64 2))))) (neg.f64 (sqrt.f64 k)))
(.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 k)))

localize34.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(*.f64 (PI.f64) (+.f64 n n))
✓	0.3b	(pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 1/2 (-.f64 1 k)))
✓	0.3b	(/.f64 16 (sqrt.f64 k))
✓	0.5b	(.f64 (sqrt.f64 k) (.f64 (sqrt.f64 k) 1/16))

Compiler

Compiled 93 to 48 computations (48.4% saved)

series3.0ms (0%)

Counts

3 → 36

Calls

12 calls:

Time	Variable		Point	Expression
1.0ms	k	@	-inf	(.f64 (sqrt.f64 k) (.f64 (sqrt.f64 k) 1/16))
0.0ms	k	@	-inf	(/.f64 16 (sqrt.f64 k))
0.0ms	k	@	0	(.f64 (sqrt.f64 k) (.f64 (sqrt.f64 k) 1/16))
0.0ms	k	@	inf	(.f64 (sqrt.f64 k) (.f64 (sqrt.f64 k) 1/16))
0.0ms	k	@	0	(/.f64 16 (sqrt.f64 k))

rewrite79.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

1644×	`bool.json-1`
1644×	`bool.json-2`
1572×	`rational.json-1`
1572×	`rational.json-2`
1572×	`rational.json-3`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	65
1	198	65
2	487	65
3	983	65
4	2051	65
5	5208	65

Stop Event

1×	node limit

Counts

3 → 49

Calls

Call 1

Inputs
(.f64 (sqrt.f64 k) (.f64 (sqrt.f64 k) 1/16))
(/.f64 16 (sqrt.f64 k))
(pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 1/2 (-.f64 1 k)))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (sqrt.f64 k) (*.f64 (sqrt.f64 k) 1/16)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 (sqrt.f64 k) (*.f64 (sqrt.f64 k) 1/16)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (*.f64 (sqrt.f64 k) (*.f64 (sqrt.f64 k) 1/16)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (sqrt.f64 k) (*.f64 (sqrt.f64 k) 1/16)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (sqrt.f64 k) (*.f64 (sqrt.f64 k) 1/8)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (*.f64 (sqrt.f64 k) (sqrt.f64 k)) 1/4) 4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 (*.f64 (sqrt.f64 k) (sqrt.f64 k)) 1/4)) 8)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (*.f64 2 (*.f64 (*.f64 (sqrt.f64 k) (sqrt.f64 k)) 1/4)) (*.f64 2 (*.f64 (*.f64 (sqrt.f64 k) (sqrt.f64 k)) 1/4))) 16)))) (#(struct:change #<rule egg-rr> (2) ((x not (not (*.f64 (sqrt.f64 k) (*.f64 (sqrt.f64 k) 1/16))))))) (#(struct:change #<rule egg-rr> (2) ((x and (*.f64 (sqrt.f64 k) (*.f64 (sqrt.f64 k) 1/16)) (*.f64 (sqrt.f64 k) (*.f64 (sqrt.f64 k) 1/16)))))) (#(struct:change #<rule egg-rr> (2) ((x or (*.f64 (sqrt.f64 k) (*.f64 (sqrt.f64 k) 1/16)) (*.f64 (sqrt.f64 k) (*.f64 (sqrt.f64 k) 1/16)))))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 16 (sqrt.f64 k)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 16 (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 16 (sqrt.f64 k)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 k) (/.f64 1/16 (*.f64 (*.f64 (sqrt.f64 k) (sqrt.f64 k)) 1/256)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/16 (/.f64 (sqrt.f64 k) (*.f64 (*.f64 (sqrt.f64 k) (sqrt.f64 k)) 1/256)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (sqrt.f64 k) 1/16) (/.f64 (/.f64 16 (sqrt.f64 k)) (*.f64 (sqrt.f64 k) 1/16)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 16 (sqrt.f64 k)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/2 (/.f64 32 (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 16 (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (sqrt.f64 k) 2) (/.f64 1/16 (*.f64 (*.f64 (sqrt.f64 k) 1/16) (*.f64 (sqrt.f64 k) 1/8))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 2 (/.f64 8 (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 4 (/.f64 (/.f64 16 (sqrt.f64 k)) 4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (sqrt.f64 k) 1/8) (/.f64 1/2 (*.f64 (*.f64 (sqrt.f64 k) (sqrt.f64 k)) 1/256)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (sqrt.f64 k) 1/8) (/.f64 1 (*.f64 (*.f64 (sqrt.f64 k) 1/16) (*.f64 (sqrt.f64 k) 1/8))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (/.f64 16 (sqrt.f64 k)) 4) 1/4)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/8 (/.f64 (sqrt.f64 k) (*.f64 (*.f64 (sqrt.f64 k) 1/16) (*.f64 (sqrt.f64 k) 1/8))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/32 (/.f64 (*.f64 (sqrt.f64 k) 2) (*.f64 (*.f64 (sqrt.f64 k) (sqrt.f64 k)) 1/256)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 32 (sqrt.f64 k)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (sqrt.f64 k) 1/2) (/.f64 1/8 (*.f64 (*.f64 (sqrt.f64 k) (sqrt.f64 k)) 1/256)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (sqrt.f64 k) 1/32) (/.f64 2 (*.f64 (*.f64 (sqrt.f64 k) (sqrt.f64 k)) 1/256)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 8 (sqrt.f64 k)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 k) (*.f64 (*.f64 (sqrt.f64 k) (sqrt.f64 k)) 1/256)) 1/16)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1/16 (*.f64 (*.f64 (sqrt.f64 k) (sqrt.f64 k)) 1/256)) (sqrt.f64 k))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (/.f64 16 (sqrt.f64 k)) (*.f64 (sqrt.f64 k) 1/16)) (*.f64 (sqrt.f64 k) 1/16))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 2 (*.f64 (*.f64 (sqrt.f64 k) (sqrt.f64 k)) 1/256)) (*.f64 (sqrt.f64 k) 1/32))))) (#(struct:change #<rule egg-rr> (2) ((x not (not (/.f64 16 (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x and (/.f64 16 (sqrt.f64 k)) (/.f64 16 (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x or (/.f64 16 (sqrt.f64 k)) (/.f64 16 (sqrt.f64 k)))))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (*.f64 1/2 (-.f64 1 k))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (*.f64 1/2 (-.f64 1 k))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (*.f64 1/2 (-.f64 1 k))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/2 (*.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (*.f64 1/2 (-.f64 1 k))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (*.f64 1/2 (-.f64 1 k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (*.f64 1/2 (-.f64 1 k))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 2 (*.f64 1/2 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (*.f64 1/2 (-.f64 1 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 4 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (*.f64 1/2 (-.f64 1 k))) 4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (*.f64 1/2 (-.f64 1 k))) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (*.f64 1/2 (-.f64 1 k))) 4) 1/4)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 1/2 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (*.f64 1/2 (-.f64 1 k)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (*.f64 1/2 (-.f64 1 k))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (*.f64 1/2 (-.f64 1 k))) 2) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (*.f64 1/2 (-.f64 1 k))) 4) 4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (*.f64 1/2 (-.f64 1 k))) 4)) 8)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (*.f64 2 (*.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (*.f64 1/2 (-.f64 1 k))) 4)) (*.f64 2 (*.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (*.f64 1/2 (-.f64 1 k))) 4))) 16)))) (#(struct:change #<rule egg-rr> (2) ((x not (not (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (*.f64 1/2 (-.f64 1 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x and (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (*.f64 1/2 (-.f64 1 k))) (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (*.f64 1/2 (-.f64 1 k))))))) (#(struct:change #<rule egg-rr> (2) ((x or (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (*.f64 1/2 (-.f64 1 k))) (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (*.f64 1/2 (-.f64 1 k))))))))

simplify83.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

1434×	`rational.json-simplify-35`
1084×	`rational.json-simplify-2`
1074×	`rational.json-simplify-41`
1000×	`rational.json-simplify-59`
734×	`rational.json-simplify-55`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	179	2651
1	381	2629
2	836	2575
3	2240	2539
4	4344	2539

Stop Event

1×	node limit

Counts

85 → 95

Calls

Call 1

Inputs
(*.f64 1/16 k)
(*.f64 1/16 k)
(*.f64 1/16 k)
(*.f64 1/16 k)
(*.f64 1/16 k)
(*.f64 1/16 k)
(*.f64 1/16 k)
(*.f64 1/16 k)
(.f64 -1/16 (.f64 k (pow.f64 (sqrt.f64 -1) 2)))
(.f64 -1/16 (.f64 k (pow.f64 (sqrt.f64 -1) 2)))
(.f64 -1/16 (.f64 k (pow.f64 (sqrt.f64 -1) 2)))
(.f64 -1/16 (.f64 k (pow.f64 (sqrt.f64 -1) 2)))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64)))))))
(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))))
(+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 (.f64 n (PI.f64))))) (.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))))
(+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 (.f64 n (PI.f64))))) (+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (.f64 1/8 (.f64 (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 2) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2))) (sqrt.f64 (.f64 n (PI.f64)))))))
(+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 (.f64 n (PI.f64))))) (+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (+.f64 (.f64 1/8 (.f64 (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 2) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2))) (sqrt.f64 (.f64 n (PI.f64))))) (.f64 -1/48 (.f64 (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 3) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 3))) (sqrt.f64 (*.f64 n (PI.f64))))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (.f64 n (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (.f64 n (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (.f64 n (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (.f64 n (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (+.f64 1 (.f64 -1 k)) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (+.f64 1 (.f64 -1 k)) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (+.f64 1 (.f64 -1 k)) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (+.f64 1 (.f64 -1 k)) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(+.f64 (.f64 (sqrt.f64 k) (.f64 (sqrt.f64 k) 1/16)) 0)
(+.f64 0 (.f64 (sqrt.f64 k) (.f64 (sqrt.f64 k) 1/16)))
(-.f64 (.f64 (sqrt.f64 k) (.f64 (sqrt.f64 k) 1/16)) 0)
(/.f64 (.f64 (sqrt.f64 k) (.f64 (sqrt.f64 k) 1/16)) 1)
(/.f64 (.f64 (sqrt.f64 k) (.f64 (sqrt.f64 k) 1/8)) 2)
(/.f64 (.f64 (.f64 (sqrt.f64 k) (sqrt.f64 k)) 1/4) 4)
(/.f64 (.f64 2 (.f64 (*.f64 (sqrt.f64 k) (sqrt.f64 k)) 1/4)) 8)
(/.f64 (+.f64 (.f64 2 (.f64 (.f64 (sqrt.f64 k) (sqrt.f64 k)) 1/4)) (.f64 2 (.f64 (.f64 (sqrt.f64 k) (sqrt.f64 k)) 1/4))) 16)
(+.f64 (/.f64 16 (sqrt.f64 k)) 0)
(+.f64 0 (/.f64 16 (sqrt.f64 k)))
(-.f64 (/.f64 16 (sqrt.f64 k)) 0)
(.f64 (sqrt.f64 k) (/.f64 1/16 (.f64 (*.f64 (sqrt.f64 k) (sqrt.f64 k)) 1/256)))
(.f64 1/16 (/.f64 (sqrt.f64 k) (.f64 (*.f64 (sqrt.f64 k) (sqrt.f64 k)) 1/256)))
(.f64 (.f64 (sqrt.f64 k) 1/16) (/.f64 (/.f64 16 (sqrt.f64 k)) (*.f64 (sqrt.f64 k) 1/16)))
(*.f64 (/.f64 16 (sqrt.f64 k)) 1)
(*.f64 1/2 (/.f64 32 (sqrt.f64 k)))
(*.f64 1 (/.f64 16 (sqrt.f64 k)))
(.f64 (.f64 (sqrt.f64 k) 2) (/.f64 1/16 (.f64 (.f64 (sqrt.f64 k) 1/16) (*.f64 (sqrt.f64 k) 1/8))))
(*.f64 2 (/.f64 8 (sqrt.f64 k)))
(*.f64 4 (/.f64 (/.f64 16 (sqrt.f64 k)) 4))
(.f64 (.f64 (sqrt.f64 k) 1/8) (/.f64 1/2 (.f64 (.f64 (sqrt.f64 k) (sqrt.f64 k)) 1/256)))
(.f64 (.f64 (sqrt.f64 k) 1/8) (/.f64 1 (.f64 (.f64 (sqrt.f64 k) 1/16) (*.f64 (sqrt.f64 k) 1/8))))
(.f64 (.f64 (/.f64 16 (sqrt.f64 k)) 4) 1/4)
(.f64 1/8 (/.f64 (sqrt.f64 k) (.f64 (.f64 (sqrt.f64 k) 1/16) (.f64 (sqrt.f64 k) 1/8))))
(.f64 1/32 (/.f64 (.f64 (sqrt.f64 k) 2) (.f64 (.f64 (sqrt.f64 k) (sqrt.f64 k)) 1/256)))
(*.f64 (/.f64 32 (sqrt.f64 k)) 1/2)
(.f64 (.f64 (sqrt.f64 k) 1/2) (/.f64 1/8 (.f64 (.f64 (sqrt.f64 k) (sqrt.f64 k)) 1/256)))
(.f64 (.f64 (sqrt.f64 k) 1/32) (/.f64 2 (.f64 (.f64 (sqrt.f64 k) (sqrt.f64 k)) 1/256)))
(*.f64 (/.f64 8 (sqrt.f64 k)) 2)
(.f64 (/.f64 (sqrt.f64 k) (.f64 (*.f64 (sqrt.f64 k) (sqrt.f64 k)) 1/256)) 1/16)
(.f64 (/.f64 1/16 (.f64 (*.f64 (sqrt.f64 k) (sqrt.f64 k)) 1/256)) (sqrt.f64 k))
(.f64 (/.f64 (/.f64 16 (sqrt.f64 k)) (.f64 (sqrt.f64 k) 1/16)) (*.f64 (sqrt.f64 k) 1/16))
(.f64 (/.f64 2 (.f64 (.f64 (sqrt.f64 k) (sqrt.f64 k)) 1/256)) (.f64 (sqrt.f64 k) 1/32))
(+.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 1/2 (-.f64 1 k))) 0)
(+.f64 0 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 1/2 (-.f64 1 k))))
(-.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 1/2 (-.f64 1 k))) 0)
(.f64 1/2 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 1/2 (-.f64 1 k))) 2))
(.f64 1 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (*.f64 1/2 (-.f64 1 k))))
(.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (*.f64 1/2 (-.f64 1 k))) 1)
(.f64 2 (.f64 1/2 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 1/2 (-.f64 1 k)))))
(.f64 4 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (*.f64 1/2 (-.f64 1 k))) 4))
(.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 1/2 (-.f64 1 k))) 2) 1/2)
(.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 1/2 (-.f64 1 k))) 4) 1/4)
(.f64 (.f64 1/2 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 1/2 (-.f64 1 k)))) 2)
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 1/2 (-.f64 1 k))) 1)
(/.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (*.f64 1/2 (-.f64 1 k))) 2) 2)
(/.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (*.f64 1/2 (-.f64 1 k))) 4) 4)
(/.f64 (.f64 2 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 1/2 (-.f64 1 k))) 4)) 8)
(/.f64 (+.f64 (.f64 2 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 1/2 (-.f64 1 k))) 4)) (.f64 2 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 1/2 (-.f64 1 k))) 4))) 16)

Outputs
(*.f64 1/16 k)
(*.f64 1/16 k)
(*.f64 1/16 k)
(*.f64 1/16 k)
(*.f64 1/16 k)
(*.f64 1/16 k)
(*.f64 1/16 k)
(*.f64 1/16 k)
(.f64 -1/16 (.f64 k (pow.f64 (sqrt.f64 -1) 2)))
(.f64 k (.f64 (pow.f64 (sqrt.f64 -1) 2) -1/16))
(.f64 (pow.f64 (sqrt.f64 -1) 2) (.f64 k -1/16))
(.f64 k (.f64 -1/16 (pow.f64 (sqrt.f64 -1) 2)))
(.f64 -1/16 (.f64 k (pow.f64 (sqrt.f64 -1) 2)))
(.f64 k (.f64 (pow.f64 (sqrt.f64 -1) 2) -1/16))
(.f64 (pow.f64 (sqrt.f64 -1) 2) (.f64 k -1/16))
(.f64 k (.f64 -1/16 (pow.f64 (sqrt.f64 -1) 2)))
(.f64 -1/16 (.f64 k (pow.f64 (sqrt.f64 -1) 2)))
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(.f64 (.f64 (sqrt.f64 k) 1/8) (/.f64 1/2 (.f64 (.f64 (sqrt.f64 k) (sqrt.f64 k)) 1/256)))
(/.f64 16 (sqrt.f64 k))
(.f64 (.f64 (sqrt.f64 k) 1/8) (/.f64 1 (.f64 (.f64 (sqrt.f64 k) 1/16) (*.f64 (sqrt.f64 k) 1/8))))
(/.f64 16 (sqrt.f64 k))
(.f64 (.f64 (/.f64 16 (sqrt.f64 k)) 4) 1/4)
(/.f64 16 (sqrt.f64 k))
(.f64 1/8 (/.f64 (sqrt.f64 k) (.f64 (.f64 (sqrt.f64 k) 1/16) (.f64 (sqrt.f64 k) 1/8))))
(/.f64 16 (sqrt.f64 k))
(.f64 1/32 (/.f64 (.f64 (sqrt.f64 k) 2) (.f64 (.f64 (sqrt.f64 k) (sqrt.f64 k)) 1/256)))
(/.f64 16 (sqrt.f64 k))
(*.f64 (/.f64 32 (sqrt.f64 k)) 1/2)
(*.f64 1/2 (/.f64 32 (sqrt.f64 k)))
(.f64 (.f64 (sqrt.f64 k) 1/2) (/.f64 1/8 (.f64 (.f64 (sqrt.f64 k) (sqrt.f64 k)) 1/256)))
(.f64 (.f64 1/2 (sqrt.f64 k)) (/.f64 1/8 (.f64 (.f64 (sqrt.f64 k) (sqrt.f64 k)) 1/256)))
(.f64 (sqrt.f64 k) (.f64 1/2 (/.f64 32 (*.f64 (sqrt.f64 k) (sqrt.f64 k)))))
(.f64 1/2 (.f64 (sqrt.f64 k) (/.f64 32 (*.f64 (sqrt.f64 k) (sqrt.f64 k)))))
(.f64 (.f64 (sqrt.f64 k) 1/32) (/.f64 2 (.f64 (.f64 (sqrt.f64 k) (sqrt.f64 k)) 1/256)))
(/.f64 16 (sqrt.f64 k))
(*.f64 (/.f64 8 (sqrt.f64 k)) 2)
(*.f64 2 (/.f64 8 (sqrt.f64 k)))
(.f64 (/.f64 (sqrt.f64 k) (.f64 (*.f64 (sqrt.f64 k) (sqrt.f64 k)) 1/256)) 1/16)
(/.f64 16 (sqrt.f64 k))
(.f64 (/.f64 1/16 (.f64 (*.f64 (sqrt.f64 k) (sqrt.f64 k)) 1/256)) (sqrt.f64 k))
(/.f64 16 (sqrt.f64 k))
(.f64 (/.f64 (/.f64 16 (sqrt.f64 k)) (.f64 (sqrt.f64 k) 1/16)) (*.f64 (sqrt.f64 k) 1/16))
(/.f64 16 (sqrt.f64 k))
(.f64 (/.f64 2 (.f64 (.f64 (sqrt.f64 k) (sqrt.f64 k)) 1/256)) (.f64 (sqrt.f64 k) 1/32))
(/.f64 16 (sqrt.f64 k))
(+.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 1/2 (-.f64 1 k))) 0)
(pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 1/2 (-.f64 1 k)))
(+.f64 0 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 1/2 (-.f64 1 k))))
(pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 1/2 (-.f64 1 k)))
(-.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 1/2 (-.f64 1 k))) 0)
(pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 1/2 (-.f64 1 k)))
(.f64 1/2 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 1/2 (-.f64 1 k))) 2))
(pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 1/2 (-.f64 1 k)))
(.f64 1 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (*.f64 1/2 (-.f64 1 k))))
(pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 1/2 (-.f64 1 k)))
(.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (*.f64 1/2 (-.f64 1 k))) 1)
(pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 1/2 (-.f64 1 k)))
(.f64 2 (.f64 1/2 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 1/2 (-.f64 1 k)))))
(pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 1/2 (-.f64 1 k)))
(.f64 4 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (*.f64 1/2 (-.f64 1 k))) 4))
(pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 1/2 (-.f64 1 k)))
(.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 1/2 (-.f64 1 k))) 2) 1/2)
(pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 1/2 (-.f64 1 k)))
(.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 1/2 (-.f64 1 k))) 4) 1/4)
(pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 1/2 (-.f64 1 k)))
(.f64 (.f64 1/2 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 1/2 (-.f64 1 k)))) 2)
(pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 1/2 (-.f64 1 k)))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 1/2 (-.f64 1 k))) 1)
(pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 1/2 (-.f64 1 k)))
(/.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (*.f64 1/2 (-.f64 1 k))) 2) 2)
(pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 1/2 (-.f64 1 k)))
(/.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (*.f64 1/2 (-.f64 1 k))) 4) 4)
(pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 1/2 (-.f64 1 k)))
(/.f64 (.f64 2 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 1/2 (-.f64 1 k))) 4)) 8)
(pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 1/2 (-.f64 1 k)))
(/.f64 (+.f64 (.f64 2 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 1/2 (-.f64 1 k))) 4)) (.f64 2 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 1/2 (-.f64 1 k))) 4))) 16)
(pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 1/2 (-.f64 1 k)))

localize44.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 k (.f64 -1/2 (log.f64 (.f64 2 (.f64 (PI.f64) n)))))
✓	0.4b	(/.f64 (/.f64 (sqrt.f64 k) (sqrt.f64 2)) (neg.f64 (sqrt.f64 (*.f64 (PI.f64) n))))
✓	0.4b	(.f64 (-.f64 -1 (.f64 k (.f64 -1/2 (log.f64 (.f64 2 (.f64 (PI.f64) n)))))) (/.f64 1 (/.f64 (/.f64 (sqrt.f64 k) (sqrt.f64 2)) (neg.f64 (sqrt.f64 (.f64 (PI.f64) n))))))
✓	0.4b	(/.f64 (sqrt.f64 k) (sqrt.f64 2))

Compiler

Compiled 121 to 65 computations (46.3% saved)

series9.0ms (0.1%)

Counts

4 → 24

Calls

21 calls:

Time	Variable		Point	Expression
1.0ms	n	@	0	(/.f64 (/.f64 (sqrt.f64 k) (sqrt.f64 2)) (neg.f64 (sqrt.f64 (*.f64 (PI.f64) n))))
1.0ms	k	@	0	(/.f64 (/.f64 (sqrt.f64 k) (sqrt.f64 2)) (neg.f64 (sqrt.f64 (*.f64 (PI.f64) n))))
1.0ms	n	@	-inf	(/.f64 (/.f64 (sqrt.f64 k) (sqrt.f64 2)) (neg.f64 (sqrt.f64 (*.f64 (PI.f64) n))))
1.0ms	k	@	-inf	(/.f64 (/.f64 (sqrt.f64 k) (sqrt.f64 2)) (neg.f64 (sqrt.f64 (*.f64 (PI.f64) n))))
0.0ms	n	@	-inf	(.f64 (-.f64 -1 (.f64 k (.f64 -1/2 (log.f64 (.f64 2 (.f64 (PI.f64) n)))))) (/.f64 1 (/.f64 (/.f64 (sqrt.f64 k) (sqrt.f64 2)) (neg.f64 (sqrt.f64 (.f64 (PI.f64) n))))))

rewrite100.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

1852×	`bool.json-1`
1852×	`bool.json-2`
1824×	`rational.json-1`
1410×	`bool.json-3`
964×	`rational.json-simplify-35`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	25	162
1	261	162
2	729	162
3	1995	158
4	5623	158

Stop Event

1×	node limit

Counts

4 → 106

Calls

Call 1

Inputs
(/.f64 (sqrt.f64 k) (sqrt.f64 2))
(.f64 (-.f64 -1 (.f64 k (.f64 -1/2 (log.f64 (.f64 2 (.f64 (PI.f64) n)))))) (/.f64 1 (/.f64 (/.f64 (sqrt.f64 k) (sqrt.f64 2)) (neg.f64 (sqrt.f64 (.f64 (PI.f64) n))))))
(/.f64 (/.f64 (sqrt.f64 k) (sqrt.f64 2)) (neg.f64 (sqrt.f64 (*.f64 (PI.f64) n))))
(.f64 k (.f64 -1/2 (log.f64 (.f64 2 (.f64 (PI.f64) n)))))

Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 (sqrt.f64 k) (sqrt.f64 2)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 (sqrt.f64 k) (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (sqrt.f64 k) (sqrt.f64 2)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 k) (/.f64 1 (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (sqrt.f64 k) (sqrt.f64 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (/.f64 (sqrt.f64 k) (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (sqrt.f64 k) 2) (/.f64 1/2 (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (sqrt.f64 k) 2) (.f64 (/.f64 1/2 (sqrt.f64 2)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (sqrt.f64 k) 2) (.f64 1/2 (/.f64 1 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 2 (/.f64 (sqrt.f64 k) (sqrt.f64 2))) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1/2 (.f64 2 (/.f64 (sqrt.f64 k) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1 (sqrt.f64 2)) (sqrt.f64 k))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1/2 (sqrt.f64 2)) (.f64 (sqrt.f64 k) 2))))) (#(struct:change #<rule egg-rr> (2) ((x not (not (/.f64 (sqrt.f64 k) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x and (/.f64 (sqrt.f64 k) (sqrt.f64 2)) (/.f64 (sqrt.f64 k) (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x or (/.f64 (sqrt.f64 k) (sqrt.f64 2)) (/.f64 (sqrt.f64 k) (sqrt.f64 2)))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 (sqrt.f64 2) (/.f64 (/.f64 (sqrt.f64 k) (sqrt.f64 (.f64 (PI.f64) n))) (+.f64 (.f64 k (.f64 -1/2 (log.f64 (.f64 2 (.f64 (PI.f64) n))))) 1))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 (sqrt.f64 2) (/.f64 (/.f64 (sqrt.f64 k) (sqrt.f64 (.f64 (PI.f64) n))) (+.f64 (.f64 k (.f64 -1/2 (log.f64 (.f64 2 (.f64 (PI.f64) n))))) 1))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (sqrt.f64 2) (/.f64 (/.f64 (sqrt.f64 k) (sqrt.f64 (.f64 (PI.f64) n))) (+.f64 (.f64 k (.f64 -1/2 (log.f64 (.f64 2 (.f64 (PI.f64) n))))) 1))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 2 (/.f64 (.f64 2 (/.f64 (neg.f64 (sqrt.f64 k)) (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 (PI.f64) n))))) (-.f64 -1 (.f64 k (.f64 -1/2 (log.f64 (.f64 2 (.f64 (PI.f64) n))))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 2 (+.f64 (/.f64 (/.f64 (sqrt.f64 k) (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 (PI.f64) n)))) (+.f64 (.f64 k (.f64 -1/2 (log.f64 (.f64 2 (.f64 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simplify178.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

980×	`rational.json-simplify-43`
946×	`rational.json-simplify-2`
850×	`rational.json-simplify-50`
786×	`rational.json-simplify-53`
778×	`rational.json-simplify-41`

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	273	6980
1	825	6926
2	2607	6692
3	4365	6664
4	5701	6664
5	6765	6640

Stop Event

1×	node limit

Counts

130 → 140

Calls

Call 1

Inputs
(.f64 -1/2 (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64))))))
(.f64 -1/2 (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64))))))
(.f64 -1/2 (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64))))))
(.f64 -1/2 (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64))))))
(.f64 -1/2 (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64))))))
(.f64 -1/2 (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64))))))
(.f64 -1/2 (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64))))))
(.f64 -1/2 (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64))))))
(.f64 -1/2 (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64))))))
(.f64 -1/2 (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64))))))
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Outputs
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(+.f64 -1 (-.f64 1 (/.f64 (sqrt.f64 k) (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))))))
(/.f64 (sqrt.f64 k) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (neg.f64 (sqrt.f64 2))))
(.f64 (/.f64 -1 (sqrt.f64 (.f64 (PI.f64) n))) (/.f64 (sqrt.f64 k) (sqrt.f64 2)))
(+.f64 -1 (-.f64 1 (/.f64 (sqrt.f64 k) (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))))))
(/.f64 (sqrt.f64 k) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (neg.f64 (sqrt.f64 2))))
(.f64 1/2 (.f64 2 (/.f64 (neg.f64 (sqrt.f64 k)) (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 (PI.f64) n))))))
(+.f64 -1 (-.f64 1 (/.f64 (sqrt.f64 k) (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))))))
(/.f64 (sqrt.f64 k) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (neg.f64 (sqrt.f64 2))))
(.f64 (/.f64 -1 (.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 (PI.f64) n)))) (sqrt.f64 k))
(+.f64 -1 (-.f64 1 (/.f64 (sqrt.f64 k) (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))))))
(/.f64 (sqrt.f64 k) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (neg.f64 (sqrt.f64 2))))
(.f64 (/.f64 1 (sqrt.f64 2)) (/.f64 (sqrt.f64 k) (neg.f64 (sqrt.f64 (.f64 (PI.f64) n)))))
(+.f64 -1 (-.f64 1 (/.f64 (sqrt.f64 k) (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))))))
(/.f64 (sqrt.f64 k) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (neg.f64 (sqrt.f64 2))))
(.f64 (/.f64 (sqrt.f64 k) (.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 (PI.f64) n)))) -1)
(+.f64 -1 (-.f64 1 (/.f64 (sqrt.f64 k) (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))))))
(/.f64 (sqrt.f64 k) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (neg.f64 (sqrt.f64 2))))
(.f64 (/.f64 1/2 (neg.f64 (sqrt.f64 (.f64 (PI.f64) n)))) (*.f64 2 (/.f64 (sqrt.f64 k) (sqrt.f64 2))))
(+.f64 -1 (-.f64 1 (/.f64 (sqrt.f64 k) (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))))))
(/.f64 (sqrt.f64 k) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (neg.f64 (sqrt.f64 2))))
(.f64 (/.f64 -1/2 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 (PI.f64) n)))) (.f64 (sqrt.f64 k) 2))
(+.f64 -1 (-.f64 1 (/.f64 (sqrt.f64 k) (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))))))
(/.f64 (sqrt.f64 k) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (neg.f64 (sqrt.f64 2))))
(neg.f64 (/.f64 (sqrt.f64 k) (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 (PI.f64) n)))))
(+.f64 -1 (-.f64 1 (/.f64 (sqrt.f64 k) (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))))))
(/.f64 (sqrt.f64 k) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (neg.f64 (sqrt.f64 2))))
(+.f64 (.f64 k (.f64 -1/2 (log.f64 (.f64 2 (.f64 (PI.f64) n))))) 0)
(.f64 -1/2 (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64))))))
(.f64 k (.f64 -1/2 (log.f64 (.f64 n (.f64 2 (PI.f64))))))
(+.f64 0 (.f64 k (.f64 -1/2 (log.f64 (.f64 2 (.f64 (PI.f64) n))))))
(.f64 -1/2 (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64))))))
(.f64 k (.f64 -1/2 (log.f64 (.f64 n (.f64 2 (PI.f64))))))
(-.f64 (.f64 k (.f64 -1/2 (log.f64 (.f64 2 (.f64 (PI.f64) n))))) 0)
(.f64 -1/2 (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64))))))
(.f64 k (.f64 -1/2 (log.f64 (.f64 n (.f64 2 (PI.f64))))))
(/.f64 (.f64 k (.f64 -1/2 (log.f64 (.f64 2 (.f64 (PI.f64) n))))) 1)
(.f64 -1/2 (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64))))))
(.f64 k (.f64 -1/2 (log.f64 (.f64 n (.f64 2 (PI.f64))))))
(/.f64 (.f64 k (neg.f64 (log.f64 (.f64 2 (*.f64 (PI.f64) n))))) 2)
(.f64 -1/2 (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64))))))
(.f64 k (.f64 -1/2 (log.f64 (.f64 n (.f64 2 (PI.f64))))))
(/.f64 (.f64 2 (.f64 k (neg.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n)))))) 4)
(.f64 -1/2 (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64))))))
(.f64 k (.f64 -1/2 (log.f64 (.f64 n (.f64 2 (PI.f64))))))
(/.f64 (+.f64 (.f64 2 (.f64 k (neg.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n)))))) (.f64 2 (.f64 k (neg.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))))))) 8)
(.f64 -1/2 (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64))))))
(.f64 k (.f64 -1/2 (log.f64 (.f64 n (.f64 2 (PI.f64))))))

eval287.0ms (1.9%)

Compiler: Compiled 19260 to 12630 computations (34.4% saved)

prune148.0ms (1%)

Pruning

22 alts after pruning (13 fresh and 9 done)

	Pruned	Kept	Total
New	708	5	713
Fresh	6	8	14
Picked	1	0	1
Done	3	9	12
Total	718	22	740

Error

0.0b

Counts

740 → 22

Alt Table

Click to see full alt table

Status	Error	Program
✓	0.4b	(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k))
	0.4b	(/.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 1/2 (-.f64 1 k))) (/.f64 16 (sqrt.f64 k))) (*.f64 1/16 k))
	34.9b	(/.f64 (/.f64 (sqrt.f64 k) (exp.f64 (.f64 (-.f64 1 k) (.f64 1/2 (log.f64 (.f64 (PI.f64) (.f64 2 n))))))) (.f64 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2))) (/.f64 (sqrt.f64 k) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2)))))
✓	0.5b	(/.f64 (/.f64 2 (sqrt.f64 k)) (/.f64 2 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2))))
	23.9b	(/.f64 (+.f64 (.f64 -1/2 (.f64 (sqrt.f64 2) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 k (log.f64 (.f64 n (.f64 2 (PI.f64)))))))) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (.f64 1/8 (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 2) (pow.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) 2))))))) (sqrt.f64 k))
	23.9b	(/.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (+.f64 (.f64 1/8 (.f64 (pow.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) 2) (.f64 (sqrt.f64 2) (pow.f64 k 2)))) (+.f64 (sqrt.f64 2) (.f64 -1/2 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (.f64 (sqrt.f64 2) k)))))) (sqrt.f64 k))
	23.7b	(/.f64 (.f64 (sqrt.f64 2) (+.f64 1 (.f64 k (.f64 -1/2 (log.f64 (.f64 (PI.f64) (+.f64 n n))))))) (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 n (PI.f64)))))
	0.4b	(/.f64 (.f64 1/2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2))) (/.f64 2 (/.f64 4 (sqrt.f64 k))))
	23.8b	(/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 (sqrt.f64 k) (sqrt.f64 2)))
	23.7b	(/.f64 (sqrt.f64 2) (/.f64 (/.f64 (sqrt.f64 k) (sqrt.f64 (.f64 (PI.f64) n))) (+.f64 (.f64 k (.f64 -1/2 (log.f64 (.f64 2 (*.f64 (PI.f64) n))))) 1)))
	23.8b	(/.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 (PI.f64) n))))
	3.0b	(/.f64 (exp.f64 (+.f64 (.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 1/2) (.f64 -1/2 (.f64 k (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))) (sqrt.f64 k))
✓	3.0b	(/.f64 (exp.f64 (.f64 (-.f64 1 k) (.f64 1/2 (log.f64 (.f64 (PI.f64) (.f64 2 n)))))) (sqrt.f64 k))
✓	0.4b	(/.f64 2 (/.f64 2 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k))))
	0.5b	(/.f64 2 (.f64 (/.f64 2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2))) (/.f64 1 (/.f64 1 (sqrt.f64 k)))))
✓	0.4b	(/.f64 2 (.f64 (sqrt.f64 k) (/.f64 2 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2)))))
	23.9b	(/.f64 2 (.f64 (sqrt.f64 k) (.f64 2 (.f64 (sqrt.f64 (/.f64 1 (.f64 (PI.f64) n))) (sqrt.f64 1/2)))))
✓	0.4b	(/.f64 1 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2))))
	23.9b	(/.f64 1 (/.f64 (sqrt.f64 k) (+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 -1/2 (.f64 (log.f64 (.f64 (PI.f64) (.f64 2 n))) (*.f64 (sqrt.f64 2) k)))))))
✓	0.5b	(.f64 (/.f64 4 (sqrt.f64 k)) (/.f64 1 (/.f64 4 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)))))
✓	0.4b	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
✓	23.9b	(.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 (PI.f64) n))))

Compiler

Compiled 525 to 409 computations (22.1% saved)

regimes85.0ms (0.6%)

Accuracy

Total -36.0b remaining (-10175.5%)

Threshold costs -36.0b (-10175.5%)

Counts

43 → 1

Calls

Call 1

Inputs
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k))
(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
(/.f64 1 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2))))
(/.f64 2 (.f64 (sqrt.f64 k) (/.f64 2 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2)))))
(/.f64 2 (/.f64 2 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k))))
(/.f64 (/.f64 2 (sqrt.f64 k)) (/.f64 2 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2))))
(.f64 (/.f64 4 (sqrt.f64 k)) (/.f64 1 (/.f64 4 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)))))
(/.f64 1/4 (/.f64 (/.f64 1 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2))) (/.f64 4 (sqrt.f64 k))))
(/.f64 (.f64 1/2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2))) (/.f64 2 (/.f64 4 (sqrt.f64 k))))
(/.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 1/2 (-.f64 1 k))) (/.f64 16 (sqrt.f64 k))) (*.f64 1/16 k))
(/.f64 1 (.f64 (/.f64 1 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2))) (/.f64 -1 (/.f64 -1 (sqrt.f64 k)))))
(/.f64 2 (.f64 (/.f64 2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2))) (/.f64 1 (/.f64 1 (sqrt.f64 k)))))
(/.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 (PI.f64) n))))
(/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 (sqrt.f64 k) (sqrt.f64 2)))
(/.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (sqrt.f64 k))
(.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))))
(.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 (PI.f64) n))))
(/.f64 2 (.f64 (sqrt.f64 k) (.f64 2 (.f64 (sqrt.f64 (/.f64 1 (.f64 (PI.f64) n))) (sqrt.f64 1/2)))))
(/.f64 (exp.f64 (.f64 (-.f64 1 k) (.f64 1/2 (log.f64 (.f64 (PI.f64) (.f64 2 n)))))) (sqrt.f64 k))
(.f64 (/.f64 1 (sqrt.f64 k)) (exp.f64 (.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) (*.f64 1/2 (-.f64 1 k)))))
(.f64 (sqrt.f64 k) (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 1/2 (-.f64 1 k))) (.f64 (sqrt.f64 k) (sqrt.f64 k))))
(.f64 (/.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k)) (sqrt.f64 k)) (sqrt.f64 k))
(.f64 (.f64 (/.f64 1 (.f64 (sqrt.f64 k) (sqrt.f64 k))) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
(/.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 1/2 (-.f64 1 k))) (/.f64 16 (sqrt.f64 k))) (.f64 (sqrt.f64 k) (.f64 (sqrt.f64 k) 1/16)))
(.f64 (sqrt.f64 2) (/.f64 (+.f64 1 (.f64 -1/2 (.f64 k (log.f64 (.f64 (PI.f64) (+.f64 n n)))))) (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 (PI.f64) n)))))
(.f64 (+.f64 1 (.f64 -1/2 (.f64 k (log.f64 (.f64 (PI.f64) (+.f64 n n)))))) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (/.f64 (sqrt.f64 2) (sqrt.f64 k))))
(/.f64 (exp.f64 (+.f64 (.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 1/2) (.f64 -1/2 (.f64 k (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))) (sqrt.f64 k))
(/.f64 (sqrt.f64 2) (/.f64 (/.f64 (sqrt.f64 k) (sqrt.f64 (.f64 (PI.f64) n))) (+.f64 (.f64 k (.f64 -1/2 (log.f64 (.f64 2 (*.f64 (PI.f64) n))))) 1)))
(/.f64 (sqrt.f64 (.f64 n (PI.f64))) (/.f64 (sqrt.f64 k) (.f64 (sqrt.f64 2) (+.f64 1 (.f64 k (.f64 -1/2 (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))))))
(/.f64 (.f64 (sqrt.f64 2) (+.f64 1 (.f64 k (.f64 -1/2 (log.f64 (.f64 (PI.f64) (+.f64 n n))))))) (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 n (PI.f64)))))
(.f64 (-.f64 -1 (.f64 k (.f64 -1/2 (log.f64 (.f64 2 (.f64 (PI.f64) n)))))) (/.f64 1 (/.f64 (/.f64 (sqrt.f64 k) (sqrt.f64 2)) (neg.f64 (sqrt.f64 (.f64 (PI.f64) n))))))
(/.f64 4 (/.f64 (/.f64 (.f64 (sqrt.f64 k) 4) (sqrt.f64 (.f64 n (PI.f64)))) (.f64 (sqrt.f64 2) (+.f64 1 (.f64 k (.f64 -1/2 (log.f64 (.f64 (PI.f64) (+.f64 n n)))))))))
(.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (.f64 -1/2 (.f64 k (.f64 (sqrt.f64 2) (log.f64 (.f64 n (.f64 2 (PI.f64))))))))))
(/.f64 (/.f64 (.f64 4 (/.f64 4 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)))) (sqrt.f64 k)) (.f64 (/.f64 4 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2))) (/.f64 4 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)))))
(/.f64 1 (/.f64 (sqrt.f64 k) (+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 -1/2 (.f64 (log.f64 (.f64 (PI.f64) (.f64 2 n))) (*.f64 (sqrt.f64 2) k)))))))
(/.f64 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2))) (.f64 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2))) (/.f64 (sqrt.f64 k) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2)))))
(neg.f64 (/.f64 (/.f64 (sqrt.f64 k) (neg.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)))) (.f64 (sqrt.f64 k) (/.f64 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2))) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2))))))
(/.f64 (.f64 (sqrt.f64 k) (/.f64 2 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)))) (.f64 (.f64 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2))) (/.f64 (sqrt.f64 k) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2)))) 2))
(/.f64 (/.f64 (sqrt.f64 k) (exp.f64 (.f64 (-.f64 1 k) (.f64 1/2 (log.f64 (.f64 (PI.f64) (.f64 2 n))))))) (.f64 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2))) (/.f64 (sqrt.f64 k) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2)))))
(/.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (+.f64 (.f64 1/8 (.f64 (pow.f64 k 2) (.f64 (sqrt.f64 2) (pow.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) 2)))) (+.f64 (sqrt.f64 2) (.f64 -1/2 (.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) (.f64 k (sqrt.f64 2))))))) (sqrt.f64 k))
(/.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (+.f64 (.f64 1/8 (.f64 (pow.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) 2) (.f64 (sqrt.f64 2) (pow.f64 k 2)))) (+.f64 (sqrt.f64 2) (.f64 -1/2 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (.f64 (sqrt.f64 2) k)))))) (sqrt.f64 k))
(/.f64 (+.f64 (.f64 -1/2 (.f64 (sqrt.f64 2) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 k (log.f64 (.f64 n (.f64 2 (PI.f64)))))))) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (.f64 1/8 (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 2) (pow.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) 2))))))) (sqrt.f64 k))
(.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 -1/2 (.f64 k (.f64 (sqrt.f64 2) (log.f64 (.f64 n (.f64 2 (PI.f64)))))))) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (.f64 1/8 (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 2) (pow.f64 (log.f64 (.f64 n (*.f64 2 (PI.f64)))) 2))))))))

Outputs
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k))

Calls

4 calls:

18.0ms	(.f64 (.f64 2 (PI.f64)) n)
18.0ms	k
17.0ms	n
10.0ms	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))

Results

Error	Segments	Branch
0.4b	1	`k`
0.4b	1	`n`
0.4b	1	`(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))`
0.4b	1	`(.f64 (.f64 2 (PI.f64)) n)`

Compiler

Compiled 1105 to 643 computations (41.8% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	43

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

Inputs
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k))

Outputs
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k))

Compiler

Compiled 16 to 12 computations (25% saved)

soundness0.0ms (0%)

end14.0ms (0.1%)

Compiler: Compiled 16 to 12 computations (25% saved)