Details

analyze0.0ms (0%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	100%	0%	0%	0%	0%	0
100%	100%	0%	0%	0%	0%	0%	1

Compiler

Compiled 14 to 13 computations (7.1% saved)

sample2.5s (21.7%)

Results

1.3s	2172×	body	2048	valid
560.0ms	1092×	body	1024	valid
495.0ms	4466×	body	256	valid
123.0ms	526×	body	512	valid

Bogosity

preprocess707.0ms (6.2%)

Algorithm

2×	egg-herbie

Rules

11846×	`rational.json-simplify-41`
1180×	`rational.json-simplify-1`
328×	`rational.json-simplify-35`
12×	`rational.json-simplify-2`
6×	`rational.json-simplify-43`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	35
1	22	35
2	30	35
3	43	35
4	54	35
5	78	35
6	144	35
7	331	35
8	414	35
9	418	35
10	422	35
11	426	35
12	430	35
13	1421	35
14	1833	35
15	1837	35
16	1841	35
17	1845	35
18	1849	35
19	1853	35
20	1857	35
21	1861	35
22	1865	35
23	1869	35
24	1873	35
25	1877	35
26	1881	35
27	1885	35
28	1889	35
29	1893	35
30	1897	35
31	1901	35
32	1905	35
33	1909	35
34	1913	35
35	1917	35
36	1921	35
37	1925	35
38	1929	35
39	1933	35
40	1937	35
41	1941	35
42	1945	35
43	1949	35
44	1953	35
45	1957	35
46	1961	35
47	1965	35
48	1969	35
49	1973	35
50	1977	35
51	1981	35
52	1985	35
53	1989	35
54	1993	35
55	1997	35
56	2001	35
57	2005	35
58	2009	35
59	2013	35
60	2017	35
61	2021	35
62	2025	35
63	2029	35
64	2033	35
65	2037	35
66	2041	35
67	2045	35
68	2049	35
69	2053	35
70	2057	35
71	2061	35
72	2065	35
73	2069	35
74	2073	35
75	2077	35
76	2081	35
77	2085	35
78	2089	35
79	2093	35
80	2097	35
81	2101	35
82	2105	35
83	2109	35
84	2113	35
85	2117	35
86	2121	35
87	2125	35
88	2129	35
89	2133	35
90	2137	35
91	2141	35
92	2145	35
93	2149	35
94	2153	35
95	2157	35
96	2161	35
97	2165	35
98	2169	35
99	2173	35
100	2177	35
101	2181	35
102	2185	35
103	2189	35
104	2193	35
105	2197	35
106	2201	35
107	2205	35
108	2209	35
109	2213	35
110	2217	35
111	2221	35
112	2225	35
113	2229	35
114	2233	35
115	2237	35
116	2241	35
117	2245	35
118	2249	35
119	2253	35
120	2257	35
121	2261	35
122	2265	35
123	2269	35
124	2273	35
125	2277	35
126	2281	35
127	2285	35
128	2289	35
129	2293	35
130	2297	35
131	2301	35
132	2305	35
133	2309	35
134	2313	35
135	2317	35
136	2321	35
137	2325	35
138	2329	35
139	2333	35
140	2337	35
141	2341	35
142	2345	35
143	2349	35
144	2353	35
145	2357	35
146	2361	35
147	2365	35
148	2369	35
149	2373	35
150	2377	35
151	2381	35
152	2385	35
153	2389	35
154	2393	35
155	2397	35
156	2401	35
157	2405	35
158	2409	35
159	2413	35
160	2417	35
161	2421	35
162	2425	35
163	2429	35
0	1	1

Stop Event

1×	saturated
1×	node limit

Calls

Call 1

Inputs
0

Outputs
0

Call 2

Inputs
(-.f64 1 (sqrt.f64 (*.f64 1/2 (+.f64 1 (/.f64 1 (hypot.f64 1 x))))))

Outputs
(-.f64 1 (sqrt.f64 (*.f64 1/2 (+.f64 1 (/.f64 1 (hypot.f64 1 x))))))

Compiler

Compiled 14 to 13 computations (7.1% saved)

simplify708.0ms (6.2%)

Algorithm

1×	egg-herbie

Rules

11846×	`rational.json-simplify-41`
1180×	`rational.json-simplify-1`
328×	`rational.json-simplify-35`
12×	`rational.json-simplify-2`
6×	`rational.json-simplify-43`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	35
1	22	35
2	30	35
3	43	35
4	54	35
5	78	35
6	144	35
7	331	35
8	414	35
9	418	35
10	422	35
11	426	35
12	430	35
13	1421	35
14	1833	35
15	1837	35
16	1841	35
17	1845	35
18	1849	35
19	1853	35
20	1857	35
21	1861	35
22	1865	35
23	1869	35
24	1873	35
25	1877	35
26	1881	35
27	1885	35
28	1889	35
29	1893	35
30	1897	35
31	1901	35
32	1905	35
33	1909	35
34	1913	35
35	1917	35
36	1921	35
37	1925	35
38	1929	35
39	1933	35
40	1937	35
41	1941	35
42	1945	35
43	1949	35
44	1953	35
45	1957	35
46	1961	35
47	1965	35
48	1969	35
49	1973	35
50	1977	35
51	1981	35
52	1985	35
53	1989	35
54	1993	35
55	1997	35
56	2001	35
57	2005	35
58	2009	35
59	2013	35
60	2017	35
61	2021	35
62	2025	35
63	2029	35
64	2033	35
65	2037	35
66	2041	35
67	2045	35
68	2049	35
69	2053	35
70	2057	35
71	2061	35
72	2065	35
73	2069	35
74	2073	35
75	2077	35
76	2081	35
77	2085	35
78	2089	35
79	2093	35
80	2097	35
81	2101	35
82	2105	35
83	2109	35
84	2113	35
85	2117	35
86	2121	35
87	2125	35
88	2129	35
89	2133	35
90	2137	35
91	2141	35
92	2145	35
93	2149	35
94	2153	35
95	2157	35
96	2161	35
97	2165	35
98	2169	35
99	2173	35
100	2177	35
101	2181	35
102	2185	35
103	2189	35
104	2193	35
105	2197	35
106	2201	35
107	2205	35
108	2209	35
109	2213	35
110	2217	35
111	2221	35
112	2225	35
113	2229	35
114	2233	35
115	2237	35
116	2241	35
117	2245	35
118	2249	35
119	2253	35
120	2257	35
121	2261	35
122	2265	35
123	2269	35
124	2273	35
125	2277	35
126	2281	35
127	2285	35
128	2289	35
129	2293	35
130	2297	35
131	2301	35
132	2305	35
133	2309	35
134	2313	35
135	2317	35
136	2321	35
137	2325	35
138	2329	35
139	2333	35
140	2337	35
141	2341	35
142	2345	35
143	2349	35
144	2353	35
145	2357	35
146	2361	35
147	2365	35
148	2369	35
149	2373	35
150	2377	35
151	2381	35
152	2385	35
153	2389	35
154	2393	35
155	2397	35
156	2401	35
157	2405	35
158	2409	35
159	2413	35
160	2417	35
161	2421	35
162	2425	35
163	2429	35

Stop Event

1×	node limit

Counts

1 → 1

Calls

Call 1

Inputs
(-.f64 1 (sqrt.f64 (*.f64 1/2 (+.f64 1 (/.f64 1 (hypot.f64 1 x))))))

Outputs
(-.f64 1 (sqrt.f64 (*.f64 1/2 (+.f64 1 (/.f64 1 (hypot.f64 1 x))))))

eval0.0ms (0%)

Compiler: Compiled 13 to 12 computations (7.7% saved)

prune1.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

14.7b

Counts

2 → 1

Alt Table

Click to see full alt table

Status	Error	Program
▶	14.7b	(-.f64 1 (sqrt.f64 (*.f64 1/2 (+.f64 1 (/.f64 1 (hypot.f64 1 x))))))

Compiler

Compiled 13 to 12 computations (7.7% saved)

localize20.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 1 (/.f64 1 (hypot.f64 1 x)))
✓	0.0b	(/.f64 1 (hypot.f64 1 x))
✓	0.0b	(sqrt.f64 (*.f64 1/2 (+.f64 1 (/.f64 1 (hypot.f64 1 x)))))
✓	2.3b	(-.f64 1 (sqrt.f64 (*.f64 1/2 (+.f64 1 (/.f64 1 (hypot.f64 1 x))))))

Compiler

Compiled 50 to 43 computations (14% saved)

series4.0ms (0%)

Counts

4 → 48

Calls

12 calls:

Time	Variable		Point	Expression
2.0ms	x	@	0	(-.f64 1 (sqrt.f64 (*.f64 1/2 (+.f64 1 (/.f64 1 (hypot.f64 1 x))))))
1.0ms	x	@	inf	(-.f64 1 (sqrt.f64 (*.f64 1/2 (+.f64 1 (/.f64 1 (hypot.f64 1 x))))))
0.0ms	x	@	0	(sqrt.f64 (*.f64 1/2 (+.f64 1 (/.f64 1 (hypot.f64 1 x)))))
0.0ms	x	@	-inf	(-.f64 1 (sqrt.f64 (*.f64 1/2 (+.f64 1 (/.f64 1 (hypot.f64 1 x))))))
0.0ms	x	@	-inf	(/.f64 1 (hypot.f64 1 x))

rewrite95.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

1452×	`rational.json-1`
1452×	`rational.json-2`
1452×	`rational.json-4`
1452×	`rational.json-3`
1446×	`exponential.json-3`

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	12	96
1	92	96
2	204	96
3	407	96
4	844	96
5	2552	84
6	6016	84

Stop Event

1×	node limit

Counts

4 → 154

Calls

Call 1

Inputs
(-.f64 1 (sqrt.f64 (*.f64 1/2 (+.f64 1 (/.f64 1 (hypot.f64 1 x))))))
(sqrt.f64 (*.f64 1/2 (+.f64 1 (/.f64 1 (hypot.f64 1 x)))))
(/.f64 1 (hypot.f64 1 x))
(+.f64 1 (/.f64 1 (hypot.f64 1 x)))

Outputs
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(2) ((x /.f64 (neg.f64 (+.f64 (.f64 (hypot.f64 1 x) 2) 2)) (.f64 (hypot.f64 1 x) -2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 -1 (hypot.f64 1 x))) (hypot.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (.f64 1/2 (+.f64 1 (hypot.f64 1 x)))) (neg.f64 (.f64 1/2 (hypot.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (neg.f64 (+.f64 (.f64 (hypot.f64 1 x) 2) 2)) (neg.f64 (+.f64 (.f64 (hypot.f64 1 x) 2) 2))) (.f64 4 (neg.f64 (hypot.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (.f64 2 (.f64 (+.f64 1 (/.f64 1 (hypot.f64 1 x))) 8)) (.f64 2 (.f64 (+.f64 1 (/.f64 1 (hypot.f64 1 x))) 8))) 32)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (.f64 2 (-.f64 -1 (hypot.f64 1 x))) (.f64 2 (-.f64 -1 (hypot.f64 1 x)))) (.f64 4 (neg.f64 (hypot.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (/.f64 (-.f64 -1 (hypot.f64 1 x)) (hypot.f64 1 x)) (/.f64 (-.f64 -1 (hypot.f64 1 x)) (hypot.f64 1 x))) -2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (neg.f64 (-.f64 -1 (hypot.f64 1 x))) (neg.f64 (-.f64 -1 (hypot.f64 1 x)))) (.f64 (hypot.f64 1 x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (.f64 (+.f64 1 (hypot.f64 1 x)) 4)) (neg.f64 (.f64 (hypot.f64 1 x) 4)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (neg.f64 (+.f64 (.f64 (hypot.f64 1 x) 2) 2))) (.f64 (hypot.f64 1 x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (.f64 2 (-.f64 -1 (hypot.f64 1 x)))) (.f64 (hypot.f64 1 x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (neg.f64 (-.f64 -1 (hypot.f64 1 x)))) (neg.f64 (hypot.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 1 (/.f64 1 (hypot.f64 1 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (-.f64 -1 (hypot.f64 1 x)) (hypot.f64 1 x)))))))

simplify119.0ms (1%)

Algorithm

1×	egg-herbie

Rules

1472×	`rational.json-simplify-35`
1092×	`rational.json-simplify-46`
1090×	`rational.json-simplify-2`
780×	`rational.json-simplify-50`
736×	`rational.json-simplify-59`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	395	5858
1	938	5822
2	2466	5804
3	5517	5774

Stop Event

1×	node limit

Counts

202 → 289

Calls

Call 1

Inputs
(-.f64 1 (*.f64 (sqrt.f64 2) (sqrt.f64 1/2)))
(-.f64 (+.f64 (.f64 1/4 (/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 x 2)) (sqrt.f64 2))) 1) (*.f64 (sqrt.f64 2) (sqrt.f64 1/2)))
(-.f64 (+.f64 (.f64 1/4 (/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 x 2)) (sqrt.f64 2))) (+.f64 1 (.f64 -1/2 (/.f64 (.f64 (sqrt.f64 1/2) (.f64 (-.f64 3/8 (pow.f64 (/.f64 -1/4 (sqrt.f64 2)) 2)) (pow.f64 x 4))) (sqrt.f64 2))))) (.f64 (sqrt.f64 2) (sqrt.f64 1/2)))
(-.f64 (+.f64 (.f64 1/4 (/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 x 2)) (sqrt.f64 2))) (+.f64 1 (+.f64 (.f64 1/2 (/.f64 (.f64 (sqrt.f64 1/2) (.f64 (+.f64 (.f64 -1/4 (/.f64 (-.f64 3/8 (pow.f64 (/.f64 -1/4 (sqrt.f64 2)) 2)) (pow.f64 (sqrt.f64 2) 2))) 5/16) (pow.f64 x 6))) (sqrt.f64 2))) (.f64 -1/2 (/.f64 (.f64 (sqrt.f64 1/2) (.f64 (-.f64 3/8 (pow.f64 (/.f64 -1/4 (sqrt.f64 2)) 2)) (pow.f64 x 4))) (sqrt.f64 2)))))) (.f64 (sqrt.f64 2) (sqrt.f64 1/2)))
(-.f64 1 (sqrt.f64 1/2))
(-.f64 (+.f64 1 (*.f64 -1/2 (/.f64 (sqrt.f64 1/2) x))) (sqrt.f64 1/2))
(-.f64 (+.f64 1 (+.f64 (.f64 -1/2 (/.f64 (sqrt.f64 1/2) x)) (.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))))) (sqrt.f64 1/2))
(-.f64 (+.f64 1 (+.f64 (.f64 -1/2 (/.f64 (sqrt.f64 1/2) x)) (+.f64 (.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (*.f64 3/16 (/.f64 (sqrt.f64 1/2) (pow.f64 x 3)))))) (sqrt.f64 1/2))
(-.f64 1 (sqrt.f64 1/2))
(-.f64 (+.f64 1 (*.f64 1/2 (/.f64 (sqrt.f64 1/2) x))) (sqrt.f64 1/2))
(-.f64 (+.f64 1 (+.f64 (.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (.f64 1/2 (/.f64 (sqrt.f64 1/2) x)))) (sqrt.f64 1/2))
(-.f64 (+.f64 (.f64 -3/16 (/.f64 (sqrt.f64 1/2) (pow.f64 x 3))) (+.f64 1 (+.f64 (.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (*.f64 1/2 (/.f64 (sqrt.f64 1/2) x))))) (sqrt.f64 1/2))
(*.f64 (sqrt.f64 2) (sqrt.f64 1/2))
(+.f64 (.f64 -1/4 (/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 x 2)) (sqrt.f64 2))) (*.f64 (sqrt.f64 2) (sqrt.f64 1/2)))
(+.f64 (.f64 1/2 (/.f64 (.f64 (sqrt.f64 1/2) (.f64 (-.f64 3/8 (pow.f64 (/.f64 -1/4 (sqrt.f64 2)) 2)) (pow.f64 x 4))) (sqrt.f64 2))) (+.f64 (.f64 -1/4 (/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 x 2)) (sqrt.f64 2))) (.f64 (sqrt.f64 2) (sqrt.f64 1/2))))
(+.f64 (.f64 1/2 (/.f64 (.f64 (sqrt.f64 1/2) (.f64 (-.f64 3/8 (pow.f64 (/.f64 -1/4 (sqrt.f64 2)) 2)) (pow.f64 x 4))) (sqrt.f64 2))) (+.f64 (.f64 -1/2 (/.f64 (.f64 (sqrt.f64 1/2) (.f64 (+.f64 (.f64 -1/4 (/.f64 (-.f64 3/8 (pow.f64 (/.f64 -1/4 (sqrt.f64 2)) 2)) (pow.f64 (sqrt.f64 2) 2))) 5/16) (pow.f64 x 6))) (sqrt.f64 2))) (+.f64 (.f64 -1/4 (/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 x 2)) (sqrt.f64 2))) (.f64 (sqrt.f64 2) (sqrt.f64 1/2)))))
(sqrt.f64 1/2)
(+.f64 (sqrt.f64 1/2) (*.f64 1/2 (/.f64 (sqrt.f64 1/2) x)))
(+.f64 (sqrt.f64 1/2) (+.f64 (.f64 -1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (.f64 1/2 (/.f64 (sqrt.f64 1/2) x))))
(+.f64 (.f64 -3/16 (/.f64 (sqrt.f64 1/2) (pow.f64 x 3))) (+.f64 (sqrt.f64 1/2) (+.f64 (.f64 -1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (*.f64 1/2 (/.f64 (sqrt.f64 1/2) x)))))
(sqrt.f64 1/2)
(+.f64 (sqrt.f64 1/2) (*.f64 -1/2 (/.f64 (sqrt.f64 1/2) x)))
(+.f64 (sqrt.f64 1/2) (+.f64 (.f64 -1/2 (/.f64 (sqrt.f64 1/2) x)) (.f64 -1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2)))))
(+.f64 (sqrt.f64 1/2) (+.f64 (.f64 -1/2 (/.f64 (sqrt.f64 1/2) x)) (+.f64 (.f64 -1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (*.f64 3/16 (/.f64 (sqrt.f64 1/2) (pow.f64 x 3))))))
1
(+.f64 1 (*.f64 -1/2 (pow.f64 x 2)))
(+.f64 1 (+.f64 (.f64 -1/2 (pow.f64 x 2)) (.f64 3/8 (pow.f64 x 4))))
(+.f64 (.f64 -5/16 (pow.f64 x 6)) (+.f64 1 (+.f64 (.f64 -1/2 (pow.f64 x 2)) (*.f64 3/8 (pow.f64 x 4)))))
(/.f64 1 x)
(-.f64 (/.f64 1 x) (*.f64 1/2 (/.f64 1 (pow.f64 x 3))))
(-.f64 (+.f64 (/.f64 1 x) (.f64 3/8 (/.f64 1 (pow.f64 x 5)))) (.f64 1/2 (/.f64 1 (pow.f64 x 3))))
(-.f64 (+.f64 (/.f64 1 x) (.f64 3/8 (/.f64 1 (pow.f64 x 5)))) (+.f64 (.f64 5/16 (/.f64 1 (pow.f64 x 7))) (*.f64 1/2 (/.f64 1 (pow.f64 x 3)))))
(/.f64 -1 x)
(-.f64 (*.f64 1/2 (/.f64 1 (pow.f64 x 3))) (/.f64 1 x))
(-.f64 (.f64 1/2 (/.f64 1 (pow.f64 x 3))) (+.f64 (/.f64 1 x) (.f64 3/8 (/.f64 1 (pow.f64 x 5)))))
(-.f64 (+.f64 (.f64 5/16 (/.f64 1 (pow.f64 x 7))) (.f64 1/2 (/.f64 1 (pow.f64 x 3)))) (+.f64 (/.f64 1 x) (*.f64 3/8 (/.f64 1 (pow.f64 x 5)))))
2
(+.f64 2 (*.f64 -1/2 (pow.f64 x 2)))
(+.f64 2 (+.f64 (.f64 -1/2 (pow.f64 x 2)) (.f64 3/8 (pow.f64 x 4))))
(+.f64 (.f64 -5/16 (pow.f64 x 6)) (+.f64 2 (+.f64 (.f64 -1/2 (pow.f64 x 2)) (*.f64 3/8 (pow.f64 x 4)))))
1
(+.f64 1 (/.f64 1 x))
(-.f64 (+.f64 1 (/.f64 1 x)) (*.f64 1/2 (/.f64 1 (pow.f64 x 3))))
(-.f64 (+.f64 1 (+.f64 (/.f64 1 x) (.f64 3/8 (/.f64 1 (pow.f64 x 5))))) (.f64 1/2 (/.f64 1 (pow.f64 x 3))))
1
(-.f64 1 (/.f64 1 x))
(-.f64 (+.f64 1 (*.f64 1/2 (/.f64 1 (pow.f64 x 3)))) (/.f64 1 x))
(-.f64 (+.f64 1 (.f64 1/2 (/.f64 1 (pow.f64 x 3)))) (+.f64 (/.f64 1 x) (.f64 3/8 (/.f64 1 (pow.f64 x 5)))))
(+.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 0)
(+.f64 0 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
(+.f64 -1 (neg.f64 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -2)))
(+.f64 -2 (-.f64 1 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -2)))
(+.f64 (neg.f64 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -2)) -1)
(+.f64 (.f64 1/2 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) (.f64 1/2 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))
(+.f64 (-.f64 -1 (/.f64 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -1) 2)) (-.f64 1 (/.f64 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -1) 2)))
(*.f64 1 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
(.f64 1/2 (.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 2))
(*.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 1)
(*.f64 -1 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -1))
(.f64 2 (.f64 1/2 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))
(*.f64 4 (/.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 4))
(.f64 (.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 2) 1/2)
(*.f64 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -1) -1)
(.f64 (.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 4) 1/4)
(.f64 1/4 (.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 4))
(.f64 (.f64 1/2 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) 2)
(*.f64 (/.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 4) 4)
(/.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 1)
(/.f64 (*.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 2) 2)
(/.f64 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -1) -1)
(/.f64 (*.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 4) 4)
(/.f64 (*.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 8) 8)
(/.f64 (*.f64 2 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -1)) -2)
(/.f64 (*.f64 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -1) 4) -4)
(/.f64 (.f64 2 (.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 8)) 16)
(/.f64 (neg.f64 (*.f64 2 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -1))) 2)
(/.f64 (+.f64 (.f64 2 (.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 8)) (.f64 2 (.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 8))) 32)
(/.f64 (+.f64 (neg.f64 (.f64 2 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -1))) (neg.f64 (.f64 2 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -1)))) 4)
(pow.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 1)
(neg.f64 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -1))
(+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) 0)
(+.f64 0 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
(+.f64 (.f64 1/2 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) (.f64 1/2 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
(-.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) 0)
(*.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
(.f64 1/2 (.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) 2))
(*.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) 1)
(.f64 2 (.f64 1/2 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
(.f64 (.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) 2) 1/2)
(*.f64 4 (/.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) 4))
(.f64 (.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) 4) 1/4)
(.f64 1/4 (.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) 4))
(.f64 (.f64 1/2 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 2)
(*.f64 (/.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) 4) 4)
(/.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) 1)
(/.f64 (*.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) 2) 2)
(/.f64 (*.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) 4) 4)
(/.f64 (*.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) 8) 8)
(/.f64 (.f64 2 (.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) 8)) 16)
(/.f64 (+.f64 (.f64 2 (.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) 8)) (.f64 2 (.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) 8))) 32)
(pow.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) 1)
(+.f64 (/.f64 1 (hypot.f64 1 x)) 0)
(+.f64 0 (/.f64 1 (hypot.f64 1 x)))
(+.f64 -1 (-.f64 1 (/.f64 -1 (hypot.f64 1 x))))
(+.f64 (/.f64 1/2 (hypot.f64 1 x)) (/.f64 1/2 (hypot.f64 1 x)))
(-.f64 (/.f64 1 (hypot.f64 1 x)) 0)
(-.f64 0 (/.f64 -1 (hypot.f64 1 x)))
(*.f64 1 (/.f64 1 (hypot.f64 1 x)))
(*.f64 1/2 (/.f64 2 (hypot.f64 1 x)))
(.f64 (hypot.f64 1 x) (/.f64 1 (.f64 (hypot.f64 1 x) (hypot.f64 1 x))))
(*.f64 (/.f64 1 (hypot.f64 1 x)) 1)
(*.f64 2 (/.f64 1/2 (hypot.f64 1 x)))
(.f64 (.f64 (hypot.f64 1 x) 2) (/.f64 1/2 (*.f64 (hypot.f64 1 x) (hypot.f64 1 x))))
(*.f64 4 (/.f64 1/4 (hypot.f64 1 x)))
(*.f64 (/.f64 2 (hypot.f64 1 x)) 1/2)
(*.f64 (/.f64 4 (hypot.f64 1 x)) 1/4)
(*.f64 1/4 (/.f64 4 (hypot.f64 1 x)))
(*.f64 (/.f64 1/2 (hypot.f64 1 x)) 2)
(.f64 (/.f64 1 (.f64 (hypot.f64 1 x) (hypot.f64 1 x))) (hypot.f64 1 x))
(.f64 (/.f64 2 (.f64 (hypot.f64 1 x) (hypot.f64 1 x))) (*.f64 1/2 (hypot.f64 1 x)))
(*.f64 (/.f64 1/4 (hypot.f64 1 x)) 4)
(.f64 (.f64 1/2 (hypot.f64 1 x)) (/.f64 2 (*.f64 (hypot.f64 1 x) (hypot.f64 1 x))))
(*.f64 (/.f64 -1 (hypot.f64 1 x)) -1)
(.f64 (/.f64 1/2 (.f64 (hypot.f64 1 x) (hypot.f64 1 x))) (*.f64 (hypot.f64 1 x) 2))
(pow.f64 (/.f64 1 (hypot.f64 1 x)) 1)
(neg.f64 (/.f64 -1 (hypot.f64 1 x)))
(-.f64 (/.f64 1 (hypot.f64 1 x)) -1)
(-.f64 (+.f64 1 (/.f64 1 (hypot.f64 1 x))) 0)
(-.f64 0 (/.f64 (-.f64 -1 (hypot.f64 1 x)) (hypot.f64 1 x)))
(*.f64 1 (+.f64 1 (/.f64 1 (hypot.f64 1 x))))
(*.f64 1/2 (+.f64 2 (/.f64 2 (hypot.f64 1 x))))
(*.f64 (/.f64 1 (hypot.f64 1 x)) (+.f64 1 (hypot.f64 1 x)))
(*.f64 (+.f64 1 (/.f64 1 (hypot.f64 1 x))) 1)
(*.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 2)
(*.f64 (+.f64 1 (hypot.f64 1 x)) (/.f64 1 (hypot.f64 1 x)))
(*.f64 2 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
(*.f64 4 (+.f64 1/4 (/.f64 1/4 (hypot.f64 1 x))))
(.f64 (/.f64 2 (hypot.f64 1 x)) (.f64 1/2 (+.f64 1 (hypot.f64 1 x))))
(.f64 (/.f64 2 (hypot.f64 1 x)) (.f64 2 (*.f64 (+.f64 1 (hypot.f64 1 x)) 1/4)))
(.f64 (/.f64 2 (hypot.f64 1 x)) (+.f64 (.f64 (+.f64 1 (hypot.f64 1 x)) 1/4) (*.f64 (+.f64 1 (hypot.f64 1 x)) 1/4)))
(.f64 (/.f64 2 (hypot.f64 1 x)) (+.f64 (.f64 (+.f64 1 (hypot.f64 1 x)) 1/4) (.f64 1/2 (.f64 1/2 (+.f64 1 (hypot.f64 1 x))))))
(*.f64 (+.f64 2 (/.f64 2 (hypot.f64 1 x))) 1/2)
(.f64 (.f64 (+.f64 1 (/.f64 1 (hypot.f64 1 x))) 4) 1/4)
(.f64 (+.f64 (.f64 (hypot.f64 1 x) 2) 2) (/.f64 1/2 (hypot.f64 1 x)))
(.f64 (/.f64 4 (hypot.f64 1 x)) (.f64 (+.f64 1 (hypot.f64 1 x)) 1/4))
(.f64 (.f64 1/2 (+.f64 1 (hypot.f64 1 x))) (/.f64 2 (hypot.f64 1 x)))
(.f64 (.f64 (+.f64 1 (hypot.f64 1 x)) 4) (/.f64 1/4 (hypot.f64 1 x)))
(.f64 1/4 (.f64 (+.f64 1 (/.f64 1 (hypot.f64 1 x))) 4))
(.f64 (/.f64 1/2 (hypot.f64 1 x)) (+.f64 (.f64 (hypot.f64 1 x) 2) 2))
(*.f64 (+.f64 1/4 (/.f64 1/4 (hypot.f64 1 x))) 4)
(.f64 (/.f64 1/4 (hypot.f64 1 x)) (.f64 (+.f64 1 (hypot.f64 1 x)) 4))
(.f64 (.f64 (+.f64 1 (hypot.f64 1 x)) 1/4) (/.f64 4 (hypot.f64 1 x)))
(.f64 (.f64 2 (*.f64 (+.f64 1 (hypot.f64 1 x)) 1/4)) (/.f64 2 (hypot.f64 1 x)))
(*.f64 (/.f64 (-.f64 -1 (hypot.f64 1 x)) (hypot.f64 1 x)) -1)
(.f64 (+.f64 (/.f64 (.f64 (hypot.f64 1 x) (hypot.f64 1 x)) (hypot.f64 1 x)) 1) (/.f64 1 (hypot.f64 1 x)))
(.f64 (+.f64 (.f64 (+.f64 1 (hypot.f64 1 x)) 1/4) (*.f64 (+.f64 1 (hypot.f64 1 x)) 1/4)) (/.f64 2 (hypot.f64 1 x)))
(/.f64 1 (/.f64 1 (+.f64 1 (/.f64 1 (hypot.f64 1 x)))))
(/.f64 (+.f64 1 (/.f64 1 (hypot.f64 1 x))) 1)
(/.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 1/2)
(/.f64 -1 (/.f64 (hypot.f64 1 x) (-.f64 -1 (hypot.f64 1 x))))
(/.f64 -1 (neg.f64 (/.f64 1 (+.f64 1 (/.f64 1 (hypot.f64 1 x))))))
(/.f64 (+.f64 1 (hypot.f64 1 x)) (hypot.f64 1 x))
(/.f64 (+.f64 1 (hypot.f64 1 x)) (/.f64 (*.f64 (hypot.f64 1 x) (hypot.f64 1 x)) (hypot.f64 1 x)))
(/.f64 (+.f64 1 (hypot.f64 1 x)) (/.f64 (*.f64 1/2 (hypot.f64 1 x)) 1/2))
(/.f64 2 (/.f64 2 (+.f64 1 (/.f64 1 (hypot.f64 1 x)))))
(/.f64 4 (/.f64 4 (+.f64 1 (/.f64 1 (hypot.f64 1 x)))))
(/.f64 (+.f64 2 (/.f64 2 (hypot.f64 1 x))) 2)
(/.f64 8 (*.f64 2 (/.f64 4 (+.f64 1 (/.f64 1 (hypot.f64 1 x))))))
(/.f64 8 (/.f64 (*.f64 (hypot.f64 1 x) 8) (+.f64 1 (hypot.f64 1 x))))
(/.f64 (*.f64 (+.f64 1 (/.f64 1 (hypot.f64 1 x))) 4) 4)
(/.f64 (+.f64 (.f64 (hypot.f64 1 x) 2) 2) (.f64 (hypot.f64 1 x) 2))
(/.f64 (+.f64 (*.f64 (hypot.f64 1 x) 2) 2) (/.f64 (hypot.f64 1 x) 1/2))
(/.f64 -2 (+.f64 (/.f64 (hypot.f64 1 x) (-.f64 -1 (hypot.f64 1 x))) (/.f64 (hypot.f64 1 x) (-.f64 -1 (hypot.f64 1 x)))))
(/.f64 -2 (neg.f64 (/.f64 2 (+.f64 1 (/.f64 1 (hypot.f64 1 x))))))
(/.f64 (.f64 1/2 (+.f64 1 (hypot.f64 1 x))) (.f64 1/2 (hypot.f64 1 x)))
(/.f64 (.f64 1/2 (+.f64 1 (hypot.f64 1 x))) (/.f64 (.f64 (hypot.f64 1 x) (hypot.f64 1 x)) (*.f64 (hypot.f64 1 x) 2)))
(/.f64 16 (+.f64 (/.f64 (.f64 (hypot.f64 1 x) 8) (+.f64 1 (hypot.f64 1 x))) (/.f64 (.f64 (hypot.f64 1 x) 8) (+.f64 1 (hypot.f64 1 x)))))
(/.f64 16 (+.f64 (.f64 2 (/.f64 4 (+.f64 1 (/.f64 1 (hypot.f64 1 x))))) (.f64 2 (/.f64 4 (+.f64 1 (/.f64 1 (hypot.f64 1 x)))))))
(/.f64 (*.f64 (+.f64 1 (/.f64 1 (hypot.f64 1 x))) 8) 8)
(/.f64 (.f64 (+.f64 1 (hypot.f64 1 x)) 4) (.f64 (hypot.f64 1 x) 4))
(/.f64 -4 (neg.f64 (/.f64 4 (+.f64 1 (/.f64 1 (hypot.f64 1 x))))))
(/.f64 (+.f64 1/4 (/.f64 1/4 (hypot.f64 1 x))) 1/4)
(/.f64 (-.f64 -1 (hypot.f64 1 x)) (neg.f64 (hypot.f64 1 x)))
(/.f64 (/.f64 4 (+.f64 1 (/.f64 1 (hypot.f64 1 x)))) (*.f64 (/.f64 2 (+.f64 1 (/.f64 1 (hypot.f64 1 x)))) (/.f64 2 (+.f64 1 (/.f64 1 (hypot.f64 1 x))))))
(/.f64 (.f64 2 (.f64 (+.f64 1 (/.f64 1 (hypot.f64 1 x))) 8)) 16)
(/.f64 (.f64 2 (-.f64 -1 (hypot.f64 1 x))) (.f64 (hypot.f64 1 x) -2))
(/.f64 (.f64 2 (.f64 (+.f64 1 (hypot.f64 1 x)) 4)) (*.f64 (hypot.f64 1 x) 8))
(/.f64 (/.f64 (-.f64 -1 (hypot.f64 1 x)) (hypot.f64 1 x)) -1)
(/.f64 (neg.f64 (+.f64 (.f64 (hypot.f64 1 x) 2) 2)) (.f64 (hypot.f64 1 x) -2))
(/.f64 (neg.f64 (-.f64 -1 (hypot.f64 1 x))) (hypot.f64 1 x))
(/.f64 (neg.f64 (.f64 1/2 (+.f64 1 (hypot.f64 1 x)))) (neg.f64 (.f64 1/2 (hypot.f64 1 x))))
(/.f64 (+.f64 (neg.f64 (+.f64 (.f64 (hypot.f64 1 x) 2) 2)) (neg.f64 (+.f64 (.f64 (hypot.f64 1 x) 2) 2))) (*.f64 4 (neg.f64 (hypot.f64 1 x))))
(/.f64 (+.f64 (.f64 2 (.f64 (+.f64 1 (/.f64 1 (hypot.f64 1 x))) 8)) (.f64 2 (.f64 (+.f64 1 (/.f64 1 (hypot.f64 1 x))) 8))) 32)
(/.f64 (+.f64 (.f64 2 (-.f64 -1 (hypot.f64 1 x))) (.f64 2 (-.f64 -1 (hypot.f64 1 x)))) (*.f64 4 (neg.f64 (hypot.f64 1 x))))
(/.f64 (+.f64 (/.f64 (-.f64 -1 (hypot.f64 1 x)) (hypot.f64 1 x)) (/.f64 (-.f64 -1 (hypot.f64 1 x)) (hypot.f64 1 x))) -2)
(/.f64 (+.f64 (neg.f64 (-.f64 -1 (hypot.f64 1 x))) (neg.f64 (-.f64 -1 (hypot.f64 1 x)))) (*.f64 (hypot.f64 1 x) 2))
(/.f64 (neg.f64 (.f64 (+.f64 1 (hypot.f64 1 x)) 4)) (neg.f64 (.f64 (hypot.f64 1 x) 4)))
(/.f64 (neg.f64 (neg.f64 (+.f64 (.f64 (hypot.f64 1 x) 2) 2))) (.f64 (hypot.f64 1 x) 2))
(/.f64 (neg.f64 (.f64 2 (-.f64 -1 (hypot.f64 1 x)))) (.f64 (hypot.f64 1 x) 2))
(/.f64 (neg.f64 (neg.f64 (-.f64 -1 (hypot.f64 1 x)))) (neg.f64 (hypot.f64 1 x)))
(pow.f64 (+.f64 1 (/.f64 1 (hypot.f64 1 x))) 1)
(neg.f64 (/.f64 (-.f64 -1 (hypot.f64 1 x)) (hypot.f64 1 x)))

Outputs
(-.f64 1 (*.f64 (sqrt.f64 2) (sqrt.f64 1/2)))
0
(-.f64 (+.f64 (.f64 1/4 (/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 x 2)) (sqrt.f64 2))) 1) (*.f64 (sqrt.f64 2) (sqrt.f64 1/2)))
(+.f64 1 (-.f64 (.f64 1/4 (.f64 (pow.f64 x 2) (/.f64 (sqrt.f64 1/2) (sqrt.f64 2)))) 1))
(+.f64 (.f64 1/4 (.f64 (sqrt.f64 1/2) (/.f64 (pow.f64 x 2) (sqrt.f64 2)))) 0)
(.f64 1/4 (.f64 (sqrt.f64 1/2) (/.f64 (pow.f64 x 2) (sqrt.f64 2))))
(-.f64 (+.f64 (.f64 1/4 (/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 x 2)) (sqrt.f64 2))) (+.f64 1 (.f64 -1/2 (/.f64 (.f64 (sqrt.f64 1/2) (.f64 (-.f64 3/8 (pow.f64 (/.f64 -1/4 (sqrt.f64 2)) 2)) (pow.f64 x 4))) (sqrt.f64 2))))) (.f64 (sqrt.f64 2) (sqrt.f64 1/2)))
(+.f64 (+.f64 1 (.f64 -1/2 (.f64 (.f64 (-.f64 3/8 (pow.f64 (/.f64 -1/4 (sqrt.f64 2)) 2)) (pow.f64 x 4)) (/.f64 (sqrt.f64 1/2) (sqrt.f64 2))))) (-.f64 (.f64 1/4 (*.f64 (pow.f64 x 2) (/.f64 (sqrt.f64 1/2) (sqrt.f64 2)))) 1))
(+.f64 (+.f64 (.f64 1/4 (.f64 (sqrt.f64 1/2) (/.f64 (pow.f64 x 2) (sqrt.f64 2)))) (.f64 -1/2 (.f64 (*.f64 (sqrt.f64 1/2) (pow.f64 x 4)) (/.f64 (-.f64 3/8 (pow.f64 (/.f64 -1/4 (sqrt.f64 2)) 2)) (sqrt.f64 2))))) 0)
(+.f64 (.f64 1/4 (.f64 (sqrt.f64 1/2) (/.f64 (pow.f64 x 2) (sqrt.f64 2)))) (.f64 -1/2 (.f64 (*.f64 (sqrt.f64 1/2) (pow.f64 x 4)) (/.f64 (-.f64 3/8 (pow.f64 (/.f64 -1/4 (sqrt.f64 2)) 2)) (sqrt.f64 2)))))
(-.f64 (+.f64 (.f64 1/4 (/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 x 2)) (sqrt.f64 2))) (+.f64 1 (+.f64 (.f64 1/2 (/.f64 (.f64 (sqrt.f64 1/2) (.f64 (+.f64 (.f64 -1/4 (/.f64 (-.f64 3/8 (pow.f64 (/.f64 -1/4 (sqrt.f64 2)) 2)) (pow.f64 (sqrt.f64 2) 2))) 5/16) (pow.f64 x 6))) (sqrt.f64 2))) (.f64 -1/2 (/.f64 (.f64 (sqrt.f64 1/2) (.f64 (-.f64 3/8 (pow.f64 (/.f64 -1/4 (sqrt.f64 2)) 2)) (pow.f64 x 4))) (sqrt.f64 2)))))) (.f64 (sqrt.f64 2) (sqrt.f64 1/2)))
(+.f64 (+.f64 (.f64 1/2 (.f64 (.f64 (+.f64 (.f64 -1/4 (/.f64 (-.f64 3/8 (pow.f64 (/.f64 -1/4 (sqrt.f64 2)) 2)) 2)) 5/16) (pow.f64 x 6)) (/.f64 (sqrt.f64 1/2) (sqrt.f64 2)))) (+.f64 1 (.f64 -1/2 (.f64 (.f64 (-.f64 3/8 (pow.f64 (/.f64 -1/4 (sqrt.f64 2)) 2)) (pow.f64 x 4)) (/.f64 (sqrt.f64 1/2) (sqrt.f64 2)))))) (-.f64 (.f64 1/4 (*.f64 (pow.f64 x 2) (/.f64 (sqrt.f64 1/2) (sqrt.f64 2)))) 1))
(+.f64 (+.f64 (.f64 1/4 (.f64 (sqrt.f64 1/2) (/.f64 (pow.f64 x 2) (sqrt.f64 2)))) (+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 1/2) (pow.f64 x 4)) (/.f64 (-.f64 3/8 (pow.f64 (/.f64 -1/4 (sqrt.f64 2)) 2)) (sqrt.f64 2)))) (.f64 1/2 (.f64 (.f64 (+.f64 (*.f64 -1/4 (/.f64 (-.f64 3/8 (pow.f64 (/.f64 -1/4 (sqrt.f64 2)) 2)) 2)) 5/16) (pow.f64 x 6)) (/.f64 (sqrt.f64 1/2) (sqrt.f64 2)))))) 0)
(+.f64 (.f64 1/2 (.f64 (.f64 (sqrt.f64 1/2) (pow.f64 x 6)) (/.f64 (+.f64 (.f64 -1/4 (/.f64 (-.f64 3/8 (pow.f64 (/.f64 -1/4 (sqrt.f64 2)) 2)) 2)) 5/16) (sqrt.f64 2)))) (+.f64 (.f64 1/4 (.f64 (sqrt.f64 1/2) (/.f64 (pow.f64 x 2) (sqrt.f64 2)))) (.f64 -1/2 (.f64 (*.f64 (sqrt.f64 1/2) (pow.f64 x 4)) (/.f64 (-.f64 3/8 (pow.f64 (/.f64 -1/4 (sqrt.f64 2)) 2)) (sqrt.f64 2))))))
(+.f64 (.f64 1/2 (.f64 (.f64 (+.f64 (.f64 -1/4 (/.f64 (-.f64 3/8 (pow.f64 (/.f64 -1/4 (sqrt.f64 2)) 2)) 2)) 5/16) (pow.f64 x 6)) (/.f64 (sqrt.f64 1/2) (sqrt.f64 2)))) (+.f64 (.f64 1/4 (.f64 (sqrt.f64 1/2) (/.f64 (pow.f64 x 2) (sqrt.f64 2)))) (.f64 -1/2 (.f64 (*.f64 (sqrt.f64 1/2) (pow.f64 x 4)) (/.f64 (-.f64 3/8 (pow.f64 (/.f64 -1/4 (sqrt.f64 2)) 2)) (sqrt.f64 2))))))
(-.f64 1 (sqrt.f64 1/2))
(-.f64 (+.f64 1 (*.f64 -1/2 (/.f64 (sqrt.f64 1/2) x))) (sqrt.f64 1/2))
(+.f64 (*.f64 -1/2 (/.f64 (sqrt.f64 1/2) x)) (-.f64 1 (sqrt.f64 1/2)))
(+.f64 1 (-.f64 (*.f64 -1/2 (/.f64 (sqrt.f64 1/2) x)) (sqrt.f64 1/2)))
(+.f64 (-.f64 1 (sqrt.f64 1/2)) (*.f64 -1/2 (/.f64 (sqrt.f64 1/2) x)))
(-.f64 (+.f64 1 (+.f64 (.f64 -1/2 (/.f64 (sqrt.f64 1/2) x)) (.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))))) (sqrt.f64 1/2))
(+.f64 (+.f64 (.f64 -1/2 (/.f64 (sqrt.f64 1/2) x)) (.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2)))) (-.f64 1 (sqrt.f64 1/2)))
(+.f64 1 (-.f64 (+.f64 (.f64 -1/2 (/.f64 (sqrt.f64 1/2) x)) (.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2)))) (sqrt.f64 1/2)))
(+.f64 1 (+.f64 (.f64 -1/2 (/.f64 (sqrt.f64 1/2) x)) (-.f64 (.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (sqrt.f64 1/2))))
(+.f64 (.f64 -1/2 (/.f64 (sqrt.f64 1/2) x)) (+.f64 1 (-.f64 (.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (sqrt.f64 1/2))))
(-.f64 (+.f64 1 (+.f64 (.f64 -1/2 (/.f64 (sqrt.f64 1/2) x)) (+.f64 (.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (*.f64 3/16 (/.f64 (sqrt.f64 1/2) (pow.f64 x 3)))))) (sqrt.f64 1/2))
(+.f64 (+.f64 (.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (+.f64 (.f64 3/16 (/.f64 (sqrt.f64 1/2) (pow.f64 x 3))) (*.f64 -1/2 (/.f64 (sqrt.f64 1/2) x)))) (-.f64 1 (sqrt.f64 1/2)))
(+.f64 1 (-.f64 (+.f64 (.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (+.f64 (.f64 -1/2 (/.f64 (sqrt.f64 1/2) x)) (*.f64 3/16 (/.f64 (sqrt.f64 1/2) (pow.f64 x 3))))) (sqrt.f64 1/2)))
(+.f64 1 (+.f64 (.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (-.f64 (+.f64 (.f64 -1/2 (/.f64 (sqrt.f64 1/2) x)) (*.f64 3/16 (/.f64 (sqrt.f64 1/2) (pow.f64 x 3)))) (sqrt.f64 1/2))))
(+.f64 (.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (+.f64 (+.f64 (.f64 -1/2 (/.f64 (sqrt.f64 1/2) x)) (*.f64 3/16 (/.f64 (sqrt.f64 1/2) (pow.f64 x 3)))) (-.f64 1 (sqrt.f64 1/2))))
(-.f64 1 (sqrt.f64 1/2))
(-.f64 (+.f64 1 (*.f64 1/2 (/.f64 (sqrt.f64 1/2) x))) (sqrt.f64 1/2))
(+.f64 (*.f64 1/2 (/.f64 (sqrt.f64 1/2) x)) (-.f64 1 (sqrt.f64 1/2)))
(+.f64 (-.f64 1 (sqrt.f64 1/2)) (*.f64 1/2 (/.f64 (sqrt.f64 1/2) x)))
(-.f64 (+.f64 1 (+.f64 (.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (.f64 1/2 (/.f64 (sqrt.f64 1/2) x)))) (sqrt.f64 1/2))
(+.f64 (+.f64 (.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (.f64 1/2 (/.f64 (sqrt.f64 1/2) x))) (-.f64 1 (sqrt.f64 1/2)))
(+.f64 (-.f64 1 (sqrt.f64 1/2)) (+.f64 (.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (.f64 1/2 (/.f64 (sqrt.f64 1/2) x))))
(+.f64 (.f64 1/2 (/.f64 (sqrt.f64 1/2) x)) (+.f64 (.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (-.f64 1 (sqrt.f64 1/2))))
(+.f64 (.f64 1/2 (/.f64 (sqrt.f64 1/2) x)) (+.f64 1 (-.f64 (.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (sqrt.f64 1/2))))
(-.f64 (+.f64 (.f64 -3/16 (/.f64 (sqrt.f64 1/2) (pow.f64 x 3))) (+.f64 1 (+.f64 (.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (*.f64 1/2 (/.f64 (sqrt.f64 1/2) x))))) (sqrt.f64 1/2))
(+.f64 (+.f64 1 (+.f64 (.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (.f64 1/2 (/.f64 (sqrt.f64 1/2) x)))) (-.f64 (*.f64 (/.f64 (sqrt.f64 1/2) (pow.f64 x 3)) -3/16) (sqrt.f64 1/2)))
(+.f64 1 (+.f64 (+.f64 (.f64 1/2 (/.f64 (sqrt.f64 1/2) x)) (-.f64 (.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (sqrt.f64 1/2))) (*.f64 (/.f64 (sqrt.f64 1/2) (pow.f64 x 3)) -3/16)))
(+.f64 1 (+.f64 (+.f64 (.f64 1/2 (/.f64 (sqrt.f64 1/2) x)) (.f64 (/.f64 (sqrt.f64 1/2) (pow.f64 x 3)) -3/16)) (-.f64 (*.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (sqrt.f64 1/2))))
(*.f64 (sqrt.f64 2) (sqrt.f64 1/2))
1
(+.f64 (.f64 -1/4 (/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 x 2)) (sqrt.f64 2))) (*.f64 (sqrt.f64 2) (sqrt.f64 1/2)))
(+.f64 1 (.f64 (.f64 (pow.f64 x 2) (/.f64 (sqrt.f64 1/2) (sqrt.f64 2))) -1/4))
(+.f64 1 (.f64 (pow.f64 x 2) (.f64 (/.f64 (sqrt.f64 1/2) (sqrt.f64 2)) -1/4)))
(+.f64 1 (.f64 (pow.f64 x 2) (.f64 -1/4 (/.f64 (sqrt.f64 1/2) (sqrt.f64 2)))))
(+.f64 (.f64 1/2 (/.f64 (.f64 (sqrt.f64 1/2) (.f64 (-.f64 3/8 (pow.f64 (/.f64 -1/4 (sqrt.f64 2)) 2)) (pow.f64 x 4))) (sqrt.f64 2))) (+.f64 (.f64 -1/4 (/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 x 2)) (sqrt.f64 2))) (.f64 (sqrt.f64 2) (sqrt.f64 1/2))))
(+.f64 (+.f64 1 (.f64 (.f64 (pow.f64 x 2) (/.f64 (sqrt.f64 1/2) (sqrt.f64 2))) -1/4)) (.f64 1/2 (.f64 (*.f64 (-.f64 3/8 (pow.f64 (/.f64 -1/4 (sqrt.f64 2)) 2)) (pow.f64 x 4)) (/.f64 (sqrt.f64 1/2) (sqrt.f64 2)))))
(+.f64 (+.f64 1 (.f64 (pow.f64 x 2) (.f64 (/.f64 (sqrt.f64 1/2) (sqrt.f64 2)) -1/4))) (.f64 1/2 (.f64 (*.f64 (sqrt.f64 1/2) (pow.f64 x 4)) (/.f64 (-.f64 3/8 (pow.f64 (/.f64 -1/4 (sqrt.f64 2)) 2)) (sqrt.f64 2)))))
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(/.f64 (+.f64 2 (/.f64 2 (hypot.f64 1 x))) 2)
(/.f64 8 (*.f64 2 (/.f64 4 (+.f64 1 (/.f64 1 (hypot.f64 1 x))))))
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(/.f64 (*.f64 (+.f64 1 (/.f64 1 (hypot.f64 1 x))) 4) 4)
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(/.f64 (+.f64 (*.f64 (hypot.f64 1 x) 2) 2) (/.f64 (hypot.f64 1 x) 1/2))
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(/.f64 -2 (+.f64 (/.f64 (hypot.f64 1 x) (-.f64 -1 (hypot.f64 1 x))) (/.f64 (hypot.f64 1 x) (-.f64 -1 (hypot.f64 1 x)))))
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(/.f64 -2 (neg.f64 (/.f64 2 (+.f64 1 (/.f64 1 (hypot.f64 1 x))))))
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(/.f64 16 (+.f64 (/.f64 (.f64 (hypot.f64 1 x) 8) (+.f64 1 (hypot.f64 1 x))) (/.f64 (.f64 (hypot.f64 1 x) 8) (+.f64 1 (hypot.f64 1 x)))))
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(/.f64 16 (+.f64 (.f64 2 (/.f64 4 (+.f64 1 (/.f64 1 (hypot.f64 1 x))))) (.f64 2 (/.f64 4 (+.f64 1 (/.f64 1 (hypot.f64 1 x)))))))
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(/.f64 (*.f64 (+.f64 1 (/.f64 1 (hypot.f64 1 x))) 8) 8)
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(/.f64 (.f64 (+.f64 1 (hypot.f64 1 x)) 4) (.f64 (hypot.f64 1 x) 4))
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(/.f64 -4 (neg.f64 (/.f64 4 (+.f64 1 (/.f64 1 (hypot.f64 1 x))))))
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(/.f64 (+.f64 1/4 (/.f64 1/4 (hypot.f64 1 x))) 1/4)
(/.f64 (-.f64 -1 (hypot.f64 1 x)) (neg.f64 (hypot.f64 1 x)))
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(/.f64 (/.f64 4 (+.f64 1 (/.f64 1 (hypot.f64 1 x)))) (*.f64 (/.f64 2 (+.f64 1 (/.f64 1 (hypot.f64 1 x)))) (/.f64 2 (+.f64 1 (/.f64 1 (hypot.f64 1 x))))))
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(/.f64 (/.f64 (*.f64 2 (+.f64 1 (/.f64 1 (hypot.f64 1 x)))) (+.f64 1 (/.f64 1 (hypot.f64 1 x)))) (/.f64 2 (+.f64 1 (/.f64 1 (hypot.f64 1 x)))))
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(/.f64 (.f64 2 (.f64 (+.f64 1 (/.f64 1 (hypot.f64 1 x))) 8)) 16)
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(/.f64 (.f64 2 (-.f64 -1 (hypot.f64 1 x))) (.f64 (hypot.f64 1 x) -2))
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(/.f64 (.f64 2 (.f64 (+.f64 1 (hypot.f64 1 x)) 4)) (*.f64 (hypot.f64 1 x) 8))
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(/.f64 (neg.f64 (.f64 1/2 (+.f64 1 (hypot.f64 1 x)))) (neg.f64 (.f64 1/2 (hypot.f64 1 x))))
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(/.f64 (+.f64 (neg.f64 (+.f64 (.f64 (hypot.f64 1 x) 2) 2)) (neg.f64 (+.f64 (.f64 (hypot.f64 1 x) 2) 2))) (*.f64 4 (neg.f64 (hypot.f64 1 x))))
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(/.f64 (+.f64 (.f64 2 (.f64 (+.f64 1 (/.f64 1 (hypot.f64 1 x))) 8)) (.f64 2 (.f64 (+.f64 1 (/.f64 1 (hypot.f64 1 x))) 8))) 32)
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(/.f64 (+.f64 (/.f64 (-.f64 -1 (hypot.f64 1 x)) (hypot.f64 1 x)) (/.f64 (-.f64 -1 (hypot.f64 1 x)) (hypot.f64 1 x))) -2)
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(/.f64 (neg.f64 (.f64 2 (-.f64 -1 (hypot.f64 1 x)))) (.f64 (hypot.f64 1 x) 2))
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(pow.f64 (+.f64 1 (/.f64 1 (hypot.f64 1 x))) 1)
(+.f64 1 (/.f64 1 (hypot.f64 1 x)))
(neg.f64 (/.f64 (-.f64 -1 (hypot.f64 1 x)) (hypot.f64 1 x)))
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eval129.0ms (1.1%)

Compiler: Compiled 5896 to 5365 computations (9% saved)

prune50.0ms (0.4%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	278	11	289
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	279	11	290

Error

0.5b

Counts

290 → 11

Alt Table

Click to see full alt table

Status	Error	Program
▶	14.7b	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
▶	32.5b	(-.f64 1 (sqrt.f64 (*.f64 1/2 (-.f64 1 (/.f64 1 x)))))
	32.5b	(-.f64 1 (sqrt.f64 (*.f64 1/2 (+.f64 1 (/.f64 1 x)))))
▶	31.8b	(-.f64 1 (sqrt.f64 1/2))
▶	14.7b	(-.f64 -1 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -2))
	32.2b	(+.f64 (-.f64 1 (sqrt.f64 1/2)) (*.f64 1/2 (/.f64 (sqrt.f64 1/2) x)))
	32.3b	(+.f64 (.f64 1/2 (/.f64 (sqrt.f64 1/2) x)) (+.f64 (.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (-.f64 1 (sqrt.f64 1/2))))
	32.0b	(+.f64 (.f64 1/4 (.f64 (sqrt.f64 1/2) (/.f64 (pow.f64 x 2) (sqrt.f64 2)))) (.f64 -1/2 (.f64 (*.f64 (sqrt.f64 1/2) (pow.f64 x 4)) (/.f64 (-.f64 3/8 (pow.f64 (/.f64 -1/4 (sqrt.f64 2)) 2)) (sqrt.f64 2)))))
▶	32.3b	(+.f64 (.f64 -1/2 (/.f64 (sqrt.f64 1/2) x)) (+.f64 1 (-.f64 (.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (sqrt.f64 1/2))))
	31.5b	(.f64 1/4 (.f64 (sqrt.f64 1/2) (/.f64 (pow.f64 x 2) (sqrt.f64 2))))
	45.6b	0

Compiler

Compiled 302 to 278 computations (7.9% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))
✓	0.0b	(/.f64 1/2 (hypot.f64 1 x))
✓	0.0b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
✓	2.3b	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))

Compiler

Compiled 37 to 31 computations (16.2% saved)

series3.0ms (0%)

Counts

4 → 48

Calls

12 calls:

Time	Variable		Point	Expression
1.0ms	x	@	0	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
1.0ms	x	@	inf	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
0.0ms	x	@	-inf	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
0.0ms	x	@	inf	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
0.0ms	x	@	inf	(/.f64 1/2 (hypot.f64 1 x))

rewrite96.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

1256×	`rational.json-1`
1256×	`rational.json-2`
1256×	`rational.json-3`
1254×	`rational.json-4`
1238×	`exponential.json-3`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	84
1	83	84
2	186	84
3	390	84
4	790	84
5	2269	84
6	5434	84

Stop Event

1×	node limit

Counts

4 → 161

Calls

Call 1

Inputs
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
(/.f64 1/2 (hypot.f64 1 x))
(+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))

Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 -1 (neg.f64 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (neg.f64 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -2)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 -2 (-.f64 1 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 1/2 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) (.f64 1/2 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1/2 (.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 2 (.f64 1/2 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 4 (/.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 4))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 -1 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -1))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 4) 1/4)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1/4 (.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 4))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 1/2 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 4) 4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 2) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 4) 4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 2 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -1)) -2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 8) 8)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -1) 4) -4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 2 (.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 8)) 16)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (.f64 2 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -1))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 2 (.f64 2 (.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 8))) 32)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 2 (neg.f64 (*.f64 2 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -1)))) 4)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -1))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 1/2 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) (.f64 1/2 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1/2 (.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 2 (.f64 1/2 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 4 (/.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) 4))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) 4) 1/4)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1/4 (.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) 4))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 1/2 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) 4) 4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) 2) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) 4) 4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) 8) 8)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 2 (.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) 8)) 16)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 2 (.f64 2 (.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) 8))) 32)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) 1)))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 1/2 (hypot.f64 1 x)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 1/2 (hypot.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 -1 (-.f64 1 (/.f64 -1/2 (hypot.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 1/4 (hypot.f64 1 x)) (/.f64 1/4 (hypot.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 1/2 (hypot.f64 1 x)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 0 (/.f64 -1/2 (hypot.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (/.f64 1/2 (hypot.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1/2 (/.f64 1 (hypot.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (hypot.f64 1 x) (/.f64 1/2 (.f64 (hypot.f64 1 x) (hypot.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1/2 (hypot.f64 1 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (hypot.f64 1 x) 2) (/.f64 1/4 (.f64 (hypot.f64 1 x) (hypot.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 2 (/.f64 1/4 (hypot.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 2 (.f64 (/.f64 1/4 (.f64 (hypot.f64 1 x) (hypot.f64 1 x))) (hypot.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (hypot.f64 1 x) 4) (/.f64 1 (.f64 (hypot.f64 1 x) (.f64 (hypot.f64 1 x) 8))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1 (hypot.f64 1 x)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 4 (/.f64 (hypot.f64 1 x) (.f64 (hypot.f64 1 x) (.f64 (hypot.f64 1 x) 8))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 4 (/.f64 (/.f64 1/2 (hypot.f64 1 x)) 4))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (/.f64 1/2 (hypot.f64 1 x)) 4) 1/4)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1/4 (.f64 (/.f64 1/2 (hypot.f64 1 x)) 4))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1/4 (.f64 (hypot.f64 1 x) (hypot.f64 1 x))) (.f64 (hypot.f64 1 x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1/2 (.f64 (hypot.f64 1 x) (hypot.f64 1 x))) (hypot.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1/4 (hypot.f64 1 x)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (hypot.f64 1 x) (.f64 (hypot.f64 1 x) (.f64 (hypot.f64 1 x) 8))) 4)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 -1/2 (hypot.f64 1 x)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1 (.f64 (hypot.f64 1 x) (.f64 (hypot.f64 1 x) 8))) (.f64 (hypot.f64 1 x) 4))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (/.f64 1/2 (hypot.f64 1 x)) 4) 4)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1/2 (hypot.f64 1 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 -1/2 (hypot.f64 1 x)))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 1/2 (hypot.f64 1 x)) -1/2)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 1/2 (hypot.f64 1 x)) (neg.f64 (/.f64 (hypot.f64 1 x) (.f64 (hypot.f64 1 x) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1/2 (+.f64 1 (/.f64 1 (hypot.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1/2 (hypot.f64 1 x)) (+.f64 1 (hypot.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (+.f64 1 (hypot.f64 1 x)) (/.f64 1/2 (hypot.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 2 (+.f64 1/4 (/.f64 1/4 (hypot.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1 (hypot.f64 1 x)) (.f64 1/2 (+.f64 1 (hypot.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 4 (/.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 4))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (+.f64 1 (/.f64 1 (hypot.f64 1 x))) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 4) 1/4)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (+.f64 1 (hypot.f64 1 x)) 2) (/.f64 1/4 (hypot.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 1/2 (+.f64 1 (hypot.f64 1 x))) (/.f64 1 (hypot.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1/4 (.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 4))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1/4 (hypot.f64 1 x)) (.f64 (+.f64 1 (hypot.f64 1 x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (+.f64 1/4 (/.f64 1/4 (hypot.f64 1 x))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 4) 4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 1 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1/2 (/.f64 (hypot.f64 1 x) (+.f64 1 (hypot.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1 (hypot.f64 1 x)) (.f64 (hypot.f64 1 x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1 (hypot.f64 1 x)) (/.f64 (.f64 (hypot.f64 1 x) (.f64 (hypot.f64 1 x) 2)) (hypot.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 2 (/.f64 2 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 4 (.f64 2 (/.f64 2 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 4 (/.f64 (.f64 (hypot.f64 1 x) 8) (+.f64 1 (hypot.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1 (/.f64 1 (hypot.f64 1 x))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 -1/2 (neg.f64 (/.f64 (hypot.f64 1 x) (+.f64 1 (hypot.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 -1 (neg.f64 (/.f64 1 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 8 (/.f64 (.f64 (hypot.f64 1 x) 8) (.f64 1/2 (+.f64 1 (hypot.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 8 (.f64 2 (/.f64 (.f64 (hypot.f64 1 x) 8) (+.f64 1 (hypot.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 8 (.f64 2 (.f64 2 (/.f64 2 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 4) 4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (+.f64 1 (hypot.f64 1 x)) 2) (.f64 (hypot.f64 1 x) 4))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 16 (.f64 2 (/.f64 (.f64 (hypot.f64 1 x) 8) (.f64 1/2 (+.f64 1 (hypot.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 8) 8)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 -2 (neg.f64 (/.f64 2 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (+.f64 1 (hypot.f64 1 x)) 4) (.f64 (hypot.f64 1 x) 8))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 1/2 (+.f64 1 (hypot.f64 1 x))) (hypot.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 1/2 (+.f64 1 (hypot.f64 1 x))) (/.f64 (.f64 (hypot.f64 1 x) (.f64 (hypot.f64 1 x) 4)) (.f64 (hypot.f64 1 x) 4)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1/4 (/.f64 (hypot.f64 1 x) (.f64 (+.f64 1 (hypot.f64 1 x)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1/4 (/.f64 1/4 (hypot.f64 1 x))) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 -1 (hypot.f64 1 x)) (.f64 (hypot.f64 1 x) -2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 -1 (hypot.f64 1 x)) (-.f64 0 (/.f64 (.f64 (hypot.f64 1 x) (.f64 (hypot.f64 1 x) 2)) (hypot.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 -4 (-.f64 0 (.f64 2 (/.f64 2 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 -4 (-.f64 0 (/.f64 (.f64 (hypot.f64 1 x) 8) (+.f64 1 (hypot.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 2 (.f64 (+.f64 1 (hypot.f64 1 x)) 4)) (.f64 2 (.f64 (hypot.f64 1 x) 8)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 2 (/.f64 2 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) (.f64 (/.f64 2 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) (/.f64 2 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 2 (.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 8)) 16)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 2 (-.f64 -1 (hypot.f64 1 x))) (.f64 (neg.f64 (hypot.f64 1 x)) 4))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (+.f64 1 (hypot.f64 1 x)) 4) (.f64 1/2 (hypot.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 -1/4 (-.f64 0 (/.f64 (hypot.f64 1 x) (.f64 (+.f64 1 (hypot.f64 1 x)) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (+.f64 1 (hypot.f64 1 x)) (.f64 (hypot.f64 1 x) 8)) 1/4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 -8 (-.f64 0 (/.f64 (.f64 (hypot.f64 1 x) 8) (.f64 1/2 (+.f64 1 (hypot.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (.f64 (+.f64 1 (hypot.f64 1 x)) 2)) (neg.f64 (.f64 (hypot.f64 1 x) 4)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (.f64 1/2 (+.f64 1 (hypot.f64 1 x)))) (neg.f64 (hypot.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (.f64 1/2 (+.f64 1 (hypot.f64 1 x)))) (-.f64 0 (/.f64 (.f64 (hypot.f64 1 x) (.f64 (hypot.f64 1 x) 4)) (.f64 (hypot.f64 1 x) 4))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 2 (neg.f64 (.f64 (+.f64 1 (hypot.f64 1 x)) 2))) (.f64 2 (neg.f64 (.f64 (hypot.f64 1 x) 4))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 2 (/.f64 (+.f64 1 (hypot.f64 1 x)) 4)) (hypot.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 2 (.f64 2 (.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 8))) 32)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 2 (.f64 2 (-.f64 -1 (hypot.f64 1 x)))) (.f64 2 (.f64 (neg.f64 (hypot.f64 1 x)) 4)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 2 (/.f64 (+.f64 1 (hypot.f64 1 x)) (.f64 (hypot.f64 1 x) 8))) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 2 (neg.f64 (.f64 1/2 (+.f64 1 (hypot.f64 1 x))))) (.f64 (hypot.f64 1 x) -2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (.f64 (+.f64 1 (hypot.f64 1 x)) 4)) (neg.f64 (.f64 (hypot.f64 1 x) 8)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (neg.f64 (.f64 (+.f64 1 (hypot.f64 1 x)) 2))) (.f64 (hypot.f64 1 x) 4))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (/.f64 (+.f64 1 (hypot.f64 1 x)) 4)) (/.f64 (hypot.f64 1 x) -2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (.f64 2 (-.f64 -1 (hypot.f64 1 x)))) (/.f64 (.f64 (hypot.f64 1 x) -2) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (neg.f64 (.f64 1/2 (+.f64 1 (hypot.f64 1 x))))) (hypot.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (.f64 2 (.f64 (+.f64 1 (hypot.f64 1 x)) 4))) (neg.f64 (.f64 2 (.f64 (hypot.f64 1 x) 8))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (neg.f64 (.f64 (+.f64 1 (hypot.f64 1 x)) 4))) (.f64 (hypot.f64 1 x) 8))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (neg.f64 (.f64 (+.f64 1 (hypot.f64 1 x)) 4))) (-.f64 0 (neg.f64 (.f64 (hypot.f64 1 x) 8))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (.f64 2 (neg.f64 (.f64 (+.f64 1 (hypot.f64 1 x)) 2)))) (-.f64 0 (.f64 2 (neg.f64 (.f64 (hypot.f64 1 x) 4)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (neg.f64 (neg.f64 (.f64 (+.f64 1 (hypot.f64 1 x)) 2)))) (neg.f64 (.f64 (hypot.f64 1 x) 4)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (.f64 2 (/.f64 (+.f64 1 (hypot.f64 1 x)) 4))) (neg.f64 (hypot.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (neg.f64 (/.f64 (+.f64 1 (hypot.f64 1 x)) 4))) (.f64 1/2 (hypot.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (.f64 2 (.f64 2 (-.f64 -1 (hypot.f64 1 x))))) (-.f64 0 (.f64 2 (.f64 (neg.f64 (hypot.f64 1 x)) 4))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (.f64 2 (neg.f64 (.f64 1/2 (+.f64 1 (hypot.f64 1 x)))))) (.f64 (hypot.f64 1 x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (neg.f64 (.f64 2 (-.f64 -1 (hypot.f64 1 x))))) (.f64 (neg.f64 (hypot.f64 1 x)) 4))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (neg.f64 (neg.f64 (.f64 1/2 (+.f64 1 (hypot.f64 1 x)))))) (neg.f64 (hypot.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 1)))))

simplify149.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

1050×	`rational.json-simplify-1`
1030×	`rational.json-simplify-2`
700×	`rational.json-simplify-35`
696×	`rational.json-simplify-50`
590×	`rational.json-simplify-53`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	422	5831
1	1117	5767
2	3056	5755
3	4934	5743
4	7537	5743

Stop Event

1×	node limit

Counts

209 → 288

Calls

Call 1

Inputs
(*.f64 1/8 (pow.f64 x 2))
(+.f64 (.f64 1/8 (pow.f64 x 2)) (.f64 -11/128 (pow.f64 x 4)))
(+.f64 (.f64 1/8 (pow.f64 x 2)) (+.f64 (.f64 69/1024 (pow.f64 x 6)) (*.f64 -11/128 (pow.f64 x 4))))
(+.f64 (.f64 1/8 (pow.f64 x 2)) (+.f64 (.f64 69/1024 (pow.f64 x 6)) (+.f64 (.f64 -1843/32768 (pow.f64 x 8)) (.f64 -11/128 (pow.f64 x 4)))))
(-.f64 1 (sqrt.f64 1/2))
(-.f64 1 (+.f64 (sqrt.f64 1/2) (.f64 1/4 (/.f64 1 (.f64 (sqrt.f64 1/2) x)))))
(-.f64 (+.f64 1 (.f64 1/32 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 x 2))))) (+.f64 (sqrt.f64 1/2) (.f64 1/4 (/.f64 1 (.f64 (sqrt.f64 1/2) x)))))
(-.f64 (+.f64 1 (+.f64 (.f64 1/32 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 x 2)))) (.f64 -1/2 (/.f64 (-.f64 (.f64 1/64 (/.f64 1 (pow.f64 (sqrt.f64 1/2) 4))) 1/4) (.f64 (sqrt.f64 1/2) (pow.f64 x 3)))))) (+.f64 (sqrt.f64 1/2) (.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x)))))
(-.f64 1 (sqrt.f64 1/2))
(-.f64 (+.f64 1 (.f64 1/4 (/.f64 1 (.f64 (sqrt.f64 1/2) x)))) (sqrt.f64 1/2))
(-.f64 (+.f64 1 (+.f64 (.f64 1/4 (/.f64 1 (.f64 (sqrt.f64 1/2) x))) (.f64 1/32 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 x 2)))))) (sqrt.f64 1/2))
(-.f64 (+.f64 (.f64 1/2 (/.f64 (-.f64 (.f64 1/64 (/.f64 1 (pow.f64 (sqrt.f64 1/2) 4))) 1/4) (.f64 (sqrt.f64 1/2) (pow.f64 x 3)))) (+.f64 1 (+.f64 (.f64 1/4 (/.f64 1 (.f64 (sqrt.f64 1/2) x))) (.f64 1/32 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 x 2))))))) (sqrt.f64 1/2))
1
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) 1)
(+.f64 (.f64 -1/8 (pow.f64 x 2)) (+.f64 1 (.f64 11/128 (pow.f64 x 4))))
(+.f64 (.f64 -1/8 (pow.f64 x 2)) (+.f64 (.f64 -69/1024 (pow.f64 x 6)) (+.f64 1 (*.f64 11/128 (pow.f64 x 4)))))
(sqrt.f64 1/2)
(+.f64 (sqrt.f64 1/2) (.f64 1/4 (/.f64 1 (.f64 (sqrt.f64 1/2) x))))
(-.f64 (+.f64 (sqrt.f64 1/2) (.f64 1/4 (/.f64 1 (.f64 (sqrt.f64 1/2) x)))) (.f64 1/32 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 x 2)))))
(-.f64 (+.f64 (.f64 1/2 (/.f64 (-.f64 (.f64 1/64 (/.f64 1 (pow.f64 (sqrt.f64 1/2) 4))) 1/4) (.f64 (sqrt.f64 1/2) (pow.f64 x 3)))) (+.f64 (sqrt.f64 1/2) (.f64 1/4 (/.f64 1 (.f64 (sqrt.f64 1/2) x))))) (.f64 1/32 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 x 2)))))
(sqrt.f64 1/2)
(-.f64 (sqrt.f64 1/2) (.f64 1/4 (/.f64 1 (.f64 (sqrt.f64 1/2) x))))
(-.f64 (sqrt.f64 1/2) (+.f64 (.f64 1/4 (/.f64 1 (.f64 (sqrt.f64 1/2) x))) (.f64 1/32 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 x 2))))))
(-.f64 (+.f64 (sqrt.f64 1/2) (.f64 -1/2 (/.f64 (-.f64 (.f64 1/64 (/.f64 1 (pow.f64 (sqrt.f64 1/2) 4))) 1/4) (.f64 (sqrt.f64 1/2) (pow.f64 x 3))))) (+.f64 (.f64 1/4 (/.f64 1 (.f64 (sqrt.f64 1/2) x))) (.f64 1/32 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 x 2))))))
1/2
(+.f64 1/2 (*.f64 -1/4 (pow.f64 x 2)))
(+.f64 1/2 (+.f64 (.f64 -1/4 (pow.f64 x 2)) (.f64 3/16 (pow.f64 x 4))))
(+.f64 1/2 (+.f64 (.f64 -1/4 (pow.f64 x 2)) (+.f64 (.f64 -5/32 (pow.f64 x 6)) (*.f64 3/16 (pow.f64 x 4)))))
(/.f64 1/2 x)
(-.f64 (.f64 1/2 (/.f64 1 x)) (.f64 1/4 (/.f64 1 (pow.f64 x 3))))
(-.f64 (+.f64 (.f64 3/16 (/.f64 1 (pow.f64 x 5))) (.f64 1/2 (/.f64 1 x))) (*.f64 1/4 (/.f64 1 (pow.f64 x 3))))
(-.f64 (+.f64 (.f64 3/16 (/.f64 1 (pow.f64 x 5))) (.f64 1/2 (/.f64 1 x))) (+.f64 (.f64 1/4 (/.f64 1 (pow.f64 x 3))) (.f64 5/32 (/.f64 1 (pow.f64 x 7)))))
(/.f64 -1/2 x)
(-.f64 (.f64 1/4 (/.f64 1 (pow.f64 x 3))) (.f64 1/2 (/.f64 1 x)))
(-.f64 (.f64 1/4 (/.f64 1 (pow.f64 x 3))) (+.f64 (.f64 3/16 (/.f64 1 (pow.f64 x 5))) (*.f64 1/2 (/.f64 1 x))))
(-.f64 (+.f64 (.f64 1/4 (/.f64 1 (pow.f64 x 3))) (.f64 5/32 (/.f64 1 (pow.f64 x 7)))) (+.f64 (.f64 3/16 (/.f64 1 (pow.f64 x 5))) (.f64 1/2 (/.f64 1 x))))
1
(+.f64 1 (*.f64 -1/4 (pow.f64 x 2)))
(+.f64 1 (+.f64 (.f64 -1/4 (pow.f64 x 2)) (.f64 3/16 (pow.f64 x 4))))
(+.f64 1 (+.f64 (.f64 -1/4 (pow.f64 x 2)) (+.f64 (.f64 -5/32 (pow.f64 x 6)) (*.f64 3/16 (pow.f64 x 4)))))
1/2
(+.f64 1/2 (*.f64 1/2 (/.f64 1 x)))
(-.f64 (+.f64 (.f64 1/2 (/.f64 1 x)) 1/2) (.f64 1/4 (/.f64 1 (pow.f64 x 3))))
(-.f64 (+.f64 (.f64 1/2 (/.f64 1 x)) (+.f64 1/2 (.f64 3/16 (/.f64 1 (pow.f64 x 5))))) (*.f64 1/4 (/.f64 1 (pow.f64 x 3))))
1/2
(-.f64 1/2 (*.f64 1/2 (/.f64 1 x)))
(-.f64 (+.f64 1/2 (.f64 1/4 (/.f64 1 (pow.f64 x 3)))) (.f64 1/2 (/.f64 1 x)))
(-.f64 (+.f64 1/2 (.f64 1/4 (/.f64 1 (pow.f64 x 3)))) (+.f64 (.f64 1/2 (/.f64 1 x)) (*.f64 3/16 (/.f64 1 (pow.f64 x 5)))))
(+.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 0)
(+.f64 0 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
(+.f64 -1 (neg.f64 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -2)))
(+.f64 (neg.f64 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -2)) -1)
(+.f64 -2 (-.f64 1 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -2)))
(+.f64 (.f64 1/2 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) (.f64 1/2 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))
(*.f64 1 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
(.f64 1/2 (.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 2))
(*.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 1)
(.f64 2 (.f64 1/2 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))
(.f64 (.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 2) 1/2)
(*.f64 4 (/.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 4))
(*.f64 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -1) -1)
(*.f64 -1 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -1))
(.f64 (.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 4) 1/4)
(.f64 1/4 (.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 4))
(.f64 (.f64 1/2 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) 2)
(*.f64 (/.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 4) 4)
(/.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 1)
(/.f64 (*.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 2) 2)
(/.f64 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -1) -1)
(/.f64 (*.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 4) 4)
(/.f64 (*.f64 2 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -1)) -2)
(/.f64 (*.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 8) 8)
(/.f64 (*.f64 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -1) 4) -4)
(/.f64 (.f64 2 (.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 8)) 16)
(/.f64 (neg.f64 (*.f64 2 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -1))) 2)
(/.f64 (.f64 2 (.f64 2 (*.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 8))) 32)
(/.f64 (.f64 2 (neg.f64 (.f64 2 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -1)))) 4)
(pow.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 1)
(neg.f64 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -1))
(+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) 0)
(+.f64 0 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
(+.f64 (.f64 1/2 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) (.f64 1/2 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
(-.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) 0)
(*.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
(.f64 1/2 (.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) 2))
(*.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) 1)
(.f64 2 (.f64 1/2 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
(*.f64 4 (/.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) 4))
(.f64 (.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) 2) 1/2)
(.f64 (.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) 4) 1/4)
(.f64 1/4 (.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) 4))
(.f64 (.f64 1/2 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 2)
(*.f64 (/.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) 4) 4)
(/.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) 1)
(/.f64 (*.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) 2) 2)
(/.f64 (*.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) 4) 4)
(/.f64 (*.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) 8) 8)
(/.f64 (.f64 2 (.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) 8)) 16)
(/.f64 (.f64 2 (.f64 2 (*.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) 8))) 32)
(pow.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) 1)
(+.f64 (/.f64 1/2 (hypot.f64 1 x)) 0)
(+.f64 0 (/.f64 1/2 (hypot.f64 1 x)))
(+.f64 -1 (-.f64 1 (/.f64 -1/2 (hypot.f64 1 x))))
(+.f64 (/.f64 1/4 (hypot.f64 1 x)) (/.f64 1/4 (hypot.f64 1 x)))
(-.f64 (/.f64 1/2 (hypot.f64 1 x)) 0)
(-.f64 0 (/.f64 -1/2 (hypot.f64 1 x)))
(*.f64 1 (/.f64 1/2 (hypot.f64 1 x)))
(*.f64 1/2 (/.f64 1 (hypot.f64 1 x)))
(.f64 (hypot.f64 1 x) (/.f64 1/2 (.f64 (hypot.f64 1 x) (hypot.f64 1 x))))
(*.f64 (/.f64 1/2 (hypot.f64 1 x)) 1)
(.f64 (.f64 (hypot.f64 1 x) 2) (/.f64 1/4 (*.f64 (hypot.f64 1 x) (hypot.f64 1 x))))
(*.f64 2 (/.f64 1/4 (hypot.f64 1 x)))
(.f64 2 (.f64 (/.f64 1/4 (*.f64 (hypot.f64 1 x) (hypot.f64 1 x))) (hypot.f64 1 x)))
(.f64 (.f64 (hypot.f64 1 x) 4) (/.f64 1 (.f64 (hypot.f64 1 x) (.f64 (hypot.f64 1 x) 8))))
(*.f64 (/.f64 1 (hypot.f64 1 x)) 1/2)
(.f64 4 (/.f64 (hypot.f64 1 x) (.f64 (hypot.f64 1 x) (*.f64 (hypot.f64 1 x) 8))))
(*.f64 4 (/.f64 (/.f64 1/2 (hypot.f64 1 x)) 4))
(.f64 (.f64 (/.f64 1/2 (hypot.f64 1 x)) 4) 1/4)
(.f64 1/4 (.f64 (/.f64 1/2 (hypot.f64 1 x)) 4))
(.f64 (/.f64 1/4 (.f64 (hypot.f64 1 x) (hypot.f64 1 x))) (*.f64 (hypot.f64 1 x) 2))
(.f64 (/.f64 1/2 (.f64 (hypot.f64 1 x) (hypot.f64 1 x))) (hypot.f64 1 x))
(*.f64 (/.f64 1/4 (hypot.f64 1 x)) 2)
(.f64 (/.f64 (hypot.f64 1 x) (.f64 (hypot.f64 1 x) (*.f64 (hypot.f64 1 x) 8))) 4)
(*.f64 (/.f64 -1/2 (hypot.f64 1 x)) -1)
(.f64 (/.f64 1 (.f64 (hypot.f64 1 x) (.f64 (hypot.f64 1 x) 8))) (.f64 (hypot.f64 1 x) 4))
(*.f64 (/.f64 (/.f64 1/2 (hypot.f64 1 x)) 4) 4)
(pow.f64 (/.f64 1/2 (hypot.f64 1 x)) 1)
(neg.f64 (/.f64 -1/2 (hypot.f64 1 x)))
(-.f64 (/.f64 1/2 (hypot.f64 1 x)) -1/2)
(-.f64 (/.f64 1/2 (hypot.f64 1 x)) (neg.f64 (/.f64 (hypot.f64 1 x) (*.f64 (hypot.f64 1 x) 2))))
(-.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 0)
(*.f64 1 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
(*.f64 1/2 (+.f64 1 (/.f64 1 (hypot.f64 1 x))))
(*.f64 (/.f64 1/2 (hypot.f64 1 x)) (+.f64 1 (hypot.f64 1 x)))
(*.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 1)
(*.f64 (+.f64 1 (hypot.f64 1 x)) (/.f64 1/2 (hypot.f64 1 x)))
(*.f64 2 (+.f64 1/4 (/.f64 1/4 (hypot.f64 1 x))))
(.f64 (/.f64 1 (hypot.f64 1 x)) (.f64 1/2 (+.f64 1 (hypot.f64 1 x))))
(*.f64 4 (/.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 4))
(*.f64 (+.f64 1 (/.f64 1 (hypot.f64 1 x))) 1/2)
(.f64 (.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 4) 1/4)
(.f64 (.f64 (+.f64 1 (hypot.f64 1 x)) 2) (/.f64 1/4 (hypot.f64 1 x)))
(.f64 (.f64 1/2 (+.f64 1 (hypot.f64 1 x))) (/.f64 1 (hypot.f64 1 x)))
(.f64 1/4 (.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 4))
(.f64 (/.f64 1/4 (hypot.f64 1 x)) (.f64 (+.f64 1 (hypot.f64 1 x)) 2))
(*.f64 (+.f64 1/4 (/.f64 1/4 (hypot.f64 1 x))) 2)
(*.f64 (/.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 4) 4)
(/.f64 1 (/.f64 1 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
(/.f64 1/2 (/.f64 (hypot.f64 1 x) (+.f64 1 (hypot.f64 1 x))))
(/.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 1)
(/.f64 (+.f64 1 (hypot.f64 1 x)) (*.f64 (hypot.f64 1 x) 2))
(/.f64 (+.f64 1 (hypot.f64 1 x)) (/.f64 (.f64 (hypot.f64 1 x) (.f64 (hypot.f64 1 x) 2)) (hypot.f64 1 x)))
(/.f64 2 (/.f64 2 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
(/.f64 4 (*.f64 2 (/.f64 2 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
(/.f64 4 (/.f64 (*.f64 (hypot.f64 1 x) 8) (+.f64 1 (hypot.f64 1 x))))
(/.f64 (+.f64 1 (/.f64 1 (hypot.f64 1 x))) 2)
(/.f64 -1/2 (neg.f64 (/.f64 (hypot.f64 1 x) (+.f64 1 (hypot.f64 1 x)))))
(/.f64 -1 (neg.f64 (/.f64 1 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
(/.f64 8 (/.f64 (.f64 (hypot.f64 1 x) 8) (.f64 1/2 (+.f64 1 (hypot.f64 1 x)))))
(/.f64 8 (.f64 2 (/.f64 (.f64 (hypot.f64 1 x) 8) (+.f64 1 (hypot.f64 1 x)))))
(/.f64 8 (.f64 2 (.f64 2 (/.f64 2 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))
(/.f64 (*.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 4) 4)
(/.f64 (.f64 (+.f64 1 (hypot.f64 1 x)) 2) (.f64 (hypot.f64 1 x) 4))
(/.f64 16 (.f64 2 (/.f64 (.f64 (hypot.f64 1 x) 8) (*.f64 1/2 (+.f64 1 (hypot.f64 1 x))))))
(/.f64 (*.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 8) 8)
(/.f64 -2 (neg.f64 (/.f64 2 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
(/.f64 (.f64 (+.f64 1 (hypot.f64 1 x)) 4) (.f64 (hypot.f64 1 x) 8))
(/.f64 (*.f64 1/2 (+.f64 1 (hypot.f64 1 x))) (hypot.f64 1 x))
(/.f64 (.f64 1/2 (+.f64 1 (hypot.f64 1 x))) (/.f64 (.f64 (hypot.f64 1 x) (.f64 (hypot.f64 1 x) 4)) (.f64 (hypot.f64 1 x) 4)))
(/.f64 1/4 (/.f64 (hypot.f64 1 x) (*.f64 (+.f64 1 (hypot.f64 1 x)) 2)))
(/.f64 (+.f64 1/4 (/.f64 1/4 (hypot.f64 1 x))) 1/2)
(/.f64 (-.f64 -1 (hypot.f64 1 x)) (*.f64 (hypot.f64 1 x) -2))
(/.f64 (-.f64 -1 (hypot.f64 1 x)) (-.f64 0 (/.f64 (.f64 (hypot.f64 1 x) (.f64 (hypot.f64 1 x) 2)) (hypot.f64 1 x))))
(/.f64 -4 (-.f64 0 (*.f64 2 (/.f64 2 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))
(/.f64 -4 (-.f64 0 (/.f64 (*.f64 (hypot.f64 1 x) 8) (+.f64 1 (hypot.f64 1 x)))))
(/.f64 (.f64 2 (.f64 (+.f64 1 (hypot.f64 1 x)) 4)) (.f64 2 (.f64 (hypot.f64 1 x) 8)))
(/.f64 (.f64 2 (/.f64 2 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) (.f64 (/.f64 2 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) (/.f64 2 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
(/.f64 (.f64 2 (.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 8)) 16)
(/.f64 (.f64 2 (-.f64 -1 (hypot.f64 1 x))) (.f64 (neg.f64 (hypot.f64 1 x)) 4))
(/.f64 (/.f64 (+.f64 1 (hypot.f64 1 x)) 4) (*.f64 1/2 (hypot.f64 1 x)))
(/.f64 -1/4 (-.f64 0 (/.f64 (hypot.f64 1 x) (*.f64 (+.f64 1 (hypot.f64 1 x)) 2))))
(/.f64 (/.f64 (+.f64 1 (hypot.f64 1 x)) (*.f64 (hypot.f64 1 x) 8)) 1/4)
(/.f64 -8 (-.f64 0 (/.f64 (.f64 (hypot.f64 1 x) 8) (.f64 1/2 (+.f64 1 (hypot.f64 1 x))))))
(/.f64 (neg.f64 (.f64 (+.f64 1 (hypot.f64 1 x)) 2)) (neg.f64 (.f64 (hypot.f64 1 x) 4)))
(/.f64 (neg.f64 (*.f64 1/2 (+.f64 1 (hypot.f64 1 x)))) (neg.f64 (hypot.f64 1 x)))
(/.f64 (neg.f64 (.f64 1/2 (+.f64 1 (hypot.f64 1 x)))) (-.f64 0 (/.f64 (.f64 (hypot.f64 1 x) (.f64 (hypot.f64 1 x) 4)) (.f64 (hypot.f64 1 x) 4))))
(/.f64 (.f64 2 (neg.f64 (.f64 (+.f64 1 (hypot.f64 1 x)) 2))) (.f64 2 (neg.f64 (.f64 (hypot.f64 1 x) 4))))
(/.f64 (*.f64 2 (/.f64 (+.f64 1 (hypot.f64 1 x)) 4)) (hypot.f64 1 x))
(/.f64 (.f64 2 (.f64 2 (*.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 8))) 32)
(/.f64 (.f64 2 (.f64 2 (-.f64 -1 (hypot.f64 1 x)))) (.f64 2 (.f64 (neg.f64 (hypot.f64 1 x)) 4)))
(/.f64 (.f64 2 (/.f64 (+.f64 1 (hypot.f64 1 x)) (.f64 (hypot.f64 1 x) 8))) 1/2)
(/.f64 (.f64 2 (neg.f64 (.f64 1/2 (+.f64 1 (hypot.f64 1 x))))) (*.f64 (hypot.f64 1 x) -2))
(/.f64 (neg.f64 (.f64 (+.f64 1 (hypot.f64 1 x)) 4)) (neg.f64 (.f64 (hypot.f64 1 x) 8)))
(/.f64 (neg.f64 (neg.f64 (.f64 (+.f64 1 (hypot.f64 1 x)) 2))) (.f64 (hypot.f64 1 x) 4))
(/.f64 (neg.f64 (/.f64 (+.f64 1 (hypot.f64 1 x)) 4)) (/.f64 (hypot.f64 1 x) -2))
(/.f64 (neg.f64 (.f64 2 (-.f64 -1 (hypot.f64 1 x)))) (/.f64 (.f64 (hypot.f64 1 x) -2) -1/2))
(/.f64 (neg.f64 (neg.f64 (*.f64 1/2 (+.f64 1 (hypot.f64 1 x))))) (hypot.f64 1 x))
(/.f64 (neg.f64 (.f64 2 (.f64 (+.f64 1 (hypot.f64 1 x)) 4))) (neg.f64 (.f64 2 (.f64 (hypot.f64 1 x) 8))))
(/.f64 (neg.f64 (neg.f64 (.f64 (+.f64 1 (hypot.f64 1 x)) 4))) (.f64 (hypot.f64 1 x) 8))
(/.f64 (neg.f64 (neg.f64 (.f64 (+.f64 1 (hypot.f64 1 x)) 4))) (-.f64 0 (neg.f64 (.f64 (hypot.f64 1 x) 8))))
(/.f64 (neg.f64 (.f64 2 (neg.f64 (.f64 (+.f64 1 (hypot.f64 1 x)) 2)))) (-.f64 0 (.f64 2 (neg.f64 (.f64 (hypot.f64 1 x) 4)))))
(/.f64 (neg.f64 (neg.f64 (neg.f64 (.f64 (+.f64 1 (hypot.f64 1 x)) 2)))) (neg.f64 (.f64 (hypot.f64 1 x) 4)))
(/.f64 (neg.f64 (*.f64 2 (/.f64 (+.f64 1 (hypot.f64 1 x)) 4))) (neg.f64 (hypot.f64 1 x)))
(/.f64 (neg.f64 (neg.f64 (/.f64 (+.f64 1 (hypot.f64 1 x)) 4))) (*.f64 1/2 (hypot.f64 1 x)))
(/.f64 (neg.f64 (.f64 2 (.f64 2 (-.f64 -1 (hypot.f64 1 x))))) (-.f64 0 (.f64 2 (.f64 (neg.f64 (hypot.f64 1 x)) 4))))
(/.f64 (neg.f64 (.f64 2 (neg.f64 (.f64 1/2 (+.f64 1 (hypot.f64 1 x)))))) (*.f64 (hypot.f64 1 x) 2))
(/.f64 (neg.f64 (neg.f64 (.f64 2 (-.f64 -1 (hypot.f64 1 x))))) (.f64 (neg.f64 (hypot.f64 1 x)) 4))
(/.f64 (neg.f64 (neg.f64 (neg.f64 (*.f64 1/2 (+.f64 1 (hypot.f64 1 x)))))) (neg.f64 (hypot.f64 1 x)))
(pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 1)

Outputs
(*.f64 1/8 (pow.f64 x 2))
(+.f64 (.f64 1/8 (pow.f64 x 2)) (.f64 -11/128 (pow.f64 x 4)))
(+.f64 (.f64 1/8 (pow.f64 x 2)) (+.f64 (.f64 69/1024 (pow.f64 x 6)) (*.f64 -11/128 (pow.f64 x 4))))
(+.f64 (.f64 1/8 (pow.f64 x 2)) (+.f64 (.f64 -11/128 (pow.f64 x 4)) (*.f64 69/1024 (pow.f64 x 6))))
(+.f64 (.f64 -11/128 (pow.f64 x 4)) (+.f64 (.f64 1/8 (pow.f64 x 2)) (*.f64 69/1024 (pow.f64 x 6))))
(+.f64 (.f64 1/8 (pow.f64 x 2)) (+.f64 (.f64 69/1024 (pow.f64 x 6)) (+.f64 (.f64 -1843/32768 (pow.f64 x 8)) (.f64 -11/128 (pow.f64 x 4)))))
(+.f64 (.f64 69/1024 (pow.f64 x 6)) (+.f64 (+.f64 (.f64 -11/128 (pow.f64 x 4)) (.f64 -1843/32768 (pow.f64 x 8))) (.f64 1/8 (pow.f64 x 2))))
(+.f64 (.f64 1/8 (pow.f64 x 2)) (+.f64 (.f64 -11/128 (pow.f64 x 4)) (+.f64 (.f64 -1843/32768 (pow.f64 x 8)) (.f64 69/1024 (pow.f64 x 6)))))
(+.f64 (.f64 69/1024 (pow.f64 x 6)) (+.f64 (.f64 -11/128 (pow.f64 x 4)) (+.f64 (.f64 -1843/32768 (pow.f64 x 8)) (.f64 1/8 (pow.f64 x 2)))))
(+.f64 (.f64 69/1024 (pow.f64 x 6)) (+.f64 (.f64 -11/128 (pow.f64 x 4)) (+.f64 (.f64 1/8 (pow.f64 x 2)) (.f64 -1843/32768 (pow.f64 x 8)))))
(-.f64 1 (sqrt.f64 1/2))
(-.f64 1 (+.f64 (sqrt.f64 1/2) (.f64 1/4 (/.f64 1 (.f64 (sqrt.f64 1/2) x)))))
(-.f64 1 (+.f64 (sqrt.f64 1/2) (.f64 1/4 (/.f64 1 (.f64 x (sqrt.f64 1/2))))))
(-.f64 1 (+.f64 (sqrt.f64 1/2) (*.f64 1/4 (/.f64 (/.f64 1 x) (sqrt.f64 1/2)))))
(-.f64 (+.f64 1 (.f64 1/32 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 x 2))))) (+.f64 (sqrt.f64 1/2) (.f64 1/4 (/.f64 1 (.f64 (sqrt.f64 1/2) x)))))
(+.f64 (.f64 1/32 (/.f64 1 (.f64 (pow.f64 x 2) (sqrt.f64 1/8)))) (-.f64 1 (+.f64 (sqrt.f64 1/2) (.f64 1/4 (/.f64 1 (.f64 x (sqrt.f64 1/2)))))))
(+.f64 (-.f64 1 (+.f64 (sqrt.f64 1/2) (.f64 1/4 (/.f64 (/.f64 1 x) (sqrt.f64 1/2))))) (.f64 1/32 (/.f64 (/.f64 1 (sqrt.f64 1/8)) (pow.f64 x 2))))
(-.f64 (+.f64 1 (+.f64 (.f64 1/32 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 x 2)))) (.f64 -1/2 (/.f64 (-.f64 (.f64 1/64 (/.f64 1 (pow.f64 (sqrt.f64 1/2) 4))) 1/4) (.f64 (sqrt.f64 1/2) (pow.f64 x 3)))))) (+.f64 (sqrt.f64 1/2) (.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x)))))
(+.f64 (+.f64 (.f64 1/32 (/.f64 1 (.f64 (pow.f64 x 2) (sqrt.f64 1/8)))) (.f64 -1/2 (/.f64 -3/16 (.f64 (sqrt.f64 1/2) (pow.f64 x 3))))) (-.f64 1 (+.f64 (sqrt.f64 1/2) (.f64 1/4 (/.f64 1 (.f64 x (sqrt.f64 1/2)))))))
(+.f64 1 (-.f64 (+.f64 (.f64 1/32 (/.f64 (/.f64 1 (sqrt.f64 1/8)) (pow.f64 x 2))) (.f64 -1/2 (/.f64 -3/16 (.f64 (sqrt.f64 1/2) (pow.f64 x 3))))) (+.f64 (sqrt.f64 1/2) (.f64 1/4 (/.f64 (/.f64 1 x) (sqrt.f64 1/2))))))
(-.f64 1 (sqrt.f64 1/2))
(-.f64 (+.f64 1 (.f64 1/4 (/.f64 1 (.f64 (sqrt.f64 1/2) x)))) (sqrt.f64 1/2))
(+.f64 (.f64 1/4 (/.f64 1 (.f64 x (sqrt.f64 1/2)))) (-.f64 1 (sqrt.f64 1/2)))
(+.f64 (-.f64 1 (sqrt.f64 1/2)) (*.f64 1/4 (/.f64 (/.f64 1 x) (sqrt.f64 1/2))))
(-.f64 (+.f64 1 (+.f64 (.f64 1/4 (/.f64 1 (.f64 (sqrt.f64 1/2) x))) (.f64 1/32 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 x 2)))))) (sqrt.f64 1/2))
(+.f64 (+.f64 (.f64 1/4 (/.f64 1 (.f64 x (sqrt.f64 1/2)))) (.f64 1/32 (/.f64 1 (.f64 (pow.f64 x 2) (sqrt.f64 1/8))))) (-.f64 1 (sqrt.f64 1/2)))
(+.f64 (+.f64 1 (.f64 1/32 (/.f64 (/.f64 1 (sqrt.f64 1/8)) (pow.f64 x 2)))) (-.f64 (.f64 1/4 (/.f64 (/.f64 1 x) (sqrt.f64 1/2))) (sqrt.f64 1/2)))
(+.f64 (.f64 1/32 (/.f64 (/.f64 1 (sqrt.f64 1/8)) (pow.f64 x 2))) (+.f64 (-.f64 1 (sqrt.f64 1/2)) (.f64 1/4 (/.f64 (/.f64 1 x) (sqrt.f64 1/2)))))
(-.f64 (+.f64 (.f64 1/2 (/.f64 (-.f64 (.f64 1/64 (/.f64 1 (pow.f64 (sqrt.f64 1/2) 4))) 1/4) (.f64 (sqrt.f64 1/2) (pow.f64 x 3)))) (+.f64 1 (+.f64 (.f64 1/4 (/.f64 1 (.f64 (sqrt.f64 1/2) x))) (.f64 1/32 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 x 2))))))) (sqrt.f64 1/2))
(+.f64 (+.f64 1 (+.f64 (.f64 1/4 (/.f64 1 (.f64 x (sqrt.f64 1/2)))) (.f64 1/32 (/.f64 1 (.f64 (pow.f64 x 2) (sqrt.f64 1/8)))))) (-.f64 (.f64 1/2 (/.f64 -3/16 (.f64 (sqrt.f64 1/2) (pow.f64 x 3)))) (sqrt.f64 1/2)))
(+.f64 (+.f64 1 (+.f64 (.f64 1/4 (/.f64 (/.f64 1 x) (sqrt.f64 1/2))) (.f64 1/32 (/.f64 (/.f64 1 (sqrt.f64 1/8)) (pow.f64 x 2))))) (-.f64 (.f64 1/2 (/.f64 -3/16 (.f64 (sqrt.f64 1/2) (pow.f64 x 3)))) (sqrt.f64 1/2)))
(+.f64 (+.f64 1 (.f64 1/32 (/.f64 (/.f64 1 (sqrt.f64 1/8)) (pow.f64 x 2)))) (+.f64 (-.f64 (.f64 1/4 (/.f64 (/.f64 1 x) (sqrt.f64 1/2))) (sqrt.f64 1/2)) (.f64 1/2 (/.f64 -3/16 (.f64 (sqrt.f64 1/2) (pow.f64 x 3))))))
(+.f64 (+.f64 1 (.f64 1/32 (/.f64 (/.f64 1 (sqrt.f64 1/8)) (pow.f64 x 2)))) (+.f64 (.f64 1/2 (/.f64 -3/16 (.f64 (sqrt.f64 1/2) (pow.f64 x 3)))) (-.f64 (.f64 1/4 (/.f64 (/.f64 1 x) (sqrt.f64 1/2))) (sqrt.f64 1/2))))
1
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) 1)
(+.f64 1 (*.f64 (pow.f64 x 2) -1/8))
(+.f64 (.f64 -1/8 (pow.f64 x 2)) (+.f64 1 (.f64 11/128 (pow.f64 x 4))))
(+.f64 1 (+.f64 (.f64 (pow.f64 x 4) 11/128) (.f64 (pow.f64 x 2) -1/8)))
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(+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))
(/.f64 (neg.f64 (.f64 1/2 (+.f64 1 (hypot.f64 1 x)))) (-.f64 0 (/.f64 (.f64 (hypot.f64 1 x) (.f64 (hypot.f64 1 x) 4)) (.f64 (hypot.f64 1 x) 4))))
(/.f64 (.f64 1/2 (+.f64 1 (hypot.f64 1 x))) (.f64 (.f64 4 (hypot.f64 1 x)) (/.f64 (hypot.f64 1 x) (.f64 4 (hypot.f64 1 x)))))
(/.f64 (.f64 1/4 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) (/.f64 (hypot.f64 1 x) (.f64 4 (hypot.f64 1 x))))
(/.f64 (+.f64 1/8 (/.f64 1/8 (hypot.f64 1 x))) (/.f64 (hypot.f64 1 x) (*.f64 4 (hypot.f64 1 x))))
(/.f64 (.f64 2 (neg.f64 (.f64 (+.f64 1 (hypot.f64 1 x)) 2))) (.f64 2 (neg.f64 (.f64 (hypot.f64 1 x) 4))))
(-.f64 (/.f64 1/2 (hypot.f64 1 x)) -1/2)
(+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))
(/.f64 (*.f64 2 (/.f64 (+.f64 1 (hypot.f64 1 x)) 4)) (hypot.f64 1 x))
(-.f64 (/.f64 1/2 (hypot.f64 1 x)) -1/2)
(+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))
(/.f64 (.f64 2 (.f64 2 (*.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 8))) 32)
(-.f64 (/.f64 1/2 (hypot.f64 1 x)) -1/2)
(+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))
(/.f64 (.f64 2 (.f64 2 (-.f64 -1 (hypot.f64 1 x)))) (.f64 2 (.f64 (neg.f64 (hypot.f64 1 x)) 4)))
(-.f64 (/.f64 1/2 (hypot.f64 1 x)) -1/2)
(+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))
(/.f64 (.f64 2 (/.f64 (+.f64 1 (hypot.f64 1 x)) (.f64 (hypot.f64 1 x) 8))) 1/2)
(-.f64 (/.f64 1/2 (hypot.f64 1 x)) -1/2)
(+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))
(/.f64 (.f64 2 (neg.f64 (.f64 1/2 (+.f64 1 (hypot.f64 1 x))))) (*.f64 (hypot.f64 1 x) -2))
(-.f64 (/.f64 1/2 (hypot.f64 1 x)) -1/2)
(+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))
(/.f64 (neg.f64 (.f64 (+.f64 1 (hypot.f64 1 x)) 4)) (neg.f64 (.f64 (hypot.f64 1 x) 8)))
(-.f64 (/.f64 1/2 (hypot.f64 1 x)) -1/2)
(+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))
(/.f64 (neg.f64 (neg.f64 (.f64 (+.f64 1 (hypot.f64 1 x)) 2))) (.f64 (hypot.f64 1 x) 4))
(-.f64 (/.f64 1/2 (hypot.f64 1 x)) -1/2)
(+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))
(/.f64 (neg.f64 (/.f64 (+.f64 1 (hypot.f64 1 x)) 4)) (/.f64 (hypot.f64 1 x) -2))
(-.f64 (/.f64 1/2 (hypot.f64 1 x)) -1/2)
(+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))
(/.f64 (neg.f64 (.f64 2 (-.f64 -1 (hypot.f64 1 x)))) (/.f64 (.f64 (hypot.f64 1 x) -2) -1/2))
(-.f64 (/.f64 1/2 (hypot.f64 1 x)) -1/2)
(+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))
(/.f64 (neg.f64 (neg.f64 (*.f64 1/2 (+.f64 1 (hypot.f64 1 x))))) (hypot.f64 1 x))
(-.f64 (/.f64 1/2 (hypot.f64 1 x)) -1/2)
(+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))
(/.f64 (neg.f64 (.f64 2 (.f64 (+.f64 1 (hypot.f64 1 x)) 4))) (neg.f64 (.f64 2 (.f64 (hypot.f64 1 x) 8))))
(-.f64 (/.f64 1/2 (hypot.f64 1 x)) -1/2)
(+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))
(/.f64 (neg.f64 (neg.f64 (.f64 (+.f64 1 (hypot.f64 1 x)) 4))) (.f64 (hypot.f64 1 x) 8))
(-.f64 (/.f64 1/2 (hypot.f64 1 x)) -1/2)
(+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))
(/.f64 (neg.f64 (neg.f64 (.f64 (+.f64 1 (hypot.f64 1 x)) 4))) (-.f64 0 (neg.f64 (.f64 (hypot.f64 1 x) 8))))
(-.f64 (/.f64 1/2 (hypot.f64 1 x)) -1/2)
(+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))
(/.f64 (neg.f64 (.f64 2 (neg.f64 (.f64 (+.f64 1 (hypot.f64 1 x)) 2)))) (-.f64 0 (.f64 2 (neg.f64 (.f64 (hypot.f64 1 x) 4)))))
(-.f64 (/.f64 1/2 (hypot.f64 1 x)) -1/2)
(+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))
(/.f64 (neg.f64 (neg.f64 (neg.f64 (.f64 (+.f64 1 (hypot.f64 1 x)) 2)))) (neg.f64 (.f64 (hypot.f64 1 x) 4)))
(-.f64 (/.f64 1/2 (hypot.f64 1 x)) -1/2)
(+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))
(/.f64 (neg.f64 (*.f64 2 (/.f64 (+.f64 1 (hypot.f64 1 x)) 4))) (neg.f64 (hypot.f64 1 x)))
(-.f64 (/.f64 1/2 (hypot.f64 1 x)) -1/2)
(+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))
(/.f64 (neg.f64 (neg.f64 (/.f64 (+.f64 1 (hypot.f64 1 x)) 4))) (*.f64 1/2 (hypot.f64 1 x)))
(-.f64 (/.f64 1/2 (hypot.f64 1 x)) -1/2)
(+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))
(/.f64 (neg.f64 (.f64 2 (.f64 2 (-.f64 -1 (hypot.f64 1 x))))) (-.f64 0 (.f64 2 (.f64 (neg.f64 (hypot.f64 1 x)) 4))))
(-.f64 (/.f64 1/2 (hypot.f64 1 x)) -1/2)
(+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))
(/.f64 (neg.f64 (.f64 2 (neg.f64 (.f64 1/2 (+.f64 1 (hypot.f64 1 x)))))) (*.f64 (hypot.f64 1 x) 2))
(-.f64 (/.f64 1/2 (hypot.f64 1 x)) -1/2)
(+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))
(/.f64 (neg.f64 (neg.f64 (.f64 2 (-.f64 -1 (hypot.f64 1 x))))) (.f64 (neg.f64 (hypot.f64 1 x)) 4))
(-.f64 (/.f64 1/2 (hypot.f64 1 x)) -1/2)
(+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))
(/.f64 (neg.f64 (neg.f64 (neg.f64 (*.f64 1/2 (+.f64 1 (hypot.f64 1 x)))))) (neg.f64 (hypot.f64 1 x)))
(-.f64 (/.f64 1/2 (hypot.f64 1 x)) -1/2)
(+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))
(pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 1)
(-.f64 (/.f64 1/2 (hypot.f64 1 x)) -1/2)
(+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))

localize4.0ms (0%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	1.0b	(-.f64 1 (sqrt.f64 1/2))

Compiler

Compiled 9 to 9 computations (0% saved)

series0.0ms (0%)

Counts: 1 → 0

rewrite238.0ms (2.1%)

Algorithm

1×	batch-egg-rewrite

Rules

2242×	`rational.json-simplify-2`
1804×	`rational.json-simplify-35`
1228×	`exponential.json-3`
1228×	`rational.json-1`
1228×	`rational.json-2`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	11
1	53	11
2	117	11
3	210	11
4	364	11
5	755	11
6	1835	11
7	3084	11
8	3833	11
9	4822	11
10	5887	11
11	6578	11
12	6788	11
13	7015	11
14	7904	11

Stop Event

1×	node limit

Counts

1 → 51

Calls

Call 1

Inputs
(-.f64 1 (sqrt.f64 1/2))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 1 (sqrt.f64 1/2)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (-.f64 1 (sqrt.f64 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 -1 (neg.f64 (+.f64 (sqrt.f64 1/2) -2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (neg.f64 (+.f64 (sqrt.f64 1/2) -2)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 1/2 (-.f64 1 (sqrt.f64 1/2))) (*.f64 1/2 (-.f64 1 (sqrt.f64 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 -2 (neg.f64 (+.f64 (sqrt.f64 1/2) -3)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (neg.f64 (+.f64 (sqrt.f64 1/2) -3)) -2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (-.f64 1 (sqrt.f64 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/2 (*.f64 (+.f64 (sqrt.f64 1/2) -1) -2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 1 (sqrt.f64 1/2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 2 (*.f64 1/2 (-.f64 1 (sqrt.f64 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 4 (*.f64 (-.f64 1 (sqrt.f64 1/2)) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (+.f64 (sqrt.f64 1/2) -1) -2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (sqrt.f64 1/2) -1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -1 (+.f64 (sqrt.f64 1/2) -1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (-.f64 1 (sqrt.f64 1/2)) 4) 1/4)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (*.f64 (sqrt.f64 1/2) 2) -2) -1/2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (-.f64 1 (sqrt.f64 1/2)) 8) 1/8)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/4 (*.f64 (-.f64 1 (sqrt.f64 1/2)) 4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 1/2 (-.f64 1 (sqrt.f64 1/2))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -2 (*.f64 1/2 (+.f64 (sqrt.f64 1/2) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 1/2 (+.f64 (sqrt.f64 1/2) -1)) -2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (-.f64 1 (sqrt.f64 1/2)) 1/4) 4)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/8 (*.f64 (-.f64 1 (sqrt.f64 1/2)) 8))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -1/2 (+.f64 (*.f64 (sqrt.f64 1/2) 2) -2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (+.f64 (sqrt.f64 1/2) -3) -2) -1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1 (sqrt.f64 1/2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (+.f64 (sqrt.f64 1/2) -1) -2) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (sqrt.f64 1/2) -1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (-.f64 1 (sqrt.f64 1/2)) 4) 4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (*.f64 (sqrt.f64 1/2) 2) -2) -2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (-.f64 1 (sqrt.f64 1/2)) 8) 8)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 4 (+.f64 (sqrt.f64 1/2) -1)) -4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 (-.f64 1 (sqrt.f64 1/2)) 8)) 16)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 4 (+.f64 (sqrt.f64 1/2) -1))) -8)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 2 (*.f64 (-.f64 1 (sqrt.f64 1/2)) 8))) 32)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 2 (*.f64 4 (+.f64 (sqrt.f64 1/2) -1)))) -16)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 (-.f64 1 (sqrt.f64 1/2)) 8)))) 64)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (*.f64 2 (*.f64 4 (+.f64 (sqrt.f64 1/2) -1)))) 8)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 4 (+.f64 (sqrt.f64 1/2) -1))))) -32)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 (-.f64 1 (sqrt.f64 1/2)) 8))))) 128)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (neg.f64 (*.f64 2 (*.f64 4 (+.f64 (sqrt.f64 1/2) -1))))) 16)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 4 (+.f64 (sqrt.f64 1/2) -1)))))) -64)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 (-.f64 1 (sqrt.f64 1/2)) 8)))))) 256)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 2 (neg.f64 (*.f64 2 (*.f64 4 (+.f64 (sqrt.f64 1/2) -1)))))) 32)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 (-.f64 1 (sqrt.f64 1/2)) 8))))))) 512)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 2 (*.f64 2 (neg.f64 (*.f64 2 (*.f64 4 (+.f64 (sqrt.f64 1/2) -1))))))) 64)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (+.f64 (sqrt.f64 1/2) -3) -2) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (-.f64 1 (sqrt.f64 1/2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (+.f64 (sqrt.f64 1/2) -1))))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (-.f64 (+.f64 (sqrt.f64 1/2) -3) -2))))))

simplify206.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

2364×	`rational.json-simplify-35`
1532×	`rational.json-simplify-2`
1110×	`rational.json-simplify-45`
956×	`rational.json-simplify-1`
766×	`rational.json-simplify-44`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	108	597
1	260	597
2	597	597
3	1740	597
4	3830	597
5	5027	597
6	5476	597
7	5793	597
8	6124	597
9	6361	597
10	6821	597
11	7943	597

Stop Event

1×	node limit

Counts

51 → 54

Calls

Call 1

Inputs
(+.f64 (-.f64 1 (sqrt.f64 1/2)) 0)
(+.f64 0 (-.f64 1 (sqrt.f64 1/2)))
(+.f64 -1 (neg.f64 (+.f64 (sqrt.f64 1/2) -2)))
(+.f64 (neg.f64 (+.f64 (sqrt.f64 1/2) -2)) -1)
(+.f64 (.f64 1/2 (-.f64 1 (sqrt.f64 1/2))) (.f64 1/2 (-.f64 1 (sqrt.f64 1/2))))
(+.f64 -2 (neg.f64 (+.f64 (sqrt.f64 1/2) -3)))
(+.f64 (neg.f64 (+.f64 (sqrt.f64 1/2) -3)) -2)
(*.f64 1 (-.f64 1 (sqrt.f64 1/2)))
(.f64 1/2 (.f64 (+.f64 (sqrt.f64 1/2) -1) -2))
(*.f64 (-.f64 1 (sqrt.f64 1/2)) 1)
(.f64 2 (.f64 1/2 (-.f64 1 (sqrt.f64 1/2))))
(.f64 4 (.f64 (-.f64 1 (sqrt.f64 1/2)) 1/4))
(.f64 (.f64 (+.f64 (sqrt.f64 1/2) -1) -2) 1/2)
(*.f64 (+.f64 (sqrt.f64 1/2) -1) -1)
(*.f64 -1 (+.f64 (sqrt.f64 1/2) -1))
(.f64 (.f64 (-.f64 1 (sqrt.f64 1/2)) 4) 1/4)
(.f64 (+.f64 (.f64 (sqrt.f64 1/2) 2) -2) -1/2)
(.f64 (.f64 (-.f64 1 (sqrt.f64 1/2)) 8) 1/8)
(.f64 1/4 (.f64 (-.f64 1 (sqrt.f64 1/2)) 4))
(.f64 (.f64 1/2 (-.f64 1 (sqrt.f64 1/2))) 2)
(.f64 -2 (.f64 1/2 (+.f64 (sqrt.f64 1/2) -1)))
(.f64 (.f64 1/2 (+.f64 (sqrt.f64 1/2) -1)) -2)
(.f64 (.f64 (-.f64 1 (sqrt.f64 1/2)) 1/4) 4)
(.f64 1/8 (.f64 (-.f64 1 (sqrt.f64 1/2)) 8))
(.f64 -1/2 (+.f64 (.f64 (sqrt.f64 1/2) 2) -2))
(*.f64 (-.f64 (+.f64 (sqrt.f64 1/2) -3) -2) -1)
(/.f64 (-.f64 1 (sqrt.f64 1/2)) 1)
(/.f64 (*.f64 (+.f64 (sqrt.f64 1/2) -1) -2) 2)
(/.f64 (+.f64 (sqrt.f64 1/2) -1) -1)
(/.f64 (*.f64 (-.f64 1 (sqrt.f64 1/2)) 4) 4)
(/.f64 (+.f64 (*.f64 (sqrt.f64 1/2) 2) -2) -2)
(/.f64 (*.f64 (-.f64 1 (sqrt.f64 1/2)) 8) 8)
(/.f64 (*.f64 4 (+.f64 (sqrt.f64 1/2) -1)) -4)
(/.f64 (.f64 2 (.f64 (-.f64 1 (sqrt.f64 1/2)) 8)) 16)
(/.f64 (.f64 2 (.f64 4 (+.f64 (sqrt.f64 1/2) -1))) -8)
(/.f64 (.f64 2 (.f64 2 (*.f64 (-.f64 1 (sqrt.f64 1/2)) 8))) 32)
(/.f64 (.f64 2 (.f64 2 (*.f64 4 (+.f64 (sqrt.f64 1/2) -1)))) -16)
(/.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 (-.f64 1 (sqrt.f64 1/2)) 8)))) 64)
(/.f64 (neg.f64 (.f64 2 (.f64 4 (+.f64 (sqrt.f64 1/2) -1)))) 8)
(/.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 4 (+.f64 (sqrt.f64 1/2) -1))))) -32)
(/.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (*.f64 (-.f64 1 (sqrt.f64 1/2)) 8))))) 128)
(/.f64 (.f64 2 (neg.f64 (.f64 2 (*.f64 4 (+.f64 (sqrt.f64 1/2) -1))))) 16)
(/.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (*.f64 4 (+.f64 (sqrt.f64 1/2) -1)))))) -64)
(/.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 (-.f64 1 (sqrt.f64 1/2)) 8)))))) 256)
(/.f64 (.f64 2 (.f64 2 (neg.f64 (.f64 2 (.f64 4 (+.f64 (sqrt.f64 1/2) -1)))))) 32)
(/.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (*.f64 (-.f64 1 (sqrt.f64 1/2)) 8))))))) 512)
(/.f64 (.f64 2 (.f64 2 (.f64 2 (neg.f64 (.f64 2 (*.f64 4 (+.f64 (sqrt.f64 1/2) -1))))))) 64)
(/.f64 (-.f64 (+.f64 (sqrt.f64 1/2) -3) -2) -1)
(pow.f64 (-.f64 1 (sqrt.f64 1/2)) 1)
(neg.f64 (+.f64 (sqrt.f64 1/2) -1))
(neg.f64 (-.f64 (+.f64 (sqrt.f64 1/2) -3) -2))

Outputs
(+.f64 (-.f64 1 (sqrt.f64 1/2)) 0)
(-.f64 1 (sqrt.f64 1/2))
(+.f64 0 (-.f64 1 (sqrt.f64 1/2)))
(-.f64 1 (sqrt.f64 1/2))
(+.f64 -1 (neg.f64 (+.f64 (sqrt.f64 1/2) -2)))
(-.f64 1 (sqrt.f64 1/2))
(+.f64 (neg.f64 (+.f64 (sqrt.f64 1/2) -2)) -1)
(-.f64 1 (sqrt.f64 1/2))
(+.f64 (.f64 1/2 (-.f64 1 (sqrt.f64 1/2))) (.f64 1/2 (-.f64 1 (sqrt.f64 1/2))))
(-.f64 1 (sqrt.f64 1/2))
(+.f64 -2 (neg.f64 (+.f64 (sqrt.f64 1/2) -3)))
(-.f64 1 (sqrt.f64 1/2))
(+.f64 (neg.f64 (+.f64 (sqrt.f64 1/2) -3)) -2)
(-.f64 1 (sqrt.f64 1/2))
(*.f64 1 (-.f64 1 (sqrt.f64 1/2)))
(-.f64 1 (sqrt.f64 1/2))
(.f64 1/2 (.f64 (+.f64 (sqrt.f64 1/2) -1) -2))
(-.f64 1 (sqrt.f64 1/2))
(*.f64 (-.f64 1 (sqrt.f64 1/2)) 1)
(-.f64 1 (sqrt.f64 1/2))
(.f64 2 (.f64 1/2 (-.f64 1 (sqrt.f64 1/2))))
(-.f64 1 (sqrt.f64 1/2))
(.f64 4 (.f64 (-.f64 1 (sqrt.f64 1/2)) 1/4))
(-.f64 1 (sqrt.f64 1/2))
(.f64 (.f64 (+.f64 (sqrt.f64 1/2) -1) -2) 1/2)
(-.f64 1 (sqrt.f64 1/2))
(*.f64 (+.f64 (sqrt.f64 1/2) -1) -1)
(-.f64 1 (sqrt.f64 1/2))
(*.f64 -1 (+.f64 (sqrt.f64 1/2) -1))
(-.f64 1 (sqrt.f64 1/2))
(.f64 (.f64 (-.f64 1 (sqrt.f64 1/2)) 4) 1/4)
(-.f64 1 (sqrt.f64 1/2))
(.f64 (+.f64 (.f64 (sqrt.f64 1/2) 2) -2) -1/2)
(.f64 (+.f64 -2 (.f64 (sqrt.f64 1/2) 2)) -1/2)
(.f64 (.f64 (-.f64 1 (sqrt.f64 1/2)) 8) 1/8)
(-.f64 1 (sqrt.f64 1/2))
(.f64 1/4 (.f64 (-.f64 1 (sqrt.f64 1/2)) 4))
(-.f64 1 (sqrt.f64 1/2))
(.f64 (.f64 1/2 (-.f64 1 (sqrt.f64 1/2))) 2)
(-.f64 1 (sqrt.f64 1/2))
(.f64 -2 (.f64 1/2 (+.f64 (sqrt.f64 1/2) -1)))
(-.f64 1 (sqrt.f64 1/2))
(.f64 (.f64 1/2 (+.f64 (sqrt.f64 1/2) -1)) -2)
(-.f64 1 (sqrt.f64 1/2))
(.f64 (.f64 (-.f64 1 (sqrt.f64 1/2)) 1/4) 4)
(-.f64 1 (sqrt.f64 1/2))
(.f64 1/8 (.f64 (-.f64 1 (sqrt.f64 1/2)) 8))
(-.f64 1 (sqrt.f64 1/2))
(.f64 -1/2 (+.f64 (.f64 (sqrt.f64 1/2) 2) -2))
(.f64 (+.f64 -2 (.f64 (sqrt.f64 1/2) 2)) -1/2)
(*.f64 (-.f64 (+.f64 (sqrt.f64 1/2) -3) -2) -1)
(-.f64 1 (sqrt.f64 1/2))
(/.f64 (-.f64 1 (sqrt.f64 1/2)) 1)
(-.f64 1 (sqrt.f64 1/2))
(/.f64 (*.f64 (+.f64 (sqrt.f64 1/2) -1) -2) 2)
(-.f64 1 (sqrt.f64 1/2))
(/.f64 (+.f64 (sqrt.f64 1/2) -1) -1)
(-.f64 1 (sqrt.f64 1/2))
(/.f64 (*.f64 (-.f64 1 (sqrt.f64 1/2)) 4) 4)
(-.f64 1 (sqrt.f64 1/2))
(/.f64 (+.f64 (*.f64 (sqrt.f64 1/2) 2) -2) -2)
(/.f64 (+.f64 -2 (*.f64 (sqrt.f64 1/2) 2)) -2)
(/.f64 (*.f64 (-.f64 1 (sqrt.f64 1/2)) 8) 8)
(-.f64 1 (sqrt.f64 1/2))
(/.f64 (*.f64 4 (+.f64 (sqrt.f64 1/2) -1)) -4)
(-.f64 1 (sqrt.f64 1/2))
(/.f64 (.f64 2 (.f64 (-.f64 1 (sqrt.f64 1/2)) 8)) 16)
(-.f64 1 (sqrt.f64 1/2))
(/.f64 (.f64 2 (.f64 4 (+.f64 (sqrt.f64 1/2) -1))) -8)
(-.f64 1 (sqrt.f64 1/2))
(/.f64 (.f64 2 (.f64 2 (*.f64 (-.f64 1 (sqrt.f64 1/2)) 8))) 32)
(-.f64 1 (sqrt.f64 1/2))
(/.f64 (.f64 2 (.f64 2 (*.f64 4 (+.f64 (sqrt.f64 1/2) -1)))) -16)
(-.f64 1 (sqrt.f64 1/2))
(/.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 (-.f64 1 (sqrt.f64 1/2)) 8)))) 64)
(-.f64 1 (sqrt.f64 1/2))
(/.f64 (neg.f64 (.f64 2 (.f64 4 (+.f64 (sqrt.f64 1/2) -1)))) 8)
(-.f64 1 (sqrt.f64 1/2))
(/.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 4 (+.f64 (sqrt.f64 1/2) -1))))) -32)
(-.f64 1 (sqrt.f64 1/2))
(/.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (*.f64 (-.f64 1 (sqrt.f64 1/2)) 8))))) 128)
(-.f64 1 (sqrt.f64 1/2))
(/.f64 (.f64 2 (neg.f64 (.f64 2 (*.f64 4 (+.f64 (sqrt.f64 1/2) -1))))) 16)
(-.f64 1 (sqrt.f64 1/2))
(/.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (*.f64 4 (+.f64 (sqrt.f64 1/2) -1)))))) -64)
(-.f64 1 (sqrt.f64 1/2))
(/.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 (-.f64 1 (sqrt.f64 1/2)) 8)))))) 256)
(-.f64 1 (sqrt.f64 1/2))
(/.f64 (.f64 2 (.f64 2 (neg.f64 (.f64 2 (.f64 4 (+.f64 (sqrt.f64 1/2) -1)))))) 32)
(-.f64 1 (sqrt.f64 1/2))
(/.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (*.f64 (-.f64 1 (sqrt.f64 1/2)) 8))))))) 512)
(-.f64 1 (sqrt.f64 1/2))
(/.f64 (.f64 2 (.f64 2 (.f64 2 (neg.f64 (.f64 2 (*.f64 4 (+.f64 (sqrt.f64 1/2) -1))))))) 64)
(-.f64 1 (sqrt.f64 1/2))
(/.f64 (-.f64 (+.f64 (sqrt.f64 1/2) -3) -2) -1)
(-.f64 1 (sqrt.f64 1/2))
(pow.f64 (-.f64 1 (sqrt.f64 1/2)) 1)
(-.f64 1 (sqrt.f64 1/2))
(neg.f64 (+.f64 (sqrt.f64 1/2) -1))
(-.f64 1 (sqrt.f64 1/2))
(neg.f64 (-.f64 (+.f64 (sqrt.f64 1/2) -3) -2))
(-.f64 1 (sqrt.f64 1/2))

localize15.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (*.f64 1/2 (-.f64 1 (/.f64 1 x))))
✓	0.5b	(-.f64 1 (sqrt.f64 (*.f64 1/2 (-.f64 1 (/.f64 1 x)))))

Compiler

Compiled 37 to 31 computations (16.2% saved)

series2.0ms (0%)

Counts

2 → 16

Calls

6 calls:

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

rewrite71.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

1242×	`rational.json-1`
1242×	`rational.json-2`
1242×	`rational.json-4`
1242×	`rational.json-3`
1238×	`exponential.json-3`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	52
1	81	52
2	176	52
3	357	52
4	681	52
5	1780	52
6	4937	52

Stop Event

1×	node limit

Counts

2 → 50

Calls

Call 1

Inputs
(-.f64 1 (sqrt.f64 (*.f64 1/2 (-.f64 1 (/.f64 1 x)))))
(sqrt.f64 (*.f64 1/2 (-.f64 1 (/.f64 1 x))))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 1 (sqrt.f64 (*.f64 1/2 (-.f64 1 (/.f64 1 x))))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (-.f64 1 (sqrt.f64 (*.f64 1/2 (-.f64 1 (/.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 -1 (neg.f64 (+.f64 (sqrt.f64 (*.f64 1/2 (-.f64 1 (/.f64 1 x)))) -2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 -2 (-.f64 1 (+.f64 (sqrt.f64 (*.f64 1/2 (-.f64 1 (/.f64 1 x)))) -2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (neg.f64 (+.f64 (sqrt.f64 (*.f64 1/2 (-.f64 1 (/.f64 1 x)))) -2)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 1/2 (-.f64 1 (sqrt.f64 (*.f64 1/2 (-.f64 1 (/.f64 1 x)))))) (*.f64 1/2 (-.f64 1 (sqrt.f64 (*.f64 1/2 (-.f64 1 (/.f64 1 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (-.f64 1 (sqrt.f64 (*.f64 1/2 (-.f64 1 (/.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/2 (*.f64 (-.f64 1 (sqrt.f64 (*.f64 1/2 (-.f64 1 (/.f64 1 x))))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 1 (sqrt.f64 (*.f64 1/2 (-.f64 1 (/.f64 1 x))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 2 (*.f64 1/2 (-.f64 1 (sqrt.f64 (*.f64 1/2 (-.f64 1 (/.f64 1 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (-.f64 1 (sqrt.f64 (*.f64 1/2 (-.f64 1 (/.f64 1 x))))) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 4 (/.f64 (-.f64 1 (sqrt.f64 (*.f64 1/2 (-.f64 1 (/.f64 1 x))))) 4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (sqrt.f64 (*.f64 1/2 (-.f64 1 (/.f64 1 x)))) -1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -1 (+.f64 (sqrt.f64 (*.f64 1/2 (-.f64 1 (/.f64 1 x)))) -1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (-.f64 1 (sqrt.f64 (*.f64 1/2 (-.f64 1 (/.f64 1 x))))) 4) 1/4)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/4 (*.f64 (-.f64 1 (sqrt.f64 (*.f64 1/2 (-.f64 1 (/.f64 1 x))))) 4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 1/2 (-.f64 1 (sqrt.f64 (*.f64 1/2 (-.f64 1 (/.f64 1 x)))))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (-.f64 1 (sqrt.f64 (*.f64 1/2 (-.f64 1 (/.f64 1 x))))) 4) 4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1 (sqrt.f64 (*.f64 1/2 (-.f64 1 (/.f64 1 x))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (-.f64 1 (sqrt.f64 (*.f64 1/2 (-.f64 1 (/.f64 1 x))))) 2) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (sqrt.f64 (*.f64 1/2 (-.f64 1 (/.f64 1 x)))) -1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (-.f64 1 (sqrt.f64 (*.f64 1/2 (-.f64 1 (/.f64 1 x))))) 4) 4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (+.f64 (sqrt.f64 (*.f64 1/2 (-.f64 1 (/.f64 1 x)))) -1)) -2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (-.f64 1 (sqrt.f64 (*.f64 1/2 (-.f64 1 (/.f64 1 x))))) 8) 8)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 4 (+.f64 (sqrt.f64 (*.f64 1/2 (-.f64 1 (/.f64 1 x)))) -1)) -4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 (-.f64 1 (sqrt.f64 (*.f64 1/2 (-.f64 1 (/.f64 1 x))))) 8)) 16)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 2 (*.f64 (-.f64 1 (sqrt.f64 (*.f64 1/2 (-.f64 1 (/.f64 1 x))))) 8))) 32)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (-.f64 1 (sqrt.f64 (*.f64 1/2 (-.f64 1 (/.f64 1 x))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (+.f64 (sqrt.f64 (*.f64 1/2 (-.f64 1 (/.f64 1 x)))) -1))))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (sqrt.f64 (*.f64 1/2 (-.f64 1 (/.f64 1 x)))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (sqrt.f64 (*.f64 1/2 (-.f64 1 (/.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 1/2 (sqrt.f64 (*.f64 1/2 (-.f64 1 (/.f64 1 x))))) (*.f64 1/2 (sqrt.f64 (*.f64 1/2 (-.f64 1 (/.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (sqrt.f64 (*.f64 1/2 (-.f64 1 (/.f64 1 x)))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (sqrt.f64 (*.f64 1/2 (-.f64 1 (/.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/2 (*.f64 (sqrt.f64 (*.f64 1/2 (-.f64 1 (/.f64 1 x)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 1/2 (-.f64 1 (/.f64 1 x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 2 (*.f64 1/2 (sqrt.f64 (*.f64 1/2 (-.f64 1 (/.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 4 (/.f64 (sqrt.f64 (*.f64 1/2 (-.f64 1 (/.f64 1 x)))) 4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (sqrt.f64 (*.f64 1/2 (-.f64 1 (/.f64 1 x)))) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (sqrt.f64 (*.f64 1/2 (-.f64 1 (/.f64 1 x)))) 4) 1/4)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/4 (*.f64 (sqrt.f64 (*.f64 1/2 (-.f64 1 (/.f64 1 x)))) 4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 1/2 (sqrt.f64 (*.f64 1/2 (-.f64 1 (/.f64 1 x))))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (*.f64 1/2 (-.f64 1 (/.f64 1 x)))) 4) 4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (*.f64 1/2 (-.f64 1 (/.f64 1 x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (sqrt.f64 (*.f64 1/2 (-.f64 1 (/.f64 1 x)))) 2) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (sqrt.f64 (*.f64 1/2 (-.f64 1 (/.f64 1 x)))) 4) 4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (sqrt.f64 (*.f64 1/2 (-.f64 1 (/.f64 1 x)))) 8) 8)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 (sqrt.f64 (*.f64 1/2 (-.f64 1 (/.f64 1 x)))) 8)) 16)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 2 (*.f64 (sqrt.f64 (*.f64 1/2 (-.f64 1 (/.f64 1 x)))) 8))) 32)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 1/2 (-.f64 1 (/.f64 1 x)))) 1)))))

simplify359.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

2684×	`rational.json-simplify-2`
1968×	`rational.json-simplify-35`
1714×	`rational.json-simplify-1`
1564×	`rational.json-simplify-52`
888×	`rational.json-simplify-48`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	122	2052
1	249	2052
2	632	2052
3	1810	2052
4	2986	2052
5	3628	2052
6	3818	2052
7	4045	2052
8	4331	2052
9	4765	2052
10	5590	2052
11	6284	2052
12	7137	2052
13	7340	2052
14	7961	2052
15	7961	2052

Stop Event

1×	node limit

Counts

66 → 80

Calls

Call 1

Inputs
(-.f64 1 (sqrt.f64 1/2))
(-.f64 (+.f64 1 (*.f64 1/2 (/.f64 (sqrt.f64 1/2) x))) (sqrt.f64 1/2))
(-.f64 (+.f64 1 (+.f64 (.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (.f64 1/2 (/.f64 (sqrt.f64 1/2) x)))) (sqrt.f64 1/2))
(-.f64 (+.f64 1 (+.f64 (.f64 1/16 (/.f64 (sqrt.f64 1/2) (pow.f64 x 3))) (+.f64 (.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (*.f64 1/2 (/.f64 (sqrt.f64 1/2) x))))) (sqrt.f64 1/2))
(-.f64 1 (sqrt.f64 1/2))
(-.f64 (+.f64 1 (*.f64 1/2 (/.f64 (sqrt.f64 1/2) x))) (sqrt.f64 1/2))
(-.f64 (+.f64 1 (+.f64 (.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (.f64 1/2 (/.f64 (sqrt.f64 1/2) x)))) (sqrt.f64 1/2))
(-.f64 (+.f64 1 (+.f64 (.f64 1/16 (/.f64 (sqrt.f64 1/2) (pow.f64 x 3))) (+.f64 (.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (*.f64 1/2 (/.f64 (sqrt.f64 1/2) x))))) (sqrt.f64 1/2))
(sqrt.f64 1/2)
(+.f64 (sqrt.f64 1/2) (*.f64 -1/2 (/.f64 (sqrt.f64 1/2) x)))
(+.f64 (sqrt.f64 1/2) (+.f64 (.f64 -1/2 (/.f64 (sqrt.f64 1/2) x)) (.f64 -1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2)))))
(+.f64 (.f64 -1/16 (/.f64 (sqrt.f64 1/2) (pow.f64 x 3))) (+.f64 (sqrt.f64 1/2) (+.f64 (.f64 -1/2 (/.f64 (sqrt.f64 1/2) x)) (*.f64 -1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))))))
(sqrt.f64 1/2)
(+.f64 (sqrt.f64 1/2) (*.f64 -1/2 (/.f64 (sqrt.f64 1/2) x)))
(+.f64 (sqrt.f64 1/2) (+.f64 (.f64 -1/2 (/.f64 (sqrt.f64 1/2) x)) (.f64 -1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2)))))
(+.f64 (.f64 -1/16 (/.f64 (sqrt.f64 1/2) (pow.f64 x 3))) (+.f64 (sqrt.f64 1/2) (+.f64 (.f64 -1/2 (/.f64 (sqrt.f64 1/2) x)) (*.f64 -1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))))))
(+.f64 (-.f64 1 (sqrt.f64 (*.f64 1/2 (-.f64 1 (/.f64 1 x))))) 0)
(+.f64 0 (-.f64 1 (sqrt.f64 (*.f64 1/2 (-.f64 1 (/.f64 1 x))))))
(+.f64 -1 (neg.f64 (+.f64 (sqrt.f64 (*.f64 1/2 (-.f64 1 (/.f64 1 x)))) -2)))
(+.f64 -2 (-.f64 1 (+.f64 (sqrt.f64 (*.f64 1/2 (-.f64 1 (/.f64 1 x)))) -2)))
(+.f64 (neg.f64 (+.f64 (sqrt.f64 (*.f64 1/2 (-.f64 1 (/.f64 1 x)))) -2)) -1)
(+.f64 (.f64 1/2 (-.f64 1 (sqrt.f64 (.f64 1/2 (-.f64 1 (/.f64 1 x)))))) (.f64 1/2 (-.f64 1 (sqrt.f64 (.f64 1/2 (-.f64 1 (/.f64 1 x)))))))
(.f64 1 (-.f64 1 (sqrt.f64 (.f64 1/2 (-.f64 1 (/.f64 1 x))))))
(.f64 1/2 (.f64 (-.f64 1 (sqrt.f64 (*.f64 1/2 (-.f64 1 (/.f64 1 x))))) 2))
(.f64 (-.f64 1 (sqrt.f64 (.f64 1/2 (-.f64 1 (/.f64 1 x))))) 1)
(.f64 2 (.f64 1/2 (-.f64 1 (sqrt.f64 (*.f64 1/2 (-.f64 1 (/.f64 1 x)))))))
(.f64 (.f64 (-.f64 1 (sqrt.f64 (*.f64 1/2 (-.f64 1 (/.f64 1 x))))) 2) 1/2)
(.f64 4 (/.f64 (-.f64 1 (sqrt.f64 (.f64 1/2 (-.f64 1 (/.f64 1 x))))) 4))
(.f64 (+.f64 (sqrt.f64 (.f64 1/2 (-.f64 1 (/.f64 1 x)))) -1) -1)
(.f64 -1 (+.f64 (sqrt.f64 (.f64 1/2 (-.f64 1 (/.f64 1 x)))) -1))
(.f64 (.f64 (-.f64 1 (sqrt.f64 (*.f64 1/2 (-.f64 1 (/.f64 1 x))))) 4) 1/4)
(.f64 1/4 (.f64 (-.f64 1 (sqrt.f64 (*.f64 1/2 (-.f64 1 (/.f64 1 x))))) 4))
(.f64 (.f64 1/2 (-.f64 1 (sqrt.f64 (*.f64 1/2 (-.f64 1 (/.f64 1 x)))))) 2)
(.f64 (/.f64 (-.f64 1 (sqrt.f64 (.f64 1/2 (-.f64 1 (/.f64 1 x))))) 4) 4)
(/.f64 (-.f64 1 (sqrt.f64 (*.f64 1/2 (-.f64 1 (/.f64 1 x))))) 1)
(/.f64 (.f64 (-.f64 1 (sqrt.f64 (.f64 1/2 (-.f64 1 (/.f64 1 x))))) 2) 2)
(/.f64 (+.f64 (sqrt.f64 (*.f64 1/2 (-.f64 1 (/.f64 1 x)))) -1) -1)
(/.f64 (.f64 (-.f64 1 (sqrt.f64 (.f64 1/2 (-.f64 1 (/.f64 1 x))))) 4) 4)
(/.f64 (.f64 2 (+.f64 (sqrt.f64 (.f64 1/2 (-.f64 1 (/.f64 1 x)))) -1)) -2)
(/.f64 (.f64 (-.f64 1 (sqrt.f64 (.f64 1/2 (-.f64 1 (/.f64 1 x))))) 8) 8)
(/.f64 (.f64 4 (+.f64 (sqrt.f64 (.f64 1/2 (-.f64 1 (/.f64 1 x)))) -1)) -4)
(/.f64 (.f64 2 (.f64 (-.f64 1 (sqrt.f64 (*.f64 1/2 (-.f64 1 (/.f64 1 x))))) 8)) 16)
(/.f64 (.f64 2 (.f64 2 (.f64 (-.f64 1 (sqrt.f64 (.f64 1/2 (-.f64 1 (/.f64 1 x))))) 8))) 32)
(pow.f64 (-.f64 1 (sqrt.f64 (*.f64 1/2 (-.f64 1 (/.f64 1 x))))) 1)
(neg.f64 (+.f64 (sqrt.f64 (*.f64 1/2 (-.f64 1 (/.f64 1 x)))) -1))
(+.f64 (sqrt.f64 (*.f64 1/2 (-.f64 1 (/.f64 1 x)))) 0)
(+.f64 0 (sqrt.f64 (*.f64 1/2 (-.f64 1 (/.f64 1 x)))))
(+.f64 (.f64 1/2 (sqrt.f64 (.f64 1/2 (-.f64 1 (/.f64 1 x))))) (.f64 1/2 (sqrt.f64 (.f64 1/2 (-.f64 1 (/.f64 1 x))))))
(-.f64 (sqrt.f64 (*.f64 1/2 (-.f64 1 (/.f64 1 x)))) 0)
(.f64 1 (sqrt.f64 (.f64 1/2 (-.f64 1 (/.f64 1 x)))))
(.f64 1/2 (.f64 (sqrt.f64 (*.f64 1/2 (-.f64 1 (/.f64 1 x)))) 2))
(.f64 (sqrt.f64 (.f64 1/2 (-.f64 1 (/.f64 1 x)))) 1)
(.f64 2 (.f64 1/2 (sqrt.f64 (*.f64 1/2 (-.f64 1 (/.f64 1 x))))))
(.f64 4 (/.f64 (sqrt.f64 (.f64 1/2 (-.f64 1 (/.f64 1 x)))) 4))
(.f64 (.f64 (sqrt.f64 (*.f64 1/2 (-.f64 1 (/.f64 1 x)))) 2) 1/2)
(.f64 (.f64 (sqrt.f64 (*.f64 1/2 (-.f64 1 (/.f64 1 x)))) 4) 1/4)
(.f64 1/4 (.f64 (sqrt.f64 (*.f64 1/2 (-.f64 1 (/.f64 1 x)))) 4))
(.f64 (.f64 1/2 (sqrt.f64 (*.f64 1/2 (-.f64 1 (/.f64 1 x))))) 2)
(.f64 (/.f64 (sqrt.f64 (.f64 1/2 (-.f64 1 (/.f64 1 x)))) 4) 4)
(/.f64 (sqrt.f64 (*.f64 1/2 (-.f64 1 (/.f64 1 x)))) 1)
(/.f64 (.f64 (sqrt.f64 (.f64 1/2 (-.f64 1 (/.f64 1 x)))) 2) 2)
(/.f64 (.f64 (sqrt.f64 (.f64 1/2 (-.f64 1 (/.f64 1 x)))) 4) 4)
(/.f64 (.f64 (sqrt.f64 (.f64 1/2 (-.f64 1 (/.f64 1 x)))) 8) 8)
(/.f64 (.f64 2 (.f64 (sqrt.f64 (*.f64 1/2 (-.f64 1 (/.f64 1 x)))) 8)) 16)
(/.f64 (.f64 2 (.f64 2 (.f64 (sqrt.f64 (.f64 1/2 (-.f64 1 (/.f64 1 x)))) 8))) 32)
(pow.f64 (sqrt.f64 (*.f64 1/2 (-.f64 1 (/.f64 1 x)))) 1)

Outputs
(-.f64 1 (sqrt.f64 1/2))
(-.f64 (+.f64 1 (*.f64 1/2 (/.f64 (sqrt.f64 1/2) x))) (sqrt.f64 1/2))
(+.f64 (*.f64 1/2 (/.f64 (sqrt.f64 1/2) x)) (-.f64 1 (sqrt.f64 1/2)))
(+.f64 (-.f64 1 (sqrt.f64 1/2)) (*.f64 1/2 (/.f64 (sqrt.f64 1/2) x)))
(-.f64 (+.f64 1 (+.f64 (.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (.f64 1/2 (/.f64 (sqrt.f64 1/2) x)))) (sqrt.f64 1/2))
(+.f64 (+.f64 (.f64 1/2 (/.f64 (sqrt.f64 1/2) x)) (.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2)))) (-.f64 1 (sqrt.f64 1/2)))
(+.f64 (-.f64 1 (sqrt.f64 1/2)) (+.f64 (.f64 1/2 (/.f64 (sqrt.f64 1/2) x)) (.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2)))))
(+.f64 1 (-.f64 (+.f64 (.f64 1/2 (/.f64 (sqrt.f64 1/2) x)) (.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2)))) (sqrt.f64 1/2)))
(+.f64 1 (+.f64 (.f64 1/2 (/.f64 (sqrt.f64 1/2) x)) (-.f64 (.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (sqrt.f64 1/2))))
(-.f64 (+.f64 1 (+.f64 (.f64 1/16 (/.f64 (sqrt.f64 1/2) (pow.f64 x 3))) (+.f64 (.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (*.f64 1/2 (/.f64 (sqrt.f64 1/2) x))))) (sqrt.f64 1/2))
(+.f64 (+.f64 (.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (+.f64 (.f64 1/2 (/.f64 (sqrt.f64 1/2) x)) (*.f64 1/16 (/.f64 (sqrt.f64 1/2) (pow.f64 x 3))))) (-.f64 1 (sqrt.f64 1/2)))
(+.f64 (-.f64 1 (sqrt.f64 1/2)) (+.f64 (.f64 1/2 (/.f64 (sqrt.f64 1/2) x)) (+.f64 (.f64 1/16 (/.f64 (sqrt.f64 1/2) (pow.f64 x 3))) (*.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))))))
(+.f64 1 (+.f64 (.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (-.f64 (+.f64 (.f64 1/2 (/.f64 (sqrt.f64 1/2) x)) (*.f64 1/16 (/.f64 (sqrt.f64 1/2) (pow.f64 x 3)))) (sqrt.f64 1/2))))
(+.f64 1 (+.f64 (.f64 1/2 (/.f64 (sqrt.f64 1/2) x)) (-.f64 (+.f64 (.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (*.f64 1/16 (/.f64 (sqrt.f64 1/2) (pow.f64 x 3)))) (sqrt.f64 1/2))))
(+.f64 1 (+.f64 (.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (+.f64 (.f64 1/2 (/.f64 (sqrt.f64 1/2) x)) (-.f64 (*.f64 1/16 (/.f64 (sqrt.f64 1/2) (pow.f64 x 3))) (sqrt.f64 1/2)))))
(-.f64 1 (sqrt.f64 1/2))
(-.f64 (+.f64 1 (*.f64 1/2 (/.f64 (sqrt.f64 1/2) x))) (sqrt.f64 1/2))
(+.f64 (*.f64 1/2 (/.f64 (sqrt.f64 1/2) x)) (-.f64 1 (sqrt.f64 1/2)))
(+.f64 (-.f64 1 (sqrt.f64 1/2)) (*.f64 1/2 (/.f64 (sqrt.f64 1/2) x)))
(-.f64 (+.f64 1 (+.f64 (.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (.f64 1/2 (/.f64 (sqrt.f64 1/2) x)))) (sqrt.f64 1/2))
(+.f64 (+.f64 (.f64 1/2 (/.f64 (sqrt.f64 1/2) x)) (.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2)))) (-.f64 1 (sqrt.f64 1/2)))
(+.f64 (-.f64 1 (sqrt.f64 1/2)) (+.f64 (.f64 1/2 (/.f64 (sqrt.f64 1/2) x)) (.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2)))))
(+.f64 1 (-.f64 (+.f64 (.f64 1/2 (/.f64 (sqrt.f64 1/2) x)) (.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2)))) (sqrt.f64 1/2)))
(+.f64 1 (+.f64 (.f64 1/2 (/.f64 (sqrt.f64 1/2) x)) (-.f64 (.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (sqrt.f64 1/2))))
(-.f64 (+.f64 1 (+.f64 (.f64 1/16 (/.f64 (sqrt.f64 1/2) (pow.f64 x 3))) (+.f64 (.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (*.f64 1/2 (/.f64 (sqrt.f64 1/2) x))))) (sqrt.f64 1/2))
(+.f64 (+.f64 (.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (+.f64 (.f64 1/2 (/.f64 (sqrt.f64 1/2) x)) (*.f64 1/16 (/.f64 (sqrt.f64 1/2) (pow.f64 x 3))))) (-.f64 1 (sqrt.f64 1/2)))
(+.f64 (-.f64 1 (sqrt.f64 1/2)) (+.f64 (.f64 1/2 (/.f64 (sqrt.f64 1/2) x)) (+.f64 (.f64 1/16 (/.f64 (sqrt.f64 1/2) (pow.f64 x 3))) (*.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))))))
(+.f64 1 (+.f64 (.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (-.f64 (+.f64 (.f64 1/2 (/.f64 (sqrt.f64 1/2) x)) (*.f64 1/16 (/.f64 (sqrt.f64 1/2) (pow.f64 x 3)))) (sqrt.f64 1/2))))
(+.f64 1 (+.f64 (.f64 1/2 (/.f64 (sqrt.f64 1/2) x)) (-.f64 (+.f64 (.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (*.f64 1/16 (/.f64 (sqrt.f64 1/2) (pow.f64 x 3)))) (sqrt.f64 1/2))))
(+.f64 1 (+.f64 (.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (+.f64 (.f64 1/2 (/.f64 (sqrt.f64 1/2) x)) (-.f64 (*.f64 1/16 (/.f64 (sqrt.f64 1/2) (pow.f64 x 3))) (sqrt.f64 1/2)))))
(sqrt.f64 1/2)
(+.f64 (sqrt.f64 1/2) (*.f64 -1/2 (/.f64 (sqrt.f64 1/2) x)))
(+.f64 (sqrt.f64 1/2) (*.f64 (/.f64 (sqrt.f64 1/2) x) -1/2))
(+.f64 (sqrt.f64 1/2) (+.f64 (.f64 -1/2 (/.f64 (sqrt.f64 1/2) x)) (.f64 -1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2)))))
(+.f64 (sqrt.f64 1/2) (+.f64 (.f64 (/.f64 (sqrt.f64 1/2) x) -1/2) (.f64 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2)) -1/8)))
(+.f64 (.f64 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2)) -1/8) (+.f64 (sqrt.f64 1/2) (.f64 (/.f64 (sqrt.f64 1/2) x) -1/2)))
(+.f64 (.f64 (/.f64 (sqrt.f64 1/2) x) -1/2) (+.f64 (sqrt.f64 1/2) (.f64 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2)) -1/8)))
(+.f64 (.f64 -1/16 (/.f64 (sqrt.f64 1/2) (pow.f64 x 3))) (+.f64 (sqrt.f64 1/2) (+.f64 (.f64 -1/2 (/.f64 (sqrt.f64 1/2) x)) (*.f64 -1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))))))
(+.f64 (sqrt.f64 1/2) (+.f64 (+.f64 (.f64 (/.f64 (sqrt.f64 1/2) x) -1/2) (.f64 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2)) -1/8)) (*.f64 (/.f64 (sqrt.f64 1/2) (pow.f64 x 3)) -1/16)))
(+.f64 (+.f64 (.f64 (/.f64 (sqrt.f64 1/2) x) -1/2) (.f64 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2)) -1/8)) (+.f64 (*.f64 (/.f64 (sqrt.f64 1/2) (pow.f64 x 3)) -1/16) (sqrt.f64 1/2)))
(+.f64 (.f64 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2)) -1/8) (+.f64 (+.f64 (sqrt.f64 1/2) (.f64 (/.f64 (sqrt.f64 1/2) x) -1/2)) (*.f64 (/.f64 (sqrt.f64 1/2) (pow.f64 x 3)) -1/16)))
(+.f64 (.f64 (/.f64 (sqrt.f64 1/2) x) -1/2) (+.f64 (.f64 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2)) -1/8) (+.f64 (sqrt.f64 1/2) (*.f64 (/.f64 (sqrt.f64 1/2) (pow.f64 x 3)) -1/16))))
(+.f64 (sqrt.f64 1/2) (+.f64 (.f64 (/.f64 (sqrt.f64 1/2) x) -1/2) (+.f64 (.f64 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2)) -1/8) (*.f64 (/.f64 (sqrt.f64 1/2) (pow.f64 x 3)) -1/16))))
(sqrt.f64 1/2)
(+.f64 (sqrt.f64 1/2) (*.f64 -1/2 (/.f64 (sqrt.f64 1/2) x)))
(+.f64 (sqrt.f64 1/2) (*.f64 (/.f64 (sqrt.f64 1/2) x) -1/2))
(+.f64 (sqrt.f64 1/2) (+.f64 (.f64 -1/2 (/.f64 (sqrt.f64 1/2) x)) (.f64 -1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2)))))
(+.f64 (sqrt.f64 1/2) (+.f64 (.f64 (/.f64 (sqrt.f64 1/2) x) -1/2) (.f64 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2)) -1/8)))
(+.f64 (.f64 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2)) -1/8) (+.f64 (sqrt.f64 1/2) (.f64 (/.f64 (sqrt.f64 1/2) x) -1/2)))
(+.f64 (.f64 (/.f64 (sqrt.f64 1/2) x) -1/2) (+.f64 (sqrt.f64 1/2) (.f64 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2)) -1/8)))
(+.f64 (.f64 -1/16 (/.f64 (sqrt.f64 1/2) (pow.f64 x 3))) (+.f64 (sqrt.f64 1/2) (+.f64 (.f64 -1/2 (/.f64 (sqrt.f64 1/2) x)) (*.f64 -1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))))))
(+.f64 (sqrt.f64 1/2) (+.f64 (+.f64 (.f64 (/.f64 (sqrt.f64 1/2) x) -1/2) (.f64 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2)) -1/8)) (*.f64 (/.f64 (sqrt.f64 1/2) (pow.f64 x 3)) -1/16)))
(+.f64 (+.f64 (.f64 (/.f64 (sqrt.f64 1/2) x) -1/2) (.f64 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2)) -1/8)) (+.f64 (*.f64 (/.f64 (sqrt.f64 1/2) (pow.f64 x 3)) -1/16) (sqrt.f64 1/2)))
(+.f64 (.f64 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2)) -1/8) (+.f64 (+.f64 (sqrt.f64 1/2) (.f64 (/.f64 (sqrt.f64 1/2) x) -1/2)) (*.f64 (/.f64 (sqrt.f64 1/2) (pow.f64 x 3)) -1/16)))
(+.f64 (.f64 (/.f64 (sqrt.f64 1/2) x) -1/2) (+.f64 (.f64 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2)) -1/8) (+.f64 (sqrt.f64 1/2) (*.f64 (/.f64 (sqrt.f64 1/2) (pow.f64 x 3)) -1/16))))
(+.f64 (sqrt.f64 1/2) (+.f64 (.f64 (/.f64 (sqrt.f64 1/2) x) -1/2) (+.f64 (.f64 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2)) -1/8) (*.f64 (/.f64 (sqrt.f64 1/2) (pow.f64 x 3)) -1/16))))
(+.f64 (-.f64 1 (sqrt.f64 (*.f64 1/2 (-.f64 1 (/.f64 1 x))))) 0)
(-.f64 1 (sqrt.f64 (*.f64 1/2 (-.f64 1 (/.f64 1 x)))))
(+.f64 0 (-.f64 1 (sqrt.f64 (*.f64 1/2 (-.f64 1 (/.f64 1 x))))))
(-.f64 1 (sqrt.f64 (*.f64 1/2 (-.f64 1 (/.f64 1 x)))))
(+.f64 -1 (neg.f64 (+.f64 (sqrt.f64 (*.f64 1/2 (-.f64 1 (/.f64 1 x)))) -2)))
(-.f64 1 (sqrt.f64 (*.f64 1/2 (-.f64 1 (/.f64 1 x)))))
(+.f64 -2 (-.f64 1 (+.f64 (sqrt.f64 (*.f64 1/2 (-.f64 1 (/.f64 1 x)))) -2)))
(-.f64 1 (sqrt.f64 (*.f64 1/2 (-.f64 1 (/.f64 1 x)))))
(+.f64 (neg.f64 (+.f64 (sqrt.f64 (*.f64 1/2 (-.f64 1 (/.f64 1 x)))) -2)) -1)
(-.f64 1 (sqrt.f64 (*.f64 1/2 (-.f64 1 (/.f64 1 x)))))
(+.f64 (.f64 1/2 (-.f64 1 (sqrt.f64 (.f64 1/2 (-.f64 1 (/.f64 1 x)))))) (.f64 1/2 (-.f64 1 (sqrt.f64 (.f64 1/2 (-.f64 1 (/.f64 1 x)))))))
(-.f64 1 (sqrt.f64 (*.f64 1/2 (-.f64 1 (/.f64 1 x)))))
(.f64 1 (-.f64 1 (sqrt.f64 (.f64 1/2 (-.f64 1 (/.f64 1 x))))))
(-.f64 1 (sqrt.f64 (*.f64 1/2 (-.f64 1 (/.f64 1 x)))))
(.f64 1/2 (.f64 (-.f64 1 (sqrt.f64 (*.f64 1/2 (-.f64 1 (/.f64 1 x))))) 2))
(-.f64 1 (sqrt.f64 (*.f64 1/2 (-.f64 1 (/.f64 1 x)))))
(.f64 (-.f64 1 (sqrt.f64 (.f64 1/2 (-.f64 1 (/.f64 1 x))))) 1)
(-.f64 1 (sqrt.f64 (*.f64 1/2 (-.f64 1 (/.f64 1 x)))))
(.f64 2 (.f64 1/2 (-.f64 1 (sqrt.f64 (*.f64 1/2 (-.f64 1 (/.f64 1 x)))))))
(-.f64 1 (sqrt.f64 (*.f64 1/2 (-.f64 1 (/.f64 1 x)))))
(.f64 (.f64 (-.f64 1 (sqrt.f64 (*.f64 1/2 (-.f64 1 (/.f64 1 x))))) 2) 1/2)
(-.f64 1 (sqrt.f64 (*.f64 1/2 (-.f64 1 (/.f64 1 x)))))
(.f64 4 (/.f64 (-.f64 1 (sqrt.f64 (.f64 1/2 (-.f64 1 (/.f64 1 x))))) 4))
(-.f64 1 (sqrt.f64 (*.f64 1/2 (-.f64 1 (/.f64 1 x)))))
(.f64 (+.f64 (sqrt.f64 (.f64 1/2 (-.f64 1 (/.f64 1 x)))) -1) -1)
(-.f64 1 (sqrt.f64 (*.f64 1/2 (-.f64 1 (/.f64 1 x)))))
(.f64 -1 (+.f64 (sqrt.f64 (.f64 1/2 (-.f64 1 (/.f64 1 x)))) -1))
(-.f64 1 (sqrt.f64 (*.f64 1/2 (-.f64 1 (/.f64 1 x)))))
(.f64 (.f64 (-.f64 1 (sqrt.f64 (*.f64 1/2 (-.f64 1 (/.f64 1 x))))) 4) 1/4)
(-.f64 1 (sqrt.f64 (*.f64 1/2 (-.f64 1 (/.f64 1 x)))))
(.f64 1/4 (.f64 (-.f64 1 (sqrt.f64 (*.f64 1/2 (-.f64 1 (/.f64 1 x))))) 4))
(-.f64 1 (sqrt.f64 (*.f64 1/2 (-.f64 1 (/.f64 1 x)))))
(.f64 (.f64 1/2 (-.f64 1 (sqrt.f64 (*.f64 1/2 (-.f64 1 (/.f64 1 x)))))) 2)
(-.f64 1 (sqrt.f64 (*.f64 1/2 (-.f64 1 (/.f64 1 x)))))
(.f64 (/.f64 (-.f64 1 (sqrt.f64 (.f64 1/2 (-.f64 1 (/.f64 1 x))))) 4) 4)
(-.f64 1 (sqrt.f64 (*.f64 1/2 (-.f64 1 (/.f64 1 x)))))
(/.f64 (-.f64 1 (sqrt.f64 (*.f64 1/2 (-.f64 1 (/.f64 1 x))))) 1)
(-.f64 1 (sqrt.f64 (*.f64 1/2 (-.f64 1 (/.f64 1 x)))))
(/.f64 (.f64 (-.f64 1 (sqrt.f64 (.f64 1/2 (-.f64 1 (/.f64 1 x))))) 2) 2)
(-.f64 1 (sqrt.f64 (*.f64 1/2 (-.f64 1 (/.f64 1 x)))))
(/.f64 (+.f64 (sqrt.f64 (*.f64 1/2 (-.f64 1 (/.f64 1 x)))) -1) -1)
(-.f64 1 (sqrt.f64 (*.f64 1/2 (-.f64 1 (/.f64 1 x)))))
(/.f64 (.f64 (-.f64 1 (sqrt.f64 (.f64 1/2 (-.f64 1 (/.f64 1 x))))) 4) 4)
(-.f64 1 (sqrt.f64 (*.f64 1/2 (-.f64 1 (/.f64 1 x)))))
(/.f64 (.f64 2 (+.f64 (sqrt.f64 (.f64 1/2 (-.f64 1 (/.f64 1 x)))) -1)) -2)
(-.f64 1 (sqrt.f64 (*.f64 1/2 (-.f64 1 (/.f64 1 x)))))
(/.f64 (.f64 (-.f64 1 (sqrt.f64 (.f64 1/2 (-.f64 1 (/.f64 1 x))))) 8) 8)
(-.f64 1 (sqrt.f64 (*.f64 1/2 (-.f64 1 (/.f64 1 x)))))
(/.f64 (.f64 4 (+.f64 (sqrt.f64 (.f64 1/2 (-.f64 1 (/.f64 1 x)))) -1)) -4)
(-.f64 1 (sqrt.f64 (*.f64 1/2 (-.f64 1 (/.f64 1 x)))))
(/.f64 (.f64 2 (.f64 (-.f64 1 (sqrt.f64 (*.f64 1/2 (-.f64 1 (/.f64 1 x))))) 8)) 16)
(-.f64 1 (sqrt.f64 (*.f64 1/2 (-.f64 1 (/.f64 1 x)))))
(/.f64 (.f64 2 (.f64 2 (.f64 (-.f64 1 (sqrt.f64 (.f64 1/2 (-.f64 1 (/.f64 1 x))))) 8))) 32)
(-.f64 1 (sqrt.f64 (*.f64 1/2 (-.f64 1 (/.f64 1 x)))))
(pow.f64 (-.f64 1 (sqrt.f64 (*.f64 1/2 (-.f64 1 (/.f64 1 x))))) 1)
(-.f64 1 (sqrt.f64 (*.f64 1/2 (-.f64 1 (/.f64 1 x)))))
(neg.f64 (+.f64 (sqrt.f64 (*.f64 1/2 (-.f64 1 (/.f64 1 x)))) -1))
(-.f64 1 (sqrt.f64 (*.f64 1/2 (-.f64 1 (/.f64 1 x)))))
(+.f64 (sqrt.f64 (*.f64 1/2 (-.f64 1 (/.f64 1 x)))) 0)
(sqrt.f64 (*.f64 1/2 (-.f64 1 (/.f64 1 x))))
(+.f64 0 (sqrt.f64 (*.f64 1/2 (-.f64 1 (/.f64 1 x)))))
(sqrt.f64 (*.f64 1/2 (-.f64 1 (/.f64 1 x))))
(+.f64 (.f64 1/2 (sqrt.f64 (.f64 1/2 (-.f64 1 (/.f64 1 x))))) (.f64 1/2 (sqrt.f64 (.f64 1/2 (-.f64 1 (/.f64 1 x))))))
(sqrt.f64 (*.f64 1/2 (-.f64 1 (/.f64 1 x))))
(-.f64 (sqrt.f64 (*.f64 1/2 (-.f64 1 (/.f64 1 x)))) 0)
(sqrt.f64 (*.f64 1/2 (-.f64 1 (/.f64 1 x))))
(.f64 1 (sqrt.f64 (.f64 1/2 (-.f64 1 (/.f64 1 x)))))
(sqrt.f64 (*.f64 1/2 (-.f64 1 (/.f64 1 x))))
(.f64 1/2 (.f64 (sqrt.f64 (*.f64 1/2 (-.f64 1 (/.f64 1 x)))) 2))
(sqrt.f64 (*.f64 1/2 (-.f64 1 (/.f64 1 x))))
(.f64 (sqrt.f64 (.f64 1/2 (-.f64 1 (/.f64 1 x)))) 1)
(sqrt.f64 (*.f64 1/2 (-.f64 1 (/.f64 1 x))))
(.f64 2 (.f64 1/2 (sqrt.f64 (*.f64 1/2 (-.f64 1 (/.f64 1 x))))))
(sqrt.f64 (*.f64 1/2 (-.f64 1 (/.f64 1 x))))
(.f64 4 (/.f64 (sqrt.f64 (.f64 1/2 (-.f64 1 (/.f64 1 x)))) 4))
(sqrt.f64 (*.f64 1/2 (-.f64 1 (/.f64 1 x))))
(.f64 (.f64 (sqrt.f64 (*.f64 1/2 (-.f64 1 (/.f64 1 x)))) 2) 1/2)
(sqrt.f64 (*.f64 1/2 (-.f64 1 (/.f64 1 x))))
(.f64 (.f64 (sqrt.f64 (*.f64 1/2 (-.f64 1 (/.f64 1 x)))) 4) 1/4)
(sqrt.f64 (*.f64 1/2 (-.f64 1 (/.f64 1 x))))
(.f64 1/4 (.f64 (sqrt.f64 (*.f64 1/2 (-.f64 1 (/.f64 1 x)))) 4))
(sqrt.f64 (*.f64 1/2 (-.f64 1 (/.f64 1 x))))
(.f64 (.f64 1/2 (sqrt.f64 (*.f64 1/2 (-.f64 1 (/.f64 1 x))))) 2)
(sqrt.f64 (*.f64 1/2 (-.f64 1 (/.f64 1 x))))
(.f64 (/.f64 (sqrt.f64 (.f64 1/2 (-.f64 1 (/.f64 1 x)))) 4) 4)
(sqrt.f64 (*.f64 1/2 (-.f64 1 (/.f64 1 x))))
(/.f64 (sqrt.f64 (*.f64 1/2 (-.f64 1 (/.f64 1 x)))) 1)
(sqrt.f64 (*.f64 1/2 (-.f64 1 (/.f64 1 x))))
(/.f64 (.f64 (sqrt.f64 (.f64 1/2 (-.f64 1 (/.f64 1 x)))) 2) 2)
(sqrt.f64 (*.f64 1/2 (-.f64 1 (/.f64 1 x))))
(/.f64 (.f64 (sqrt.f64 (.f64 1/2 (-.f64 1 (/.f64 1 x)))) 4) 4)
(sqrt.f64 (*.f64 1/2 (-.f64 1 (/.f64 1 x))))
(/.f64 (.f64 (sqrt.f64 (.f64 1/2 (-.f64 1 (/.f64 1 x)))) 8) 8)
(sqrt.f64 (*.f64 1/2 (-.f64 1 (/.f64 1 x))))
(/.f64 (.f64 2 (.f64 (sqrt.f64 (*.f64 1/2 (-.f64 1 (/.f64 1 x)))) 8)) 16)
(sqrt.f64 (*.f64 1/2 (-.f64 1 (/.f64 1 x))))
(/.f64 (.f64 2 (.f64 2 (.f64 (sqrt.f64 (.f64 1/2 (-.f64 1 (/.f64 1 x)))) 8))) 32)
(sqrt.f64 (*.f64 1/2 (-.f64 1 (/.f64 1 x))))
(pow.f64 (sqrt.f64 (*.f64 1/2 (-.f64 1 (/.f64 1 x)))) 1)
(sqrt.f64 (*.f64 1/2 (-.f64 1 (/.f64 1 x))))

localize20.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(/.f64 1/2 (hypot.f64 1 x))
	0.0b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
✓	0.0b	(+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -2)
✓	2.3b	(-.f64 -1 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -2))

Compiler

Compiled 51 to 44 computations (13.7% saved)

series1.0ms (0%)

Counts

2 → 24

Calls

6 calls:

Time	Variable		Point	Expression
0.0ms	x	@	inf	(+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -2)
0.0ms	x	@	-inf	(+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -2)
0.0ms	x	@	inf	(-.f64 -1 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -2))
0.0ms	x	@	0	(-.f64 -1 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -2))
0.0ms	x	@	-inf	(-.f64 -1 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -2))

rewrite87.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

1360×	`rational.json-1`
1360×	`rational.json-2`
1360×	`rational.json-3`
1358×	`rational.json-4`
1342×	`exponential.json-3`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	14	64
1	103	64
2	211	62
3	433	62
4	880	58
5	2479	58
6	5907	58

Stop Event

1×	node limit

Counts

2 → 51

Calls

Call 1

Inputs
(-.f64 -1 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -2))
(+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -2)

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 -1 (neg.f64 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 -2 (-.f64 1 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (neg.f64 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -2)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 (+.f64 -1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) -2) (/.f64 (+.f64 -1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) -2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -1 (+.f64 -1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/2 (*.f64 -2 (+.f64 -1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 2 (/.f64 (+.f64 -1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) -2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 -2 (+.f64 -1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 4 (/.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 -1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 4) 1/4)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/4 (*.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (+.f64 -1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) -2) 2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 4) 4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 -2 (+.f64 -1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 -1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 4) 4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (+.f64 -1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) -2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 8) 8)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 8)) 16)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (+.f64 -1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 4) -4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (*.f64 2 (+.f64 -1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 2 (*.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 8))) 32)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (neg.f64 (*.f64 2 (+.f64 -1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))) 4)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (+.f64 -1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))))))

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -2) 0)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 -1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -3) -1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/2 (*.f64 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -2) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 2 (*.f64 1/2 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 4 (/.f64 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -2) 4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -2) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -2) 4) 1/4)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/4 (*.f64 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -2) 4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 1/2 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -2)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -2) 4) 4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -2) 2) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -2) 4) 4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -2) 8) 8)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -2) 8)) 16)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 2 (*.f64 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -2) 8))) 32)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -2) 1)))))

simplify199.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

1724×	`rational.json-simplify-1`
1478×	`rational.json-simplify-35`
1022×	`rational.json-simplify-52`
798×	`rational.json-simplify-48`
738×	`rational.json-simplify-41`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	175	2981
1	387	2857
2	841	2671
3	2199	2671
4	3852	2671
5	4306	2671
6	5047	2671
7	6312	2671
8	7306	2671
9	7755	2671

Stop Event

1×	node limit

Counts

75 → 148

Calls

Call 1

Inputs
(*.f64 1/8 (pow.f64 x 2))
(+.f64 (.f64 1/8 (pow.f64 x 2)) (.f64 -11/128 (pow.f64 x 4)))
(+.f64 (.f64 1/8 (pow.f64 x 2)) (+.f64 (.f64 69/1024 (pow.f64 x 6)) (*.f64 -11/128 (pow.f64 x 4))))
(+.f64 (.f64 1/8 (pow.f64 x 2)) (+.f64 (.f64 69/1024 (pow.f64 x 6)) (+.f64 (.f64 -1843/32768 (pow.f64 x 8)) (.f64 -11/128 (pow.f64 x 4)))))
(-.f64 1 (sqrt.f64 1/2))
(-.f64 1 (+.f64 (sqrt.f64 1/2) (.f64 1/4 (/.f64 1 (.f64 (sqrt.f64 1/2) x)))))
(-.f64 (+.f64 1 (.f64 1/32 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 x 2))))) (+.f64 (sqrt.f64 1/2) (.f64 1/4 (/.f64 1 (.f64 (sqrt.f64 1/2) x)))))
(-.f64 (+.f64 1 (+.f64 (.f64 1/32 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 x 2)))) (.f64 -1/2 (/.f64 (-.f64 (.f64 1/64 (/.f64 1 (pow.f64 (sqrt.f64 1/2) 4))) 1/4) (.f64 (sqrt.f64 1/2) (pow.f64 x 3)))))) (+.f64 (sqrt.f64 1/2) (.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x)))))
(-.f64 1 (sqrt.f64 1/2))
(-.f64 (+.f64 1 (.f64 1/4 (/.f64 1 (.f64 (sqrt.f64 1/2) x)))) (sqrt.f64 1/2))
(-.f64 (+.f64 1 (+.f64 (.f64 1/4 (/.f64 1 (.f64 (sqrt.f64 1/2) x))) (.f64 1/32 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 x 2)))))) (sqrt.f64 1/2))
(-.f64 (+.f64 (.f64 1/2 (/.f64 (-.f64 (.f64 1/64 (/.f64 1 (pow.f64 (sqrt.f64 1/2) 4))) 1/4) (.f64 (sqrt.f64 1/2) (pow.f64 x 3)))) (+.f64 1 (+.f64 (.f64 1/4 (/.f64 1 (.f64 (sqrt.f64 1/2) x))) (.f64 1/32 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 x 2))))))) (sqrt.f64 1/2))
-1
(-.f64 (*.f64 -1/8 (pow.f64 x 2)) 1)
(-.f64 (+.f64 (.f64 -1/8 (pow.f64 x 2)) (.f64 11/128 (pow.f64 x 4))) 1)
(-.f64 (+.f64 (.f64 -1/8 (pow.f64 x 2)) (+.f64 (.f64 -69/1024 (pow.f64 x 6)) (*.f64 11/128 (pow.f64 x 4)))) 1)
(-.f64 (sqrt.f64 1/2) 2)
(-.f64 (+.f64 (sqrt.f64 1/2) (.f64 1/4 (/.f64 1 (.f64 (sqrt.f64 1/2) x)))) 2)
(-.f64 (+.f64 (sqrt.f64 1/2) (.f64 1/4 (/.f64 1 (.f64 (sqrt.f64 1/2) x)))) (+.f64 2 (.f64 1/32 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 x 2))))))
(-.f64 (+.f64 (.f64 1/2 (/.f64 (-.f64 (.f64 1/64 (/.f64 1 (pow.f64 (sqrt.f64 1/2) 4))) 1/4) (.f64 (sqrt.f64 1/2) (pow.f64 x 3)))) (+.f64 (sqrt.f64 1/2) (.f64 1/4 (/.f64 1 (.f64 (sqrt.f64 1/2) x))))) (+.f64 2 (.f64 1/32 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 x 2))))))
(-.f64 (sqrt.f64 1/2) 2)
(-.f64 (sqrt.f64 1/2) (+.f64 2 (.f64 1/4 (/.f64 1 (.f64 (sqrt.f64 1/2) x)))))
(-.f64 (sqrt.f64 1/2) (+.f64 2 (+.f64 (.f64 1/4 (/.f64 1 (.f64 (sqrt.f64 1/2) x))) (.f64 1/32 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 x 2)))))))
(-.f64 (+.f64 (sqrt.f64 1/2) (.f64 -1/2 (/.f64 (-.f64 (.f64 1/64 (/.f64 1 (pow.f64 (sqrt.f64 1/2) 4))) 1/4) (.f64 (sqrt.f64 1/2) (pow.f64 x 3))))) (+.f64 2 (+.f64 (.f64 1/4 (/.f64 1 (.f64 (sqrt.f64 1/2) x))) (.f64 1/32 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 x 2)))))))
(+.f64 -1 (neg.f64 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -2)))
(+.f64 -2 (-.f64 1 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -2)))
(+.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 0)
(+.f64 0 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
(+.f64 (neg.f64 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -2)) -1)
(+.f64 (/.f64 (+.f64 -1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) -2) (/.f64 (+.f64 -1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) -2))
(*.f64 -1 (+.f64 -1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
(.f64 1/2 (.f64 -2 (+.f64 -1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))
(*.f64 1 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
(*.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 1)
(*.f64 2 (/.f64 (+.f64 -1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) -2))
(.f64 (.f64 -2 (+.f64 -1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) 1/2)
(*.f64 4 (/.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 4))
(*.f64 (+.f64 -1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) -1)
(.f64 (.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 4) 1/4)
(.f64 1/4 (.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 4))
(*.f64 (/.f64 (+.f64 -1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) -2) 2)
(*.f64 (/.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 4) 4)
(/.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 1)
(/.f64 (*.f64 -2 (+.f64 -1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) 2)
(/.f64 (+.f64 -1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) -1)
(/.f64 (*.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 4) 4)
(/.f64 (*.f64 2 (+.f64 -1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) -2)
(/.f64 (*.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 8) 8)
(/.f64 (.f64 2 (.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 8)) 16)
(/.f64 (*.f64 (+.f64 -1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 4) -4)
(/.f64 (neg.f64 (*.f64 2 (+.f64 -1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))) 2)
(/.f64 (.f64 2 (.f64 2 (*.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 8))) 32)
(/.f64 (.f64 2 (neg.f64 (.f64 2 (+.f64 -1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))) 4)
(pow.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 1)
(neg.f64 (+.f64 -1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
(-.f64 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -2) 0)
(-.f64 (+.f64 -1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 1)
(-.f64 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -3) -1)
(.f64 1/2 (.f64 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -2) 2))
(*.f64 1 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -2))
(*.f64 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -2) 1)
(.f64 2 (.f64 1/2 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -2)))
(*.f64 4 (/.f64 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -2) 4))
(.f64 (.f64 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -2) 2) 1/2)
(.f64 (.f64 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -2) 4) 1/4)
(.f64 1/4 (.f64 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -2) 4))
(.f64 (.f64 1/2 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -2)) 2)
(*.f64 (/.f64 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -2) 4) 4)
(/.f64 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -2) 1)
(/.f64 (*.f64 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -2) 2) 2)
(/.f64 (*.f64 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -2) 4) 4)
(/.f64 (*.f64 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -2) 8) 8)
(/.f64 (.f64 2 (.f64 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -2) 8)) 16)
(/.f64 (.f64 2 (.f64 2 (*.f64 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -2) 8))) 32)
(pow.f64 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -2) 1)

Outputs
(*.f64 1/8 (pow.f64 x 2))
(+.f64 (.f64 1/8 (pow.f64 x 2)) (.f64 -11/128 (pow.f64 x 4)))
(+.f64 (.f64 1/8 (pow.f64 x 2)) (+.f64 (.f64 69/1024 (pow.f64 x 6)) (*.f64 -11/128 (pow.f64 x 4))))
(+.f64 (.f64 1/8 (pow.f64 x 2)) (+.f64 (.f64 -11/128 (pow.f64 x 4)) (*.f64 69/1024 (pow.f64 x 6))))
(+.f64 (.f64 -11/128 (pow.f64 x 4)) (+.f64 (.f64 1/8 (pow.f64 x 2)) (*.f64 69/1024 (pow.f64 x 6))))
(+.f64 (.f64 1/8 (pow.f64 x 2)) (+.f64 (.f64 69/1024 (pow.f64 x 6)) (+.f64 (.f64 -1843/32768 (pow.f64 x 8)) (.f64 -11/128 (pow.f64 x 4)))))
(+.f64 (.f64 1/8 (pow.f64 x 2)) (+.f64 (.f64 -1843/32768 (pow.f64 x 8)) (+.f64 (.f64 -11/128 (pow.f64 x 4)) (.f64 69/1024 (pow.f64 x 6)))))
(+.f64 (.f64 1/8 (pow.f64 x 2)) (+.f64 (.f64 -11/128 (pow.f64 x 4)) (+.f64 (.f64 69/1024 (pow.f64 x 6)) (.f64 -1843/32768 (pow.f64 x 8)))))
(+.f64 (.f64 -11/128 (pow.f64 x 4)) (+.f64 (+.f64 (.f64 69/1024 (pow.f64 x 6)) (.f64 -1843/32768 (pow.f64 x 8))) (.f64 1/8 (pow.f64 x 2))))
(+.f64 (.f64 -11/128 (pow.f64 x 4)) (+.f64 (.f64 1/8 (pow.f64 x 2)) (+.f64 (.f64 69/1024 (pow.f64 x 6)) (.f64 -1843/32768 (pow.f64 x 8)))))
(-.f64 1 (sqrt.f64 1/2))
(-.f64 1 (+.f64 (sqrt.f64 1/2) (.f64 1/4 (/.f64 1 (.f64 (sqrt.f64 1/2) x)))))
(-.f64 1 (+.f64 (sqrt.f64 1/2) (.f64 1/4 (/.f64 1 (.f64 x (sqrt.f64 1/2))))))
(-.f64 1 (+.f64 (sqrt.f64 1/2) (*.f64 1/4 (/.f64 (/.f64 1 (sqrt.f64 1/2)) x))))
(-.f64 (+.f64 1 (.f64 1/32 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 x 2))))) (+.f64 (sqrt.f64 1/2) (.f64 1/4 (/.f64 1 (.f64 (sqrt.f64 1/2) x)))))
(-.f64 (+.f64 1 (.f64 1/32 (/.f64 1 (.f64 (pow.f64 x 2) (sqrt.f64 1/8))))) (+.f64 (sqrt.f64 1/2) (.f64 1/4 (/.f64 1 (.f64 x (sqrt.f64 1/2))))))
(+.f64 (-.f64 1 (+.f64 (sqrt.f64 1/2) (.f64 1/4 (/.f64 1 (.f64 x (sqrt.f64 1/2)))))) (*.f64 1/32 (/.f64 (/.f64 1 (pow.f64 x 2)) (sqrt.f64 1/8))))
(+.f64 1 (-.f64 (.f64 1/32 (/.f64 (/.f64 1 (pow.f64 x 2)) (sqrt.f64 1/8))) (+.f64 (sqrt.f64 1/2) (.f64 1/4 (/.f64 (/.f64 1 (sqrt.f64 1/2)) x)))))
(+.f64 1 (-.f64 (.f64 1/32 (/.f64 (/.f64 1 (sqrt.f64 1/8)) (pow.f64 x 2))) (+.f64 (sqrt.f64 1/2) (.f64 1/4 (/.f64 (/.f64 1 (sqrt.f64 1/2)) x)))))
(+.f64 1 (-.f64 (.f64 1/32 (/.f64 (/.f64 1 (sqrt.f64 1/8)) (pow.f64 x 2))) (+.f64 (sqrt.f64 1/2) (.f64 1/4 (/.f64 1 (*.f64 x (sqrt.f64 1/2)))))))
(-.f64 (+.f64 1 (+.f64 (.f64 1/32 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 x 2)))) (.f64 -1/2 (/.f64 (-.f64 (.f64 1/64 (/.f64 1 (pow.f64 (sqrt.f64 1/2) 4))) 1/4) (.f64 (sqrt.f64 1/2) (pow.f64 x 3)))))) (+.f64 (sqrt.f64 1/2) (.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x)))))
(+.f64 (+.f64 (.f64 1/32 (/.f64 1 (.f64 (pow.f64 x 2) (sqrt.f64 1/8)))) (.f64 -1/2 (/.f64 -3/16 (.f64 (sqrt.f64 1/2) (pow.f64 x 3))))) (-.f64 1 (+.f64 (sqrt.f64 1/2) (.f64 1/4 (/.f64 1 (.f64 x (sqrt.f64 1/2)))))))
(+.f64 (-.f64 1 (+.f64 (sqrt.f64 1/2) (.f64 1/4 (/.f64 1 (.f64 x (sqrt.f64 1/2)))))) (+.f64 (.f64 1/32 (/.f64 (/.f64 1 (pow.f64 x 2)) (sqrt.f64 1/8))) (.f64 -1/2 (/.f64 -3/16 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3))))))
(+.f64 1 (+.f64 (.f64 1/32 (/.f64 (/.f64 1 (pow.f64 x 2)) (sqrt.f64 1/8))) (-.f64 (.f64 -1/2 (/.f64 (/.f64 -3/16 (sqrt.f64 1/2)) (pow.f64 x 3))) (+.f64 (sqrt.f64 1/2) (*.f64 1/4 (/.f64 (/.f64 1 (sqrt.f64 1/2)) x))))))
(+.f64 1 (+.f64 (.f64 -1/2 (/.f64 -3/16 (.f64 (sqrt.f64 1/2) (pow.f64 x 3)))) (-.f64 (.f64 1/32 (/.f64 (/.f64 1 (sqrt.f64 1/8)) (pow.f64 x 2))) (+.f64 (sqrt.f64 1/2) (.f64 1/4 (/.f64 (/.f64 1 (sqrt.f64 1/2)) x))))))
(+.f64 1 (+.f64 (.f64 -1/2 (/.f64 (sqrt.f64 1/2) (/.f64 (pow.f64 x 3) -3/8))) (-.f64 (.f64 1/32 (/.f64 (/.f64 1 (sqrt.f64 1/8)) (pow.f64 x 2))) (+.f64 (sqrt.f64 1/2) (*.f64 1/4 (/.f64 (/.f64 1 (sqrt.f64 1/2)) x))))))
(-.f64 (+.f64 1 (+.f64 (.f64 1/32 (/.f64 (/.f64 1 (sqrt.f64 1/8)) (pow.f64 x 2))) (.f64 -1/2 (/.f64 (sqrt.f64 1/2) (/.f64 (pow.f64 x 3) -3/8))))) (+.f64 (sqrt.f64 1/2) (.f64 1/4 (/.f64 1 (.f64 x (sqrt.f64 1/2))))))
(-.f64 1 (sqrt.f64 1/2))
(-.f64 (+.f64 1 (.f64 1/4 (/.f64 1 (.f64 (sqrt.f64 1/2) x)))) (sqrt.f64 1/2))
(+.f64 (.f64 1/4 (/.f64 1 (.f64 x (sqrt.f64 1/2)))) (-.f64 1 (sqrt.f64 1/2)))
(+.f64 1 (-.f64 (.f64 1/4 (/.f64 1 (.f64 x (sqrt.f64 1/2)))) (sqrt.f64 1/2)))
(+.f64 1 (-.f64 (*.f64 1/4 (/.f64 (/.f64 1 (sqrt.f64 1/2)) x)) (sqrt.f64 1/2)))
(-.f64 (+.f64 1 (+.f64 (.f64 1/4 (/.f64 1 (.f64 (sqrt.f64 1/2) x))) (.f64 1/32 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 x 2)))))) (sqrt.f64 1/2))
(+.f64 (+.f64 (.f64 1/4 (/.f64 1 (.f64 x (sqrt.f64 1/2)))) (.f64 1/32 (/.f64 1 (.f64 (pow.f64 x 2) (sqrt.f64 1/8))))) (-.f64 1 (sqrt.f64 1/2)))
(+.f64 (-.f64 1 (sqrt.f64 1/2)) (+.f64 (.f64 1/4 (/.f64 1 (.f64 x (sqrt.f64 1/2)))) (*.f64 1/32 (/.f64 (/.f64 1 (pow.f64 x 2)) (sqrt.f64 1/8)))))
(+.f64 (-.f64 1 (sqrt.f64 1/2)) (+.f64 (.f64 1/4 (/.f64 (/.f64 1 (sqrt.f64 1/2)) x)) (.f64 1/32 (/.f64 (/.f64 1 (pow.f64 x 2)) (sqrt.f64 1/8)))))
(+.f64 (.f64 1/32 (/.f64 (/.f64 1 (sqrt.f64 1/8)) (pow.f64 x 2))) (+.f64 1 (-.f64 (.f64 1/4 (/.f64 (/.f64 1 (sqrt.f64 1/2)) x)) (sqrt.f64 1/2))))
(+.f64 1 (+.f64 (.f64 1/32 (/.f64 (/.f64 1 (sqrt.f64 1/8)) (pow.f64 x 2))) (-.f64 (.f64 1/4 (/.f64 1 (*.f64 x (sqrt.f64 1/2)))) (sqrt.f64 1/2))))
(-.f64 (+.f64 (.f64 1/2 (/.f64 (-.f64 (.f64 1/64 (/.f64 1 (pow.f64 (sqrt.f64 1/2) 4))) 1/4) (.f64 (sqrt.f64 1/2) (pow.f64 x 3)))) (+.f64 1 (+.f64 (.f64 1/4 (/.f64 1 (.f64 (sqrt.f64 1/2) x))) (.f64 1/32 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 x 2))))))) (sqrt.f64 1/2))
(+.f64 (+.f64 1 (+.f64 (.f64 1/4 (/.f64 1 (.f64 x (sqrt.f64 1/2)))) (.f64 1/32 (/.f64 1 (.f64 (pow.f64 x 2) (sqrt.f64 1/8)))))) (-.f64 (.f64 1/2 (/.f64 -3/16 (.f64 (sqrt.f64 1/2) (pow.f64 x 3)))) (sqrt.f64 1/2)))
(+.f64 (+.f64 1 (+.f64 (.f64 1/4 (/.f64 1 (.f64 x (sqrt.f64 1/2)))) (.f64 1/32 (/.f64 (/.f64 1 (pow.f64 x 2)) (sqrt.f64 1/8))))) (-.f64 (.f64 1/2 (/.f64 -3/16 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3)))) (sqrt.f64 1/2)))
(+.f64 1 (+.f64 (+.f64 (.f64 1/4 (/.f64 (/.f64 1 (sqrt.f64 1/2)) x)) (.f64 1/32 (/.f64 (/.f64 1 (pow.f64 x 2)) (sqrt.f64 1/8)))) (-.f64 (*.f64 1/2 (/.f64 (/.f64 -3/16 (sqrt.f64 1/2)) (pow.f64 x 3))) (sqrt.f64 1/2))))
(+.f64 (.f64 1/4 (/.f64 (/.f64 1 (sqrt.f64 1/2)) x)) (+.f64 (+.f64 1 (.f64 1/32 (/.f64 (/.f64 1 (pow.f64 x 2)) (sqrt.f64 1/8)))) (-.f64 (*.f64 1/2 (/.f64 (/.f64 -3/16 (sqrt.f64 1/2)) (pow.f64 x 3))) (sqrt.f64 1/2))))
(+.f64 (.f64 1/4 (/.f64 (/.f64 1 (sqrt.f64 1/2)) x)) (+.f64 (.f64 1/2 (/.f64 (/.f64 -3/16 (sqrt.f64 1/2)) (pow.f64 x 3))) (+.f64 (-.f64 1 (sqrt.f64 1/2)) (*.f64 1/32 (/.f64 (/.f64 1 (pow.f64 x 2)) (sqrt.f64 1/8))))))
(+.f64 (.f64 1/32 (/.f64 (/.f64 1 (sqrt.f64 1/8)) (pow.f64 x 2))) (+.f64 (.f64 1/2 (/.f64 -3/16 (.f64 (sqrt.f64 1/2) (pow.f64 x 3)))) (+.f64 1 (-.f64 (.f64 1/4 (/.f64 (/.f64 1 (sqrt.f64 1/2)) x)) (sqrt.f64 1/2)))))
(+.f64 (.f64 1/32 (/.f64 (/.f64 1 (sqrt.f64 1/8)) (pow.f64 x 2))) (+.f64 (.f64 1/2 (/.f64 (sqrt.f64 1/2) (/.f64 (pow.f64 x 3) -3/8))) (+.f64 1 (-.f64 (*.f64 1/4 (/.f64 (/.f64 1 (sqrt.f64 1/2)) x)) (sqrt.f64 1/2)))))
(+.f64 1 (+.f64 (.f64 1/2 (/.f64 (sqrt.f64 1/2) (/.f64 (pow.f64 x 3) -3/8))) (+.f64 (.f64 1/32 (/.f64 (/.f64 1 (sqrt.f64 1/8)) (pow.f64 x 2))) (-.f64 (.f64 1/4 (/.f64 1 (.f64 x (sqrt.f64 1/2)))) (sqrt.f64 1/2)))))
-1
(-.f64 (*.f64 -1/8 (pow.f64 x 2)) 1)
(+.f64 (*.f64 (pow.f64 x 2) -1/8) -1)
(+.f64 -1 (*.f64 (pow.f64 x 2) -1/8))
(-.f64 (+.f64 (.f64 -1/8 (pow.f64 x 2)) (.f64 11/128 (pow.f64 x 4))) 1)
(+.f64 (.f64 (pow.f64 x 4) 11/128) (+.f64 (.f64 (pow.f64 x 2) -1/8) -1))
(+.f64 -1 (+.f64 (.f64 (pow.f64 x 2) -1/8) (.f64 (pow.f64 x 4) 11/128)))
(+.f64 (+.f64 -1 (.f64 (pow.f64 x 2) -1/8)) (.f64 (pow.f64 x 4) 11/128))
(-.f64 (+.f64 (.f64 -1/8 (pow.f64 x 2)) (+.f64 (.f64 -69/1024 (pow.f64 x 6)) (*.f64 11/128 (pow.f64 x 4)))) 1)
(+.f64 (+.f64 (.f64 (pow.f64 x 4) 11/128) (.f64 (pow.f64 x 6) -69/1024)) (+.f64 (*.f64 (pow.f64 x 2) -1/8) -1))
(+.f64 -1 (+.f64 (.f64 (pow.f64 x 2) -1/8) (+.f64 (.f64 (pow.f64 x 4) 11/128) (*.f64 (pow.f64 x 6) -69/1024))))
(+.f64 (+.f64 -1 (.f64 (pow.f64 x 2) -1/8)) (+.f64 (.f64 (pow.f64 x 4) 11/128) (*.f64 (pow.f64 x 6) -69/1024)))
(+.f64 (.f64 (pow.f64 x 4) 11/128) (+.f64 (+.f64 -1 (.f64 (pow.f64 x 2) -1/8)) (*.f64 (pow.f64 x 6) -69/1024)))
(-.f64 (sqrt.f64 1/2) 2)
(-.f64 (+.f64 (sqrt.f64 1/2) (.f64 1/4 (/.f64 1 (.f64 (sqrt.f64 1/2) x)))) 2)
(+.f64 (.f64 1/4 (/.f64 1 (.f64 x (sqrt.f64 1/2)))) (-.f64 (sqrt.f64 1/2) 2))
(+.f64 (sqrt.f64 1/2) (-.f64 (*.f64 1/4 (/.f64 (/.f64 1 (sqrt.f64 1/2)) x)) 2))
(+.f64 (sqrt.f64 1/2) (-.f64 (.f64 1/4 (/.f64 1 (.f64 x (sqrt.f64 1/2)))) 2))
(-.f64 (+.f64 (sqrt.f64 1/2) (.f64 1/4 (/.f64 1 (.f64 (sqrt.f64 1/2) x)))) (+.f64 2 (.f64 1/32 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 x 2))))))
(+.f64 (.f64 1/4 (/.f64 1 (.f64 x (sqrt.f64 1/2)))) (-.f64 (sqrt.f64 1/2) (+.f64 2 (.f64 1/32 (/.f64 1 (.f64 (pow.f64 x 2) (sqrt.f64 1/8)))))))
(+.f64 (sqrt.f64 1/2) (-.f64 (.f64 1/4 (/.f64 1 (.f64 x (sqrt.f64 1/2)))) (+.f64 2 (*.f64 1/32 (/.f64 (/.f64 1 (pow.f64 x 2)) (sqrt.f64 1/8))))))
(+.f64 (sqrt.f64 1/2) (-.f64 (.f64 1/4 (/.f64 (/.f64 1 (sqrt.f64 1/2)) x)) (+.f64 2 (.f64 1/32 (/.f64 (/.f64 1 (pow.f64 x 2)) (sqrt.f64 1/8))))))
(+.f64 (sqrt.f64 1/2) (-.f64 (.f64 1/4 (/.f64 (/.f64 1 (sqrt.f64 1/2)) x)) (+.f64 2 (.f64 1/32 (/.f64 (/.f64 1 (sqrt.f64 1/8)) (pow.f64 x 2))))))
(+.f64 (sqrt.f64 1/2) (-.f64 (.f64 1/4 (/.f64 1 (.f64 x (sqrt.f64 1/2)))) (+.f64 2 (*.f64 1/32 (/.f64 (/.f64 1 (sqrt.f64 1/8)) (pow.f64 x 2))))))
(-.f64 (+.f64 (.f64 1/2 (/.f64 (-.f64 (.f64 1/64 (/.f64 1 (pow.f64 (sqrt.f64 1/2) 4))) 1/4) (.f64 (sqrt.f64 1/2) (pow.f64 x 3)))) (+.f64 (sqrt.f64 1/2) (.f64 1/4 (/.f64 1 (.f64 (sqrt.f64 1/2) x))))) (+.f64 2 (.f64 1/32 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 x 2))))))
(+.f64 (+.f64 (sqrt.f64 1/2) (.f64 1/4 (/.f64 1 (.f64 x (sqrt.f64 1/2))))) (-.f64 (.f64 1/2 (/.f64 -3/16 (.f64 (sqrt.f64 1/2) (pow.f64 x 3)))) (+.f64 2 (.f64 1/32 (/.f64 1 (.f64 (pow.f64 x 2) (sqrt.f64 1/8)))))))
(+.f64 (+.f64 (sqrt.f64 1/2) (.f64 1/4 (/.f64 1 (.f64 x (sqrt.f64 1/2))))) (-.f64 (.f64 1/2 (/.f64 -3/16 (.f64 (sqrt.f64 1/2) (pow.f64 x 3)))) (+.f64 2 (*.f64 1/32 (/.f64 (/.f64 1 (pow.f64 x 2)) (sqrt.f64 1/8))))))
(+.f64 (sqrt.f64 1/2) (+.f64 (-.f64 (.f64 1/4 (/.f64 (/.f64 1 (sqrt.f64 1/2)) x)) (+.f64 2 (.f64 1/32 (/.f64 (/.f64 1 (pow.f64 x 2)) (sqrt.f64 1/8))))) (*.f64 1/2 (/.f64 (/.f64 -3/16 (sqrt.f64 1/2)) (pow.f64 x 3)))))
(+.f64 (sqrt.f64 1/2) (+.f64 (.f64 1/2 (/.f64 (/.f64 -3/16 (sqrt.f64 1/2)) (pow.f64 x 3))) (-.f64 (.f64 1/4 (/.f64 (/.f64 1 (sqrt.f64 1/2)) x)) (+.f64 2 (*.f64 1/32 (/.f64 (/.f64 1 (pow.f64 x 2)) (sqrt.f64 1/8)))))))
(+.f64 (sqrt.f64 1/2) (+.f64 (.f64 1/4 (/.f64 (/.f64 1 (sqrt.f64 1/2)) x)) (-.f64 (.f64 1/2 (/.f64 -3/16 (.f64 (sqrt.f64 1/2) (pow.f64 x 3)))) (+.f64 2 (.f64 1/32 (/.f64 (/.f64 1 (sqrt.f64 1/8)) (pow.f64 x 2)))))))
(+.f64 (sqrt.f64 1/2) (+.f64 (.f64 1/4 (/.f64 (/.f64 1 (sqrt.f64 1/2)) x)) (-.f64 (.f64 1/2 (/.f64 (sqrt.f64 1/2) (/.f64 (pow.f64 x 3) -3/8))) (+.f64 2 (*.f64 1/32 (/.f64 (/.f64 1 (sqrt.f64 1/8)) (pow.f64 x 2)))))))
(+.f64 (sqrt.f64 1/2) (+.f64 (.f64 1/4 (/.f64 1 (.f64 x (sqrt.f64 1/2)))) (-.f64 (.f64 1/2 (/.f64 (sqrt.f64 1/2) (/.f64 (pow.f64 x 3) -3/8))) (+.f64 2 (.f64 1/32 (/.f64 (/.f64 1 (sqrt.f64 1/8)) (pow.f64 x 2)))))))
(-.f64 (sqrt.f64 1/2) 2)
(-.f64 (sqrt.f64 1/2) (+.f64 2 (.f64 1/4 (/.f64 1 (.f64 (sqrt.f64 1/2) x)))))
(-.f64 (sqrt.f64 1/2) (+.f64 2 (.f64 1/4 (/.f64 1 (.f64 x (sqrt.f64 1/2))))))
(-.f64 (sqrt.f64 1/2) (+.f64 2 (*.f64 1/4 (/.f64 (/.f64 1 (sqrt.f64 1/2)) x))))
(-.f64 (sqrt.f64 1/2) (+.f64 2 (+.f64 (.f64 1/4 (/.f64 1 (.f64 (sqrt.f64 1/2) x))) (.f64 1/32 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 x 2)))))))
(-.f64 (sqrt.f64 1/2) (+.f64 2 (+.f64 (.f64 1/4 (/.f64 1 (.f64 x (sqrt.f64 1/2)))) (.f64 1/32 (/.f64 1 (.f64 (pow.f64 x 2) (sqrt.f64 1/8)))))))
(-.f64 (sqrt.f64 1/2) (+.f64 (.f64 1/4 (/.f64 1 (.f64 x (sqrt.f64 1/2)))) (+.f64 2 (*.f64 1/32 (/.f64 (/.f64 1 (pow.f64 x 2)) (sqrt.f64 1/8))))))
(-.f64 (sqrt.f64 1/2) (+.f64 2 (+.f64 (.f64 1/4 (/.f64 (/.f64 1 (sqrt.f64 1/2)) x)) (.f64 1/32 (/.f64 (/.f64 1 (pow.f64 x 2)) (sqrt.f64 1/8))))))
(-.f64 (sqrt.f64 1/2) (+.f64 (.f64 1/32 (/.f64 (/.f64 1 (sqrt.f64 1/8)) (pow.f64 x 2))) (+.f64 2 (.f64 1/4 (/.f64 (/.f64 1 (sqrt.f64 1/2)) x)))))
(-.f64 (sqrt.f64 1/2) (+.f64 2 (+.f64 (.f64 1/4 (/.f64 1 (.f64 x (sqrt.f64 1/2)))) (*.f64 1/32 (/.f64 (/.f64 1 (sqrt.f64 1/8)) (pow.f64 x 2))))))
(-.f64 (+.f64 (sqrt.f64 1/2) (.f64 -1/2 (/.f64 (-.f64 (.f64 1/64 (/.f64 1 (pow.f64 (sqrt.f64 1/2) 4))) 1/4) (.f64 (sqrt.f64 1/2) (pow.f64 x 3))))) (+.f64 2 (+.f64 (.f64 1/4 (/.f64 1 (.f64 (sqrt.f64 1/2) x))) (.f64 1/32 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 x 2)))))))
(+.f64 (.f64 -1/2 (/.f64 -3/16 (.f64 (sqrt.f64 1/2) (pow.f64 x 3)))) (-.f64 (sqrt.f64 1/2) (+.f64 2 (+.f64 (.f64 1/4 (/.f64 1 (.f64 x (sqrt.f64 1/2)))) (.f64 1/32 (/.f64 1 (.f64 (pow.f64 x 2) (sqrt.f64 1/8))))))))
(+.f64 (sqrt.f64 1/2) (-.f64 (.f64 -1/2 (/.f64 -3/16 (.f64 (sqrt.f64 1/2) (pow.f64 x 3)))) (+.f64 (.f64 1/4 (/.f64 1 (.f64 x (sqrt.f64 1/2)))) (+.f64 2 (*.f64 1/32 (/.f64 (/.f64 1 (pow.f64 x 2)) (sqrt.f64 1/8)))))))
(+.f64 (sqrt.f64 1/2) (-.f64 (.f64 -1/2 (/.f64 (/.f64 -3/16 (sqrt.f64 1/2)) (pow.f64 x 3))) (+.f64 2 (+.f64 (.f64 1/4 (/.f64 (/.f64 1 (sqrt.f64 1/2)) x)) (*.f64 1/32 (/.f64 (/.f64 1 (pow.f64 x 2)) (sqrt.f64 1/8)))))))
(+.f64 (sqrt.f64 1/2) (-.f64 (.f64 -1/2 (/.f64 -3/16 (.f64 (sqrt.f64 1/2) (pow.f64 x 3)))) (+.f64 (.f64 1/32 (/.f64 (/.f64 1 (sqrt.f64 1/8)) (pow.f64 x 2))) (+.f64 2 (.f64 1/4 (/.f64 (/.f64 1 (sqrt.f64 1/2)) x))))))
(+.f64 (sqrt.f64 1/2) (-.f64 (.f64 -1/2 (/.f64 (sqrt.f64 1/2) (/.f64 (pow.f64 x 3) -3/8))) (+.f64 (.f64 1/32 (/.f64 (/.f64 1 (sqrt.f64 1/8)) (pow.f64 x 2))) (+.f64 2 (*.f64 1/4 (/.f64 (/.f64 1 (sqrt.f64 1/2)) x))))))
(+.f64 (sqrt.f64 1/2) (-.f64 (.f64 -1/2 (/.f64 (sqrt.f64 1/2) (/.f64 (pow.f64 x 3) -3/8))) (+.f64 2 (+.f64 (.f64 1/4 (/.f64 1 (.f64 x (sqrt.f64 1/2)))) (.f64 1/32 (/.f64 (/.f64 1 (sqrt.f64 1/8)) (pow.f64 x 2)))))))
(+.f64 -1 (neg.f64 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -2)))
(-.f64 -1 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -2))
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
(+.f64 -2 (-.f64 1 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -2)))
(+.f64 -1 (neg.f64 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -2)))
(-.f64 -1 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -2))
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
(+.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 0)
(+.f64 -1 (neg.f64 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -2)))
(-.f64 -1 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -2))
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
(+.f64 0 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
(+.f64 -1 (neg.f64 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -2)))
(-.f64 -1 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -2))
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
(+.f64 (neg.f64 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -2)) -1)
(+.f64 -1 (neg.f64 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -2)))
(-.f64 -1 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -2))
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
(+.f64 (/.f64 (+.f64 -1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) -2) (/.f64 (+.f64 -1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) -2))
(+.f64 -1 (neg.f64 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -2)))
(-.f64 -1 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -2))
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
(*.f64 -1 (+.f64 -1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
(+.f64 -1 (neg.f64 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -2)))
(-.f64 -1 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -2))
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
(.f64 1/2 (.f64 -2 (+.f64 -1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))
(+.f64 -1 (neg.f64 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -2)))
(-.f64 -1 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -2))
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
(*.f64 1 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
(+.f64 -1 (neg.f64 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -2)))
(-.f64 -1 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -2))
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
(*.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 1)
(+.f64 -1 (neg.f64 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -2)))
(-.f64 -1 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -2))
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
(*.f64 2 (/.f64 (+.f64 -1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) -2))
(+.f64 -1 (neg.f64 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -2)))
(-.f64 -1 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -2))
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
(.f64 (.f64 -2 (+.f64 -1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) 1/2)
(+.f64 -1 (neg.f64 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -2)))
(-.f64 -1 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -2))
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
(*.f64 4 (/.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 4))
(+.f64 -1 (neg.f64 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -2)))
(-.f64 -1 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -2))
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
(*.f64 (+.f64 -1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) -1)
(+.f64 -1 (neg.f64 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -2)))
(-.f64 -1 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -2))
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
(.f64 (.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 4) 1/4)
(+.f64 -1 (neg.f64 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -2)))
(-.f64 -1 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -2))
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
(.f64 1/4 (.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 4))
(+.f64 -1 (neg.f64 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -2)))
(-.f64 -1 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -2))
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
(*.f64 (/.f64 (+.f64 -1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) -2) 2)
(+.f64 -1 (neg.f64 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -2)))
(-.f64 -1 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -2))
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
(*.f64 (/.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 4) 4)
(+.f64 -1 (neg.f64 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -2)))
(-.f64 -1 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -2))
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
(/.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 1)
(+.f64 -1 (neg.f64 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -2)))
(-.f64 -1 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -2))
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
(/.f64 (*.f64 -2 (+.f64 -1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) 2)
(+.f64 -1 (neg.f64 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -2)))
(-.f64 -1 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -2))
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
(/.f64 (+.f64 -1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) -1)
(+.f64 -1 (neg.f64 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -2)))
(-.f64 -1 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -2))
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
(/.f64 (*.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 4) 4)
(+.f64 -1 (neg.f64 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -2)))
(-.f64 -1 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -2))
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
(/.f64 (*.f64 2 (+.f64 -1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) -2)
(+.f64 -1 (neg.f64 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -2)))
(-.f64 -1 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -2))
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
(/.f64 (*.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 8) 8)
(+.f64 -1 (neg.f64 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -2)))
(-.f64 -1 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -2))
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
(/.f64 (.f64 2 (.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 8)) 16)
(+.f64 -1 (neg.f64 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -2)))
(-.f64 -1 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -2))
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
(/.f64 (*.f64 (+.f64 -1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 4) -4)
(+.f64 -1 (neg.f64 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -2)))
(-.f64 -1 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -2))
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
(/.f64 (neg.f64 (*.f64 2 (+.f64 -1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))) 2)
(+.f64 -1 (neg.f64 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -2)))
(-.f64 -1 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -2))
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
(/.f64 (.f64 2 (.f64 2 (*.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 8))) 32)
(+.f64 -1 (neg.f64 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -2)))
(-.f64 -1 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -2))
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
(/.f64 (.f64 2 (neg.f64 (.f64 2 (+.f64 -1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))) 4)
(+.f64 -1 (neg.f64 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -2)))
(-.f64 -1 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -2))
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
(pow.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 1)
(+.f64 -1 (neg.f64 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -2)))
(-.f64 -1 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -2))
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
(neg.f64 (+.f64 -1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
(+.f64 -1 (neg.f64 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -2)))
(-.f64 -1 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -2))
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
(-.f64 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -2) 0)
(+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -2)
(-.f64 (+.f64 -1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 1)
(+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -2)
(-.f64 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -3) -1)
(+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -2)
(.f64 1/2 (.f64 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -2) 2))
(+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -2)
(*.f64 1 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -2))
(+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -2)
(*.f64 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -2) 1)
(+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -2)
(.f64 2 (.f64 1/2 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -2)))
(+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -2)
(*.f64 4 (/.f64 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -2) 4))
(+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -2)
(.f64 (.f64 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -2) 2) 1/2)
(+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -2)
(.f64 (.f64 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -2) 4) 1/4)
(+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -2)
(.f64 1/4 (.f64 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -2) 4))
(+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -2)
(.f64 (.f64 1/2 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -2)) 2)
(+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -2)
(*.f64 (/.f64 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -2) 4) 4)
(+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -2)
(/.f64 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -2) 1)
(+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -2)
(/.f64 (*.f64 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -2) 2) 2)
(+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -2)
(/.f64 (*.f64 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -2) 4) 4)
(+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -2)
(/.f64 (*.f64 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -2) 8) 8)
(+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -2)
(/.f64 (.f64 2 (.f64 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -2) 8)) 16)
(+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -2)
(/.f64 (.f64 2 (.f64 2 (*.f64 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -2) 8))) 32)
(+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -2)
(pow.f64 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -2) 1)
(+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -2)

localize55.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (.f64 -1/2 (/.f64 (sqrt.f64 1/2) x)) (+.f64 1 (-.f64 (.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (sqrt.f64 1/2))))
✓	0.2b	(/.f64 (sqrt.f64 1/2) (pow.f64 x 2))
✓	0.4b	(/.f64 (sqrt.f64 1/2) x)
✓	0.5b	(+.f64 1 (-.f64 (*.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (sqrt.f64 1/2)))

Compiler

Compiled 80 to 70 computations (12.5% saved)

series3.0ms (0%)

Counts

4 → 24

Calls

12 calls:

Time	Variable		Point	Expression
1.0ms	x	@	0	(+.f64 1 (-.f64 (*.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (sqrt.f64 1/2)))
1.0ms	x	@	-inf	(+.f64 1 (-.f64 (*.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (sqrt.f64 1/2)))
0.0ms	x	@	-inf	(/.f64 (sqrt.f64 1/2) x)
0.0ms	x	@	inf	(+.f64 1 (-.f64 (*.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (sqrt.f64 1/2)))
0.0ms	x	@	inf	(/.f64 (sqrt.f64 1/2) x)

rewrite199.0ms (1.7%)

Algorithm

1×	batch-egg-rewrite

Rules

1812×	`rational.json-1`
1812×	`rational.json-2`
1812×	`rational.json-4`
1812×	`rational.json-3`
1800×	`exponential.json-3`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	18	128
1	131	128
2	284	128
3	646	128
4	1711	126
5	5325	126

Stop Event

1×	node limit

Counts

4 → 112

Calls

Call 1

Inputs
(+.f64 1 (-.f64 (*.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (sqrt.f64 1/2)))
(/.f64 (sqrt.f64 1/2) x)
(/.f64 (sqrt.f64 1/2) (pow.f64 x 2))
(+.f64 (.f64 -1/2 (/.f64 (sqrt.f64 1/2) x)) (+.f64 1 (-.f64 (.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (sqrt.f64 1/2))))

Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 1 (-.f64 (sqrt.f64 1/2) (.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (+.f64 (sqrt.f64 1/2) -1))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (-.f64 (.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (sqrt.f64 1/2)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (-.f64 (.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (sqrt.f64 1/2))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 0 (+.f64 (sqrt.f64 1/2) (-.f64 -1 (.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2)))) (sqrt.f64 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (+.f64 1 (-.f64 (.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (sqrt.f64 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1/2 (+.f64 (.f64 2 (-.f64 (.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (sqrt.f64 1/2))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 2 (/.f64 (+.f64 1 (-.f64 (.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (sqrt.f64 1/2))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 2 (.f64 (/.f64 (+.f64 1 (-.f64 (.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (sqrt.f64 1/2))) 2) 1))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (+.f64 1 (-.f64 (.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (sqrt.f64 1/2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (+.f64 (.f64 2 (-.f64 (.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (sqrt.f64 1/2))) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (+.f64 (sqrt.f64 1/2) (-.f64 -1 (.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (+.f64 1 (-.f64 (.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (sqrt.f64 1/2))) 2) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1 (-.f64 (.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (sqrt.f64 1/2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (.f64 2 (-.f64 (.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (sqrt.f64 1/2))) 2) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (+.f64 1 (-.f64 (.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (sqrt.f64 1/2))) 4) 4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (sqrt.f64 1/2) (-.f64 -1 (.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 2 (.f64 (+.f64 1 (-.f64 (.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (sqrt.f64 1/2))) 4)) 8)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (.f64 2 (.f64 (+.f64 1 (-.f64 (.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (sqrt.f64 1/2))) 4)) (.f64 2 (.f64 (+.f64 1 (-.f64 (.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (sqrt.f64 1/2))) 4))) 16)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 1 (-.f64 (.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (sqrt.f64 1/2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (+.f64 (sqrt.f64 1/2) (-.f64 -1 (.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))))))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 (sqrt.f64 1/2) x) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 (sqrt.f64 1/2) x))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 (sqrt.f64 1/2) (+.f64 x x)) (/.f64 (sqrt.f64 1/2) (+.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (sqrt.f64 1/2) x) 0)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (/.f64 (sqrt.f64 1/2) x))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1/2 (.f64 (sqrt.f64 1/2) (/.f64 2 x)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 1/2) (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 1/2) (.f64 2 (/.f64 1/2 x)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 1/2) (.f64 (.f64 2 (/.f64 1 x)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 1/2) (.f64 (/.f64 2 x) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 2 (/.f64 (sqrt.f64 1/2) (+.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 2 (.f64 (/.f64 (sqrt.f64 1/2) (+.f64 x x)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 2 (.f64 (/.f64 (sqrt.f64 1/2) x) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 2 (.f64 (/.f64 (sqrt.f64 1/2) 2) (/.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 2 (.f64 (sqrt.f64 1/2) (/.f64 1/2 x)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 2 (.f64 (/.f64 1/2 x) (sqrt.f64 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (sqrt.f64 1/2) x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 -1 (/.f64 (neg.f64 (sqrt.f64 1/2)) x))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (sqrt.f64 1/2) 2) (/.f64 1/2 x))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (sqrt.f64 1/2) 2) (.f64 1/2 (/.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (sqrt.f64 1/2) 2) (.f64 (.f64 1/2 (/.f64 1 x)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (sqrt.f64 1/2) 2) (.f64 (.f64 2 (/.f64 1/2 x)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (neg.f64 (sqrt.f64 1/2)) x) -1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (sqrt.f64 1/2) 4) (/.f64 1/2 (+.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (sqrt.f64 1/2) 4) (.f64 (/.f64 1/2 (+.f64 x x)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (sqrt.f64 1/2) 4) (.f64 1/4 (/.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (sqrt.f64 1/2) 4) (.f64 1/2 (/.f64 1/2 x)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (sqrt.f64 1/2) (/.f64 2 x)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1 x) (sqrt.f64 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (neg.f64 (sqrt.f64 1/2)) (/.f64 -1 x))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (neg.f64 (sqrt.f64 1/2)) (.f64 (/.f64 -1 x) 1))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1/2 x) (.f64 (sqrt.f64 1/2) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 1/2 (/.f64 1 x)) (.f64 (sqrt.f64 1/2) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (sqrt.f64 1/2) (+.f64 x x)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1/2 (+.f64 x x)) (.f64 (sqrt.f64 1/2) 4))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 -1 x) (neg.f64 (sqrt.f64 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (sqrt.f64 1/2) x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (neg.f64 (sqrt.f64 1/2)) x))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 (sqrt.f64 1/2) (.f64 2 (pow.f64 x 2))) (/.f64 (sqrt.f64 1/2) (.f64 2 (pow.f64 x 2))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1/2 (.f64 2 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 1/2) (/.f64 1 (pow.f64 x 2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 1/2) (.f64 2 (/.f64 1/2 (pow.f64 x 2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 1/2) (.f64 (.f64 2 (/.f64 1 (pow.f64 x 2))) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 1/2) (.f64 (/.f64 2 (pow.f64 x 2)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 2 (/.f64 (sqrt.f64 1/2) (.f64 2 (pow.f64 x 2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 2 (.f64 (/.f64 (sqrt.f64 1/2) 2) (/.f64 1 (pow.f64 x 2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 2 (.f64 (sqrt.f64 1/2) (/.f64 1/2 (pow.f64 x 2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 2 (.f64 (/.f64 1/2 (pow.f64 x 2)) (sqrt.f64 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 -1 (/.f64 (sqrt.f64 1/2) (neg.f64 (pow.f64 x 2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 -1 (.f64 (/.f64 (sqrt.f64 1/2) (neg.f64 (pow.f64 x 2))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (sqrt.f64 1/2) 2) (/.f64 1/2 (pow.f64 x 2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (sqrt.f64 1/2) 2) (.f64 1/2 (/.f64 1 (pow.f64 x 2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (sqrt.f64 1/2) 2) (.f64 (.f64 1/2 (/.f64 1 (pow.f64 x 2))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (sqrt.f64 1/2) 2) (.f64 (.f64 2 (/.f64 1/2 (pow.f64 x 2))) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 2 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (sqrt.f64 1/2) 4) (/.f64 1 (.f64 (pow.f64 x 2) 4)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (sqrt.f64 1/2) 4) (.f64 (/.f64 1 (.f64 (pow.f64 x 2) 4)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (sqrt.f64 1/2) 4) (.f64 1/4 (/.f64 1 (pow.f64 x 2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (sqrt.f64 1/2) 4) (.f64 1/2 (/.f64 1/2 (pow.f64 x 2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1 (pow.f64 x 2)) (sqrt.f64 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (neg.f64 (sqrt.f64 1/2)) (/.f64 -1 (pow.f64 x 2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (neg.f64 (sqrt.f64 1/2)) (.f64 (/.f64 -1 (pow.f64 x 2)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1/2 (pow.f64 x 2)) (.f64 (sqrt.f64 1/2) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 1/2 (/.f64 1 (pow.f64 x 2))) (.f64 (sqrt.f64 1/2) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (sqrt.f64 1/2) (neg.f64 (pow.f64 x 2))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (sqrt.f64 1/2) (.f64 2 (pow.f64 x 2))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1 (.f64 (pow.f64 x 2) 4)) (.f64 (sqrt.f64 1/2) 4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 -1 (pow.f64 x 2)) (neg.f64 (sqrt.f64 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (sqrt.f64 1/2) (neg.f64 (pow.f64 x 2))))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (.f64 (sqrt.f64 1/2) (+.f64 (.f64 -1/2 (/.f64 1 x)) (+.f64 (.f64 1/8 (/.f64 1 (pow.f64 x 2))) -1)))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (.f64 (sqrt.f64 1/2) (+.f64 (.f64 -1/2 (/.f64 1 x)) (+.f64 (.f64 1/8 (/.f64 1 (pow.f64 x 2))) -1))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (+.f64 1 (.f64 (sqrt.f64 1/2) (+.f64 (.f64 -1/2 (/.f64 1 x)) (+.f64 (.f64 1/8 (/.f64 1 (pow.f64 x 2))) -1)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1/2 (+.f64 (.f64 2 (.f64 (sqrt.f64 1/2) (+.f64 (.f64 -1/2 (/.f64 1 x)) (+.f64 (.f64 1/8 (/.f64 1 (pow.f64 x 2))) -1)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 2 (/.f64 (+.f64 1 (.f64 (sqrt.f64 1/2) (+.f64 (.f64 -1/2 (/.f64 1 x)) (+.f64 (.f64 1/8 (/.f64 1 (pow.f64 x 2))) -1)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 2 (.f64 (/.f64 (+.f64 1 (.f64 (sqrt.f64 1/2) (+.f64 (.f64 -1/2 (/.f64 1 x)) (+.f64 (.f64 1/8 (/.f64 1 (pow.f64 x 2))) -1)))) 2) 1))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (+.f64 1 (.f64 (sqrt.f64 1/2) (+.f64 (.f64 -1/2 (/.f64 1 x)) (+.f64 (.f64 1/8 (/.f64 1 (pow.f64 x 2))) -1)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (+.f64 (.f64 2 (.f64 (sqrt.f64 1/2) (+.f64 (.f64 -1/2 (/.f64 1 x)) (+.f64 (.f64 1/8 (/.f64 1 (pow.f64 x 2))) -1)))) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (+.f64 1 (.f64 (sqrt.f64 1/2) (+.f64 (.f64 -1/2 (/.f64 1 x)) (+.f64 (.f64 1/8 (/.f64 1 (pow.f64 x 2))) -1)))) 2) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1 (.f64 (sqrt.f64 1/2) (+.f64 (.f64 -1/2 (/.f64 1 x)) (+.f64 (.f64 1/8 (/.f64 1 (pow.f64 x 2))) -1)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (.f64 2 (.f64 (sqrt.f64 1/2) (+.f64 (.f64 -1/2 (/.f64 1 x)) (+.f64 (.f64 1/8 (/.f64 1 (pow.f64 x 2))) -1)))) 2) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (+.f64 1 (.f64 (sqrt.f64 1/2) (+.f64 (.f64 -1/2 (/.f64 1 x)) (+.f64 (.f64 1/8 (/.f64 1 (pow.f64 x 2))) -1)))) 4) 4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 2 (.f64 (+.f64 1 (.f64 (sqrt.f64 1/2) (+.f64 (.f64 -1/2 (/.f64 1 x)) (+.f64 (.f64 1/8 (/.f64 1 (pow.f64 x 2))) -1)))) 4)) 8)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (.f64 2 (.f64 (+.f64 1 (.f64 (sqrt.f64 1/2) (+.f64 (.f64 -1/2 (/.f64 1 x)) (+.f64 (.f64 1/8 (/.f64 1 (pow.f64 x 2))) -1)))) 4)) (.f64 2 (.f64 (+.f64 1 (.f64 (sqrt.f64 1/2) (+.f64 (.f64 -1/2 (/.f64 1 x)) (+.f64 (.f64 1/8 (/.f64 1 (pow.f64 x 2))) -1)))) 4))) 16)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 1 (.f64 (sqrt.f64 1/2) (+.f64 (.f64 -1/2 (/.f64 1 x)) (+.f64 (.f64 1/8 (/.f64 1 (pow.f64 x 2))) -1)))) 1)))))

simplify128.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

1534×	`rational.json-simplify-35`
1178×	`rational.json-simplify-2`
984×	`rational.json-simplify-61`
926×	`rational.json-simplify-1`
834×	`rational.json-simplify-46`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	221	4252
1	440	4234
2	849	4042
3	1989	4042
4	3977	4042
5	6521	4042

Stop Event

1×	node limit

Counts

136 → 142

Calls

Call 1

Inputs
(*.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2)))
(-.f64 (+.f64 1 (*.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2)))) (sqrt.f64 1/2))
(-.f64 (+.f64 1 (*.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2)))) (sqrt.f64 1/2))
(-.f64 (+.f64 1 (*.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2)))) (sqrt.f64 1/2))
(-.f64 1 (sqrt.f64 1/2))
(-.f64 (+.f64 1 (*.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2)))) (sqrt.f64 1/2))
(-.f64 (+.f64 1 (*.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2)))) (sqrt.f64 1/2))
(-.f64 (+.f64 1 (*.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2)))) (sqrt.f64 1/2))
(-.f64 1 (sqrt.f64 1/2))
(-.f64 (+.f64 1 (*.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2)))) (sqrt.f64 1/2))
(-.f64 (+.f64 1 (*.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2)))) (sqrt.f64 1/2))
(-.f64 (+.f64 1 (*.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2)))) (sqrt.f64 1/2))
(*.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2)))
(+.f64 (.f64 -1/2 (/.f64 (sqrt.f64 1/2) x)) (.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))))
(-.f64 (+.f64 1 (+.f64 (.f64 -1/2 (/.f64 (sqrt.f64 1/2) x)) (.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))))) (sqrt.f64 1/2))
(-.f64 (+.f64 1 (+.f64 (.f64 -1/2 (/.f64 (sqrt.f64 1/2) x)) (.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))))) (sqrt.f64 1/2))
(-.f64 1 (sqrt.f64 1/2))
(-.f64 (+.f64 1 (*.f64 -1/2 (/.f64 (sqrt.f64 1/2) x))) (sqrt.f64 1/2))
(-.f64 (+.f64 1 (+.f64 (.f64 -1/2 (/.f64 (sqrt.f64 1/2) x)) (.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))))) (sqrt.f64 1/2))
(-.f64 (+.f64 1 (+.f64 (.f64 -1/2 (/.f64 (sqrt.f64 1/2) x)) (.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))))) (sqrt.f64 1/2))
(-.f64 1 (sqrt.f64 1/2))
(-.f64 (+.f64 1 (*.f64 -1/2 (/.f64 (sqrt.f64 1/2) x))) (sqrt.f64 1/2))
(-.f64 (+.f64 1 (+.f64 (.f64 -1/2 (/.f64 (sqrt.f64 1/2) x)) (.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))))) (sqrt.f64 1/2))
(-.f64 (+.f64 1 (+.f64 (.f64 -1/2 (/.f64 (sqrt.f64 1/2) x)) (.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))))) (sqrt.f64 1/2))
(-.f64 1 (-.f64 (sqrt.f64 1/2) (*.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2)))))
(-.f64 (*.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (+.f64 (sqrt.f64 1/2) -1))
(-.f64 (-.f64 (*.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (sqrt.f64 1/2)) -1)
(-.f64 (+.f64 1 (-.f64 (*.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (sqrt.f64 1/2))) 0)
(-.f64 0 (+.f64 (sqrt.f64 1/2) (-.f64 -1 (*.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))))))
(-.f64 (+.f64 1 (*.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2)))) (sqrt.f64 1/2))
(.f64 1 (+.f64 1 (-.f64 (.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (sqrt.f64 1/2))))
(.f64 1/2 (+.f64 (.f64 2 (-.f64 (*.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (sqrt.f64 1/2))) 2))
(.f64 2 (/.f64 (+.f64 1 (-.f64 (.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (sqrt.f64 1/2))) 2))
(.f64 2 (.f64 (/.f64 (+.f64 1 (-.f64 (*.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (sqrt.f64 1/2))) 2) 1))
(.f64 (+.f64 1 (-.f64 (.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (sqrt.f64 1/2))) 1)
(.f64 (+.f64 (.f64 2 (-.f64 (*.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (sqrt.f64 1/2))) 2) 1/2)
(.f64 (+.f64 (sqrt.f64 1/2) (-.f64 -1 (.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))))) -1)
(.f64 (/.f64 (+.f64 1 (-.f64 (.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (sqrt.f64 1/2))) 2) 2)
(/.f64 (+.f64 1 (-.f64 (*.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (sqrt.f64 1/2))) 1)
(/.f64 (+.f64 (.f64 2 (-.f64 (.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (sqrt.f64 1/2))) 2) 2)
(/.f64 (.f64 (+.f64 1 (-.f64 (.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (sqrt.f64 1/2))) 4) 4)
(/.f64 (+.f64 (sqrt.f64 1/2) (-.f64 -1 (*.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))))) -1)
(/.f64 (.f64 2 (.f64 (+.f64 1 (-.f64 (*.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (sqrt.f64 1/2))) 4)) 8)
(/.f64 (+.f64 (.f64 2 (.f64 (+.f64 1 (-.f64 (.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (sqrt.f64 1/2))) 4)) (.f64 2 (.f64 (+.f64 1 (-.f64 (.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (sqrt.f64 1/2))) 4))) 16)
(pow.f64 (+.f64 1 (-.f64 (*.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (sqrt.f64 1/2))) 1)
(neg.f64 (+.f64 (sqrt.f64 1/2) (-.f64 -1 (*.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))))))
(+.f64 (/.f64 (sqrt.f64 1/2) x) 0)
(+.f64 0 (/.f64 (sqrt.f64 1/2) x))
(+.f64 (/.f64 (sqrt.f64 1/2) (+.f64 x x)) (/.f64 (sqrt.f64 1/2) (+.f64 x x)))
(-.f64 (/.f64 (sqrt.f64 1/2) x) 0)
(*.f64 1 (/.f64 (sqrt.f64 1/2) x))
(.f64 1/2 (.f64 (sqrt.f64 1/2) (/.f64 2 x)))
(*.f64 (sqrt.f64 1/2) (/.f64 1 x))
(.f64 (sqrt.f64 1/2) (.f64 2 (/.f64 1/2 x)))
(.f64 (sqrt.f64 1/2) (.f64 (*.f64 2 (/.f64 1 x)) 1/2))
(.f64 (sqrt.f64 1/2) (.f64 (/.f64 2 x) 1/2))
(*.f64 2 (/.f64 (sqrt.f64 1/2) (+.f64 x x)))
(.f64 2 (.f64 (/.f64 (sqrt.f64 1/2) (+.f64 x x)) 1))
(.f64 2 (.f64 (/.f64 (sqrt.f64 1/2) x) 1/2))
(.f64 2 (.f64 (/.f64 (sqrt.f64 1/2) 2) (/.f64 1 x)))
(.f64 2 (.f64 (sqrt.f64 1/2) (/.f64 1/2 x)))
(.f64 2 (.f64 (/.f64 1/2 x) (sqrt.f64 1/2)))
(*.f64 (/.f64 (sqrt.f64 1/2) x) 1)
(*.f64 -1 (/.f64 (neg.f64 (sqrt.f64 1/2)) x))
(.f64 (.f64 (sqrt.f64 1/2) 2) (/.f64 1/2 x))
(.f64 (.f64 (sqrt.f64 1/2) 2) (*.f64 1/2 (/.f64 1 x)))
(.f64 (.f64 (sqrt.f64 1/2) 2) (.f64 (.f64 1/2 (/.f64 1 x)) 1))
(.f64 (.f64 (sqrt.f64 1/2) 2) (.f64 (.f64 2 (/.f64 1/2 x)) 1/2))
(*.f64 (/.f64 (neg.f64 (sqrt.f64 1/2)) x) -1)
(.f64 (.f64 (sqrt.f64 1/2) 4) (/.f64 1/2 (+.f64 x x)))
(.f64 (.f64 (sqrt.f64 1/2) 4) (*.f64 (/.f64 1/2 (+.f64 x x)) 1))
(.f64 (.f64 (sqrt.f64 1/2) 4) (*.f64 1/4 (/.f64 1 x)))
(.f64 (.f64 (sqrt.f64 1/2) 4) (*.f64 1/2 (/.f64 1/2 x)))
(.f64 (.f64 (sqrt.f64 1/2) (/.f64 2 x)) 1/2)
(*.f64 (/.f64 1 x) (sqrt.f64 1/2))
(*.f64 (neg.f64 (sqrt.f64 1/2)) (/.f64 -1 x))
(.f64 (neg.f64 (sqrt.f64 1/2)) (.f64 (/.f64 -1 x) 1))
(.f64 (/.f64 1/2 x) (.f64 (sqrt.f64 1/2) 2))
(.f64 (.f64 1/2 (/.f64 1 x)) (*.f64 (sqrt.f64 1/2) 2))
(*.f64 (/.f64 (sqrt.f64 1/2) (+.f64 x x)) 2)
(.f64 (/.f64 1/2 (+.f64 x x)) (.f64 (sqrt.f64 1/2) 4))
(*.f64 (/.f64 -1 x) (neg.f64 (sqrt.f64 1/2)))
(pow.f64 (/.f64 (sqrt.f64 1/2) x) 1)
(neg.f64 (/.f64 (neg.f64 (sqrt.f64 1/2)) x))
(+.f64 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2)) 0)
(+.f64 0 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2)))
(+.f64 (/.f64 (sqrt.f64 1/2) (.f64 2 (pow.f64 x 2))) (/.f64 (sqrt.f64 1/2) (.f64 2 (pow.f64 x 2))))
(-.f64 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2)) 0)
(*.f64 1 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2)))
(.f64 1/2 (.f64 2 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))))
(*.f64 (sqrt.f64 1/2) (/.f64 1 (pow.f64 x 2)))
(.f64 (sqrt.f64 1/2) (.f64 2 (/.f64 1/2 (pow.f64 x 2))))
(.f64 (sqrt.f64 1/2) (.f64 (*.f64 2 (/.f64 1 (pow.f64 x 2))) 1/2))
(.f64 (sqrt.f64 1/2) (.f64 (/.f64 2 (pow.f64 x 2)) 1/2))
(.f64 2 (/.f64 (sqrt.f64 1/2) (.f64 2 (pow.f64 x 2))))
(.f64 2 (.f64 (/.f64 (sqrt.f64 1/2) 2) (/.f64 1 (pow.f64 x 2))))
(.f64 2 (.f64 (sqrt.f64 1/2) (/.f64 1/2 (pow.f64 x 2))))
(.f64 2 (.f64 (/.f64 1/2 (pow.f64 x 2)) (sqrt.f64 1/2)))
(*.f64 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2)) 1)
(*.f64 -1 (/.f64 (sqrt.f64 1/2) (neg.f64 (pow.f64 x 2))))
(.f64 -1 (.f64 (/.f64 (sqrt.f64 1/2) (neg.f64 (pow.f64 x 2))) 1))
(.f64 (.f64 (sqrt.f64 1/2) 2) (/.f64 1/2 (pow.f64 x 2)))
(.f64 (.f64 (sqrt.f64 1/2) 2) (*.f64 1/2 (/.f64 1 (pow.f64 x 2))))
(.f64 (.f64 (sqrt.f64 1/2) 2) (.f64 (.f64 1/2 (/.f64 1 (pow.f64 x 2))) 1))
(.f64 (.f64 (sqrt.f64 1/2) 2) (.f64 (.f64 2 (/.f64 1/2 (pow.f64 x 2))) 1/2))
(.f64 (.f64 2 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))) 1/2)
(.f64 (.f64 (sqrt.f64 1/2) 4) (/.f64 1 (*.f64 (pow.f64 x 2) 4)))
(.f64 (.f64 (sqrt.f64 1/2) 4) (.f64 (/.f64 1 (.f64 (pow.f64 x 2) 4)) 1))
(.f64 (.f64 (sqrt.f64 1/2) 4) (*.f64 1/4 (/.f64 1 (pow.f64 x 2))))
(.f64 (.f64 (sqrt.f64 1/2) 4) (*.f64 1/2 (/.f64 1/2 (pow.f64 x 2))))
(*.f64 (/.f64 1 (pow.f64 x 2)) (sqrt.f64 1/2))
(*.f64 (neg.f64 (sqrt.f64 1/2)) (/.f64 -1 (pow.f64 x 2)))
(.f64 (neg.f64 (sqrt.f64 1/2)) (.f64 (/.f64 -1 (pow.f64 x 2)) 1))
(.f64 (/.f64 1/2 (pow.f64 x 2)) (.f64 (sqrt.f64 1/2) 2))
(.f64 (.f64 1/2 (/.f64 1 (pow.f64 x 2))) (*.f64 (sqrt.f64 1/2) 2))
(*.f64 (/.f64 (sqrt.f64 1/2) (neg.f64 (pow.f64 x 2))) -1)
(.f64 (/.f64 (sqrt.f64 1/2) (.f64 2 (pow.f64 x 2))) 2)
(.f64 (/.f64 1 (.f64 (pow.f64 x 2) 4)) (*.f64 (sqrt.f64 1/2) 4))
(*.f64 (/.f64 -1 (pow.f64 x 2)) (neg.f64 (sqrt.f64 1/2)))
(pow.f64 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2)) 1)
(neg.f64 (/.f64 (sqrt.f64 1/2) (neg.f64 (pow.f64 x 2))))
(-.f64 (+.f64 1 (.f64 (sqrt.f64 1/2) (+.f64 (.f64 -1/2 (/.f64 1 x)) (+.f64 (*.f64 1/8 (/.f64 1 (pow.f64 x 2))) -1)))) 0)
(-.f64 (.f64 (sqrt.f64 1/2) (+.f64 (.f64 -1/2 (/.f64 1 x)) (+.f64 (*.f64 1/8 (/.f64 1 (pow.f64 x 2))) -1))) -1)
(.f64 1 (+.f64 1 (.f64 (sqrt.f64 1/2) (+.f64 (.f64 -1/2 (/.f64 1 x)) (+.f64 (.f64 1/8 (/.f64 1 (pow.f64 x 2))) -1)))))
(.f64 1/2 (+.f64 (.f64 2 (.f64 (sqrt.f64 1/2) (+.f64 (.f64 -1/2 (/.f64 1 x)) (+.f64 (*.f64 1/8 (/.f64 1 (pow.f64 x 2))) -1)))) 2))
(.f64 2 (/.f64 (+.f64 1 (.f64 (sqrt.f64 1/2) (+.f64 (.f64 -1/2 (/.f64 1 x)) (+.f64 (.f64 1/8 (/.f64 1 (pow.f64 x 2))) -1)))) 2))
(.f64 2 (.f64 (/.f64 (+.f64 1 (.f64 (sqrt.f64 1/2) (+.f64 (.f64 -1/2 (/.f64 1 x)) (+.f64 (*.f64 1/8 (/.f64 1 (pow.f64 x 2))) -1)))) 2) 1))
(.f64 (+.f64 1 (.f64 (sqrt.f64 1/2) (+.f64 (.f64 -1/2 (/.f64 1 x)) (+.f64 (.f64 1/8 (/.f64 1 (pow.f64 x 2))) -1)))) 1)
(.f64 (+.f64 (.f64 2 (.f64 (sqrt.f64 1/2) (+.f64 (.f64 -1/2 (/.f64 1 x)) (+.f64 (*.f64 1/8 (/.f64 1 (pow.f64 x 2))) -1)))) 2) 1/2)
(.f64 (/.f64 (+.f64 1 (.f64 (sqrt.f64 1/2) (+.f64 (.f64 -1/2 (/.f64 1 x)) (+.f64 (.f64 1/8 (/.f64 1 (pow.f64 x 2))) -1)))) 2) 2)
(/.f64 (+.f64 1 (.f64 (sqrt.f64 1/2) (+.f64 (.f64 -1/2 (/.f64 1 x)) (+.f64 (*.f64 1/8 (/.f64 1 (pow.f64 x 2))) -1)))) 1)
(/.f64 (+.f64 (.f64 2 (.f64 (sqrt.f64 1/2) (+.f64 (.f64 -1/2 (/.f64 1 x)) (+.f64 (.f64 1/8 (/.f64 1 (pow.f64 x 2))) -1)))) 2) 2)
(/.f64 (.f64 (+.f64 1 (.f64 (sqrt.f64 1/2) (+.f64 (.f64 -1/2 (/.f64 1 x)) (+.f64 (.f64 1/8 (/.f64 1 (pow.f64 x 2))) -1)))) 4) 4)
(/.f64 (.f64 2 (.f64 (+.f64 1 (.f64 (sqrt.f64 1/2) (+.f64 (.f64 -1/2 (/.f64 1 x)) (+.f64 (*.f64 1/8 (/.f64 1 (pow.f64 x 2))) -1)))) 4)) 8)
(/.f64 (+.f64 (.f64 2 (.f64 (+.f64 1 (.f64 (sqrt.f64 1/2) (+.f64 (.f64 -1/2 (/.f64 1 x)) (+.f64 (.f64 1/8 (/.f64 1 (pow.f64 x 2))) -1)))) 4)) (.f64 2 (.f64 (+.f64 1 (.f64 (sqrt.f64 1/2) (+.f64 (.f64 -1/2 (/.f64 1 x)) (+.f64 (.f64 1/8 (/.f64 1 (pow.f64 x 2))) -1)))) 4))) 16)
(pow.f64 (+.f64 1 (.f64 (sqrt.f64 1/2) (+.f64 (.f64 -1/2 (/.f64 1 x)) (+.f64 (*.f64 1/8 (/.f64 1 (pow.f64 x 2))) -1)))) 1)

Outputs
(*.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2)))
(-.f64 (+.f64 1 (*.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2)))) (sqrt.f64 1/2))
(+.f64 (*.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (-.f64 1 (sqrt.f64 1/2)))
(-.f64 (+.f64 1 (*.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2)))) (sqrt.f64 1/2))
(+.f64 (*.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (-.f64 1 (sqrt.f64 1/2)))
(-.f64 (+.f64 1 (*.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2)))) (sqrt.f64 1/2))
(+.f64 (*.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (-.f64 1 (sqrt.f64 1/2)))
(-.f64 1 (sqrt.f64 1/2))
(-.f64 (+.f64 1 (*.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2)))) (sqrt.f64 1/2))
(+.f64 (*.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (-.f64 1 (sqrt.f64 1/2)))
(-.f64 (+.f64 1 (*.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2)))) (sqrt.f64 1/2))
(+.f64 (*.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (-.f64 1 (sqrt.f64 1/2)))
(-.f64 (+.f64 1 (*.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2)))) (sqrt.f64 1/2))
(+.f64 (*.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (-.f64 1 (sqrt.f64 1/2)))
(-.f64 1 (sqrt.f64 1/2))
(-.f64 (+.f64 1 (*.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2)))) (sqrt.f64 1/2))
(+.f64 (*.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (-.f64 1 (sqrt.f64 1/2)))
(-.f64 (+.f64 1 (*.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2)))) (sqrt.f64 1/2))
(+.f64 (*.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (-.f64 1 (sqrt.f64 1/2)))
(-.f64 (+.f64 1 (*.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2)))) (sqrt.f64 1/2))
(+.f64 (*.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (-.f64 1 (sqrt.f64 1/2)))
(*.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2)))
(+.f64 (.f64 -1/2 (/.f64 (sqrt.f64 1/2) x)) (.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))))
(+.f64 (.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (.f64 -1/2 (/.f64 (sqrt.f64 1/2) x)))
(-.f64 (+.f64 1 (+.f64 (.f64 -1/2 (/.f64 (sqrt.f64 1/2) x)) (.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))))) (sqrt.f64 1/2))
(+.f64 (+.f64 (.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (.f64 -1/2 (/.f64 (sqrt.f64 1/2) x))) (-.f64 1 (sqrt.f64 1/2)))
(+.f64 (+.f64 (.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))) 1) (-.f64 (.f64 -1/2 (/.f64 (sqrt.f64 1/2) x)) (sqrt.f64 1/2)))
(+.f64 (.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (+.f64 (-.f64 1 (sqrt.f64 1/2)) (.f64 -1/2 (/.f64 (sqrt.f64 1/2) x))))
(+.f64 (.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (+.f64 1 (-.f64 (.f64 -1/2 (/.f64 (sqrt.f64 1/2) x)) (sqrt.f64 1/2))))
(-.f64 (+.f64 1 (+.f64 (.f64 -1/2 (/.f64 (sqrt.f64 1/2) x)) (.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))))) (sqrt.f64 1/2))
(+.f64 (+.f64 (.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (.f64 -1/2 (/.f64 (sqrt.f64 1/2) x))) (-.f64 1 (sqrt.f64 1/2)))
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(+.f64 (.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (+.f64 (-.f64 1 (sqrt.f64 1/2)) (.f64 -1/2 (/.f64 (sqrt.f64 1/2) x))))
(+.f64 (.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (+.f64 1 (-.f64 (.f64 -1/2 (/.f64 (sqrt.f64 1/2) x)) (sqrt.f64 1/2))))
(-.f64 1 (sqrt.f64 1/2))
(-.f64 (+.f64 1 (*.f64 -1/2 (/.f64 (sqrt.f64 1/2) x))) (sqrt.f64 1/2))
(+.f64 (*.f64 -1/2 (/.f64 (sqrt.f64 1/2) x)) (-.f64 1 (sqrt.f64 1/2)))
(+.f64 1 (-.f64 (*.f64 -1/2 (/.f64 (sqrt.f64 1/2) x)) (sqrt.f64 1/2)))
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(-.f64 (+.f64 1 (+.f64 (.f64 -1/2 (/.f64 (sqrt.f64 1/2) x)) (.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))))) (sqrt.f64 1/2))
(+.f64 (+.f64 (.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (.f64 -1/2 (/.f64 (sqrt.f64 1/2) x))) (-.f64 1 (sqrt.f64 1/2)))
(+.f64 (+.f64 (.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))) 1) (-.f64 (.f64 -1/2 (/.f64 (sqrt.f64 1/2) x)) (sqrt.f64 1/2)))
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(+.f64 (+.f64 (.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (.f64 -1/2 (/.f64 (sqrt.f64 1/2) x))) (-.f64 1 (sqrt.f64 1/2)))
(+.f64 (+.f64 (.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))) 1) (-.f64 (.f64 -1/2 (/.f64 (sqrt.f64 1/2) x)) (sqrt.f64 1/2)))
(+.f64 (.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (+.f64 (-.f64 1 (sqrt.f64 1/2)) (.f64 -1/2 (/.f64 (sqrt.f64 1/2) x))))
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(-.f64 1 (sqrt.f64 1/2))
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(+.f64 (*.f64 -1/2 (/.f64 (sqrt.f64 1/2) x)) (-.f64 1 (sqrt.f64 1/2)))
(+.f64 1 (-.f64 (*.f64 -1/2 (/.f64 (sqrt.f64 1/2) x)) (sqrt.f64 1/2)))
(+.f64 (-.f64 1 (sqrt.f64 1/2)) (*.f64 -1/2 (/.f64 (sqrt.f64 1/2) x)))
(-.f64 (+.f64 1 (+.f64 (.f64 -1/2 (/.f64 (sqrt.f64 1/2) x)) (.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))))) (sqrt.f64 1/2))
(+.f64 (+.f64 (.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (.f64 -1/2 (/.f64 (sqrt.f64 1/2) x))) (-.f64 1 (sqrt.f64 1/2)))
(+.f64 (+.f64 (.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))) 1) (-.f64 (.f64 -1/2 (/.f64 (sqrt.f64 1/2) x)) (sqrt.f64 1/2)))
(+.f64 (.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (+.f64 (-.f64 1 (sqrt.f64 1/2)) (.f64 -1/2 (/.f64 (sqrt.f64 1/2) x))))
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(+.f64 1 (.f64 (sqrt.f64 1/2) (+.f64 -1 (+.f64 (.f64 1/8 (/.f64 1 (pow.f64 x 2))) (*.f64 -1/2 (/.f64 1 x))))))
(+.f64 1 (.f64 (sqrt.f64 1/2) (+.f64 -1 (+.f64 (.f64 -1/2 (/.f64 1 x)) (*.f64 1/8 (/.f64 1 (pow.f64 x 2)))))))
(-.f64 (.f64 (sqrt.f64 1/2) (+.f64 (.f64 -1/2 (/.f64 1 x)) (+.f64 (*.f64 1/8 (/.f64 1 (pow.f64 x 2))) -1))) -1)
(+.f64 1 (.f64 (sqrt.f64 1/2) (+.f64 (.f64 -1/2 (/.f64 1 x)) (+.f64 -1 (*.f64 1/8 (/.f64 1 (pow.f64 x 2)))))))
(+.f64 1 (.f64 (sqrt.f64 1/2) (+.f64 -1 (+.f64 (.f64 1/8 (/.f64 1 (pow.f64 x 2))) (*.f64 -1/2 (/.f64 1 x))))))
(+.f64 1 (.f64 (sqrt.f64 1/2) (+.f64 -1 (+.f64 (.f64 -1/2 (/.f64 1 x)) (*.f64 1/8 (/.f64 1 (pow.f64 x 2)))))))
(.f64 1 (+.f64 1 (.f64 (sqrt.f64 1/2) (+.f64 (.f64 -1/2 (/.f64 1 x)) (+.f64 (.f64 1/8 (/.f64 1 (pow.f64 x 2))) -1)))))
(+.f64 1 (.f64 (sqrt.f64 1/2) (+.f64 (.f64 -1/2 (/.f64 1 x)) (+.f64 -1 (*.f64 1/8 (/.f64 1 (pow.f64 x 2)))))))
(+.f64 1 (.f64 (sqrt.f64 1/2) (+.f64 -1 (+.f64 (.f64 1/8 (/.f64 1 (pow.f64 x 2))) (*.f64 -1/2 (/.f64 1 x))))))
(+.f64 1 (.f64 (sqrt.f64 1/2) (+.f64 -1 (+.f64 (.f64 -1/2 (/.f64 1 x)) (*.f64 1/8 (/.f64 1 (pow.f64 x 2)))))))
(.f64 1/2 (+.f64 (.f64 2 (.f64 (sqrt.f64 1/2) (+.f64 (.f64 -1/2 (/.f64 1 x)) (+.f64 (*.f64 1/8 (/.f64 1 (pow.f64 x 2))) -1)))) 2))
(+.f64 1 (.f64 (sqrt.f64 1/2) (+.f64 (.f64 -1/2 (/.f64 1 x)) (+.f64 -1 (*.f64 1/8 (/.f64 1 (pow.f64 x 2)))))))
(+.f64 1 (.f64 (sqrt.f64 1/2) (+.f64 -1 (+.f64 (.f64 1/8 (/.f64 1 (pow.f64 x 2))) (*.f64 -1/2 (/.f64 1 x))))))
(+.f64 1 (.f64 (sqrt.f64 1/2) (+.f64 -1 (+.f64 (.f64 -1/2 (/.f64 1 x)) (*.f64 1/8 (/.f64 1 (pow.f64 x 2)))))))
(.f64 2 (/.f64 (+.f64 1 (.f64 (sqrt.f64 1/2) (+.f64 (.f64 -1/2 (/.f64 1 x)) (+.f64 (.f64 1/8 (/.f64 1 (pow.f64 x 2))) -1)))) 2))
(+.f64 1 (.f64 (sqrt.f64 1/2) (+.f64 (.f64 -1/2 (/.f64 1 x)) (+.f64 -1 (*.f64 1/8 (/.f64 1 (pow.f64 x 2)))))))
(+.f64 1 (.f64 (sqrt.f64 1/2) (+.f64 -1 (+.f64 (.f64 1/8 (/.f64 1 (pow.f64 x 2))) (*.f64 -1/2 (/.f64 1 x))))))
(+.f64 1 (.f64 (sqrt.f64 1/2) (+.f64 -1 (+.f64 (.f64 -1/2 (/.f64 1 x)) (*.f64 1/8 (/.f64 1 (pow.f64 x 2)))))))
(.f64 2 (.f64 (/.f64 (+.f64 1 (.f64 (sqrt.f64 1/2) (+.f64 (.f64 -1/2 (/.f64 1 x)) (+.f64 (*.f64 1/8 (/.f64 1 (pow.f64 x 2))) -1)))) 2) 1))
(+.f64 1 (.f64 (sqrt.f64 1/2) (+.f64 (.f64 -1/2 (/.f64 1 x)) (+.f64 -1 (*.f64 1/8 (/.f64 1 (pow.f64 x 2)))))))
(+.f64 1 (.f64 (sqrt.f64 1/2) (+.f64 -1 (+.f64 (.f64 1/8 (/.f64 1 (pow.f64 x 2))) (*.f64 -1/2 (/.f64 1 x))))))
(+.f64 1 (.f64 (sqrt.f64 1/2) (+.f64 -1 (+.f64 (.f64 -1/2 (/.f64 1 x)) (*.f64 1/8 (/.f64 1 (pow.f64 x 2)))))))
(.f64 (+.f64 1 (.f64 (sqrt.f64 1/2) (+.f64 (.f64 -1/2 (/.f64 1 x)) (+.f64 (.f64 1/8 (/.f64 1 (pow.f64 x 2))) -1)))) 1)
(+.f64 1 (.f64 (sqrt.f64 1/2) (+.f64 (.f64 -1/2 (/.f64 1 x)) (+.f64 -1 (*.f64 1/8 (/.f64 1 (pow.f64 x 2)))))))
(+.f64 1 (.f64 (sqrt.f64 1/2) (+.f64 -1 (+.f64 (.f64 1/8 (/.f64 1 (pow.f64 x 2))) (*.f64 -1/2 (/.f64 1 x))))))
(+.f64 1 (.f64 (sqrt.f64 1/2) (+.f64 -1 (+.f64 (.f64 -1/2 (/.f64 1 x)) (*.f64 1/8 (/.f64 1 (pow.f64 x 2)))))))
(.f64 (+.f64 (.f64 2 (.f64 (sqrt.f64 1/2) (+.f64 (.f64 -1/2 (/.f64 1 x)) (+.f64 (*.f64 1/8 (/.f64 1 (pow.f64 x 2))) -1)))) 2) 1/2)
(+.f64 1 (.f64 (sqrt.f64 1/2) (+.f64 (.f64 -1/2 (/.f64 1 x)) (+.f64 -1 (*.f64 1/8 (/.f64 1 (pow.f64 x 2)))))))
(+.f64 1 (.f64 (sqrt.f64 1/2) (+.f64 -1 (+.f64 (.f64 1/8 (/.f64 1 (pow.f64 x 2))) (*.f64 -1/2 (/.f64 1 x))))))
(+.f64 1 (.f64 (sqrt.f64 1/2) (+.f64 -1 (+.f64 (.f64 -1/2 (/.f64 1 x)) (*.f64 1/8 (/.f64 1 (pow.f64 x 2)))))))
(.f64 (/.f64 (+.f64 1 (.f64 (sqrt.f64 1/2) (+.f64 (.f64 -1/2 (/.f64 1 x)) (+.f64 (.f64 1/8 (/.f64 1 (pow.f64 x 2))) -1)))) 2) 2)
(+.f64 1 (.f64 (sqrt.f64 1/2) (+.f64 (.f64 -1/2 (/.f64 1 x)) (+.f64 -1 (*.f64 1/8 (/.f64 1 (pow.f64 x 2)))))))
(+.f64 1 (.f64 (sqrt.f64 1/2) (+.f64 -1 (+.f64 (.f64 1/8 (/.f64 1 (pow.f64 x 2))) (*.f64 -1/2 (/.f64 1 x))))))
(+.f64 1 (.f64 (sqrt.f64 1/2) (+.f64 -1 (+.f64 (.f64 -1/2 (/.f64 1 x)) (*.f64 1/8 (/.f64 1 (pow.f64 x 2)))))))
(/.f64 (+.f64 1 (.f64 (sqrt.f64 1/2) (+.f64 (.f64 -1/2 (/.f64 1 x)) (+.f64 (*.f64 1/8 (/.f64 1 (pow.f64 x 2))) -1)))) 1)
(+.f64 1 (.f64 (sqrt.f64 1/2) (+.f64 (.f64 -1/2 (/.f64 1 x)) (+.f64 -1 (*.f64 1/8 (/.f64 1 (pow.f64 x 2)))))))
(+.f64 1 (.f64 (sqrt.f64 1/2) (+.f64 -1 (+.f64 (.f64 1/8 (/.f64 1 (pow.f64 x 2))) (*.f64 -1/2 (/.f64 1 x))))))
(+.f64 1 (.f64 (sqrt.f64 1/2) (+.f64 -1 (+.f64 (.f64 -1/2 (/.f64 1 x)) (*.f64 1/8 (/.f64 1 (pow.f64 x 2)))))))
(/.f64 (+.f64 (.f64 2 (.f64 (sqrt.f64 1/2) (+.f64 (.f64 -1/2 (/.f64 1 x)) (+.f64 (.f64 1/8 (/.f64 1 (pow.f64 x 2))) -1)))) 2) 2)
(+.f64 1 (.f64 (sqrt.f64 1/2) (+.f64 (.f64 -1/2 (/.f64 1 x)) (+.f64 -1 (*.f64 1/8 (/.f64 1 (pow.f64 x 2)))))))
(+.f64 1 (.f64 (sqrt.f64 1/2) (+.f64 -1 (+.f64 (.f64 1/8 (/.f64 1 (pow.f64 x 2))) (*.f64 -1/2 (/.f64 1 x))))))
(+.f64 1 (.f64 (sqrt.f64 1/2) (+.f64 -1 (+.f64 (.f64 -1/2 (/.f64 1 x)) (*.f64 1/8 (/.f64 1 (pow.f64 x 2)))))))
(/.f64 (.f64 (+.f64 1 (.f64 (sqrt.f64 1/2) (+.f64 (.f64 -1/2 (/.f64 1 x)) (+.f64 (.f64 1/8 (/.f64 1 (pow.f64 x 2))) -1)))) 4) 4)
(+.f64 1 (.f64 (sqrt.f64 1/2) (+.f64 (.f64 -1/2 (/.f64 1 x)) (+.f64 -1 (*.f64 1/8 (/.f64 1 (pow.f64 x 2)))))))
(+.f64 1 (.f64 (sqrt.f64 1/2) (+.f64 -1 (+.f64 (.f64 1/8 (/.f64 1 (pow.f64 x 2))) (*.f64 -1/2 (/.f64 1 x))))))
(+.f64 1 (.f64 (sqrt.f64 1/2) (+.f64 -1 (+.f64 (.f64 -1/2 (/.f64 1 x)) (*.f64 1/8 (/.f64 1 (pow.f64 x 2)))))))
(/.f64 (.f64 2 (.f64 (+.f64 1 (.f64 (sqrt.f64 1/2) (+.f64 (.f64 -1/2 (/.f64 1 x)) (+.f64 (*.f64 1/8 (/.f64 1 (pow.f64 x 2))) -1)))) 4)) 8)
(+.f64 1 (.f64 (sqrt.f64 1/2) (+.f64 (.f64 -1/2 (/.f64 1 x)) (+.f64 -1 (*.f64 1/8 (/.f64 1 (pow.f64 x 2)))))))
(+.f64 1 (.f64 (sqrt.f64 1/2) (+.f64 -1 (+.f64 (.f64 1/8 (/.f64 1 (pow.f64 x 2))) (*.f64 -1/2 (/.f64 1 x))))))
(+.f64 1 (.f64 (sqrt.f64 1/2) (+.f64 -1 (+.f64 (.f64 -1/2 (/.f64 1 x)) (*.f64 1/8 (/.f64 1 (pow.f64 x 2)))))))
(/.f64 (+.f64 (.f64 2 (.f64 (+.f64 1 (.f64 (sqrt.f64 1/2) (+.f64 (.f64 -1/2 (/.f64 1 x)) (+.f64 (.f64 1/8 (/.f64 1 (pow.f64 x 2))) -1)))) 4)) (.f64 2 (.f64 (+.f64 1 (.f64 (sqrt.f64 1/2) (+.f64 (.f64 -1/2 (/.f64 1 x)) (+.f64 (.f64 1/8 (/.f64 1 (pow.f64 x 2))) -1)))) 4))) 16)
(+.f64 1 (.f64 (sqrt.f64 1/2) (+.f64 (.f64 -1/2 (/.f64 1 x)) (+.f64 -1 (*.f64 1/8 (/.f64 1 (pow.f64 x 2)))))))
(+.f64 1 (.f64 (sqrt.f64 1/2) (+.f64 -1 (+.f64 (.f64 1/8 (/.f64 1 (pow.f64 x 2))) (*.f64 -1/2 (/.f64 1 x))))))
(+.f64 1 (.f64 (sqrt.f64 1/2) (+.f64 -1 (+.f64 (.f64 -1/2 (/.f64 1 x)) (*.f64 1/8 (/.f64 1 (pow.f64 x 2)))))))
(pow.f64 (+.f64 1 (.f64 (sqrt.f64 1/2) (+.f64 (.f64 -1/2 (/.f64 1 x)) (+.f64 (*.f64 1/8 (/.f64 1 (pow.f64 x 2))) -1)))) 1)
(+.f64 1 (.f64 (sqrt.f64 1/2) (+.f64 (.f64 -1/2 (/.f64 1 x)) (+.f64 -1 (*.f64 1/8 (/.f64 1 (pow.f64 x 2)))))))
(+.f64 1 (.f64 (sqrt.f64 1/2) (+.f64 -1 (+.f64 (.f64 1/8 (/.f64 1 (pow.f64 x 2))) (*.f64 -1/2 (/.f64 1 x))))))
(+.f64 1 (.f64 (sqrt.f64 1/2) (+.f64 -1 (+.f64 (.f64 -1/2 (/.f64 1 x)) (*.f64 1/8 (/.f64 1 (pow.f64 x 2)))))))

eval334.0ms (2.9%)

Compiler: Compiled 15715 to 14289 computations (9.1% saved)

prune153.0ms (1.3%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	818	4	822
Fresh	3	3	6
Picked	0	1	1
Done	2	2	4
Total	823	10	833

Error

0.5b

Counts

833 → 10

Alt Table

Click to see full alt table

Status	Error	Program
✓	14.7b	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
▶	32.5b	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x))))
▶	32.5b	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))))
✓	31.8b	(-.f64 1 (sqrt.f64 1/2))
▶	32.2b	(+.f64 (-.f64 1 (sqrt.f64 1/2)) (*.f64 1/2 (/.f64 (sqrt.f64 1/2) x)))
	32.3b	(+.f64 (.f64 1/2 (/.f64 (sqrt.f64 1/2) x)) (+.f64 (.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (-.f64 1 (sqrt.f64 1/2))))
▶	31.9b	(+.f64 (.f64 1/8 (pow.f64 x 2)) (.f64 -11/128 (pow.f64 x 4)))
✓	32.3b	(+.f64 (.f64 -1/2 (/.f64 (sqrt.f64 1/2) x)) (+.f64 1 (-.f64 (.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (sqrt.f64 1/2))))
▶	31.4b	(*.f64 1/8 (pow.f64 x 2))
	45.6b	0

Compiler

Compiled 177 to 158 computations (10.7% saved)

localize5.0ms (0%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(pow.f64 x 2)

Compiler

Compiled 12 to 9 computations (25% saved)

series1.0ms (0%)

Counts

1 → 0

Calls

3 calls:

Time	Variable		Point	Expression
0.0ms	x	@	-inf	(pow.f64 x 2)
0.0ms	x	@	inf	(pow.f64 x 2)
0.0ms	x	@	0	(pow.f64 x 2)

rewrite246.0ms (2.2%)

Algorithm

1×	batch-egg-rewrite

Rules

2400×	`rational.json-simplify-35`
2358×	`rational.json-simplify-2`
1494×	`rational.json-simplify-1`
1132×	`exponential.json-3`
1132×	`rational.json-1`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	7
1	32	7
2	77	7
3	147	7
4	253	7
5	531	7
6	1218	7
7	2634	7
8	4193	7
9	4770	7
10	5863	7
11	6594	7
12	6594	7
13	7696	7
14	7696	7

Stop Event

1×	node limit

Counts

1 → 33

Calls

Call 1

Inputs
(pow.f64 x 2)

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (pow.f64 x 2) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (pow.f64 x 2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (pow.f64 x 2) 1/2) (*.f64 (pow.f64 x 2) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (pow.f64 x 2) 0)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 2 (*.f64 (pow.f64 x 2) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 x 2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (pow.f64 x 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 2 (pow.f64 x 2)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 4 (*.f64 (pow.f64 x 2) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (pow.f64 x 2) 4) 1/4)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (pow.f64 x 2) 8) 1/8)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/2 (*.f64 2 (pow.f64 x 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (pow.f64 x 2) 1/2) 2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 16 (*.f64 (pow.f64 x 2) 1/16))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 x 4) 2) 1/16)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/4 (*.f64 (pow.f64 x 2) 4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (pow.f64 x 2) 1/4) 4)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/8 (*.f64 (pow.f64 x 2) 8))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/16 (pow.f64 (*.f64 x 4) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (pow.f64 x 2) 1/16) 16)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/64 (*.f64 (pow.f64 x 2) 64))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (pow.f64 x 2) 64) 1/64)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 x 2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (pow.f64 x 2)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (pow.f64 x 2) 4) 4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (pow.f64 x 2) 8) 8)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 (*.f64 x 4) 2) 16)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (pow.f64 (*.f64 x 4) 2)) 32)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 2 (pow.f64 (*.f64 x 4) 2))) 64)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 2 (*.f64 2 (pow.f64 (*.f64 x 4) 2)))) 128)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 2 (pow.f64 (*.f64 x 4) 2))))) 256)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 2 (pow.f64 (*.f64 x 4) 2)))))) 512)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 2 (pow.f64 (*.f64 x 4) 2)))))) (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 2 (pow.f64 (*.f64 x 4) 2))))))) 1024)))))

simplify765.0ms (6.7%)

Algorithm

1×	egg-herbie

Rules

6456×	`rational.json-simplify-51`
2392×	`rational.json-simplify-49`
2380×	`rational.json-simplify-35`
1058×	`rational.json-simplify-1`
926×	`rational.json-simplify-2`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	69	231
1	139	231
2	506	231
3	1222	231
4	1922	231
5	2778	231
6	3245	231
7	3334	231
8	3384	231
9	3419	231
10	3454	231
11	3489	231
12	3525	231
13	3560	231
14	3595	231
15	3630	231
16	3665	231
17	3700	231
18	3735	231
19	3770	231
20	3805	231
21	3840	231
22	3875	231
23	3910	231
24	3945	231
25	3980	231
26	4015	231
27	4050	231
28	4085	231
29	4120	231
30	4155	231
31	4155	231
32	4190	231
33	4225	231
34	5724	231

Stop Event

1×	node limit

Counts

33 → 34

Calls

Call 1

Inputs
(+.f64 (pow.f64 x 2) 0)
(+.f64 0 (pow.f64 x 2))
(+.f64 (.f64 (pow.f64 x 2) 1/2) (.f64 (pow.f64 x 2) 1/2))
(-.f64 (pow.f64 x 2) 0)
(.f64 2 (.f64 (pow.f64 x 2) 1/2))
(*.f64 (pow.f64 x 2) 1)
(*.f64 1 (pow.f64 x 2))
(.f64 (.f64 2 (pow.f64 x 2)) 1/2)
(.f64 4 (.f64 (pow.f64 x 2) 1/4))
(.f64 (.f64 (pow.f64 x 2) 4) 1/4)
(.f64 (.f64 (pow.f64 x 2) 8) 1/8)
(.f64 1/2 (.f64 2 (pow.f64 x 2)))
(.f64 (.f64 (pow.f64 x 2) 1/2) 2)
(.f64 16 (.f64 (pow.f64 x 2) 1/16))
(.f64 (pow.f64 (.f64 x 4) 2) 1/16)
(.f64 1/4 (.f64 (pow.f64 x 2) 4))
(.f64 (.f64 (pow.f64 x 2) 1/4) 4)
(.f64 1/8 (.f64 (pow.f64 x 2) 8))
(.f64 1/16 (pow.f64 (.f64 x 4) 2))
(.f64 (.f64 (pow.f64 x 2) 1/16) 16)
(.f64 1/64 (.f64 (pow.f64 x 2) 64))
(.f64 (.f64 (pow.f64 x 2) 64) 1/64)
(/.f64 (pow.f64 x 2) 1)
(/.f64 (*.f64 2 (pow.f64 x 2)) 2)
(/.f64 (*.f64 (pow.f64 x 2) 4) 4)
(/.f64 (*.f64 (pow.f64 x 2) 8) 8)
(/.f64 (pow.f64 (*.f64 x 4) 2) 16)
(/.f64 (.f64 2 (pow.f64 (.f64 x 4) 2)) 32)
(/.f64 (.f64 2 (.f64 2 (pow.f64 (*.f64 x 4) 2))) 64)
(/.f64 (.f64 2 (.f64 2 (.f64 2 (pow.f64 (.f64 x 4) 2)))) 128)
(/.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (pow.f64 (*.f64 x 4) 2))))) 256)
(/.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (pow.f64 (.f64 x 4) 2)))))) 512)
(/.f64 (+.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (pow.f64 (.f64 x 4) 2)))))) (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (pow.f64 (.f64 x 4) 2))))))) 1024)

Outputs
(+.f64 (pow.f64 x 2) 0)
(pow.f64 x 2)
(+.f64 0 (pow.f64 x 2))
(pow.f64 x 2)
(+.f64 (.f64 (pow.f64 x 2) 1/2) (.f64 (pow.f64 x 2) 1/2))
(pow.f64 x 2)
(-.f64 (pow.f64 x 2) 0)
(pow.f64 x 2)
(.f64 2 (.f64 (pow.f64 x 2) 1/2))
(pow.f64 x 2)
(*.f64 (pow.f64 x 2) 1)
(pow.f64 x 2)
(*.f64 1 (pow.f64 x 2))
(pow.f64 x 2)
(.f64 (.f64 2 (pow.f64 x 2)) 1/2)
(pow.f64 x 2)
(.f64 4 (.f64 (pow.f64 x 2) 1/4))
(pow.f64 x 2)
(.f64 (.f64 (pow.f64 x 2) 4) 1/4)
(pow.f64 x 2)
(.f64 (.f64 (pow.f64 x 2) 8) 1/8)
(pow.f64 x 2)
(.f64 1/2 (.f64 2 (pow.f64 x 2)))
(pow.f64 x 2)
(.f64 (.f64 (pow.f64 x 2) 1/2) 2)
(pow.f64 x 2)
(.f64 16 (.f64 (pow.f64 x 2) 1/16))
(pow.f64 x 2)
(.f64 (pow.f64 (.f64 x 4) 2) 1/16)
(pow.f64 x 2)
(.f64 1/4 (.f64 (pow.f64 x 2) 4))
(pow.f64 x 2)
(.f64 (.f64 (pow.f64 x 2) 1/4) 4)
(pow.f64 x 2)
(.f64 1/8 (.f64 (pow.f64 x 2) 8))
(pow.f64 x 2)
(.f64 1/16 (pow.f64 (.f64 x 4) 2))
(pow.f64 x 2)
(.f64 (.f64 (pow.f64 x 2) 1/16) 16)
(pow.f64 x 2)
(.f64 1/64 (.f64 (pow.f64 x 2) 64))
(pow.f64 x 2)
(.f64 (.f64 (pow.f64 x 2) 64) 1/64)
(pow.f64 x 2)
(/.f64 (pow.f64 x 2) 1)
(pow.f64 x 2)
(/.f64 (*.f64 2 (pow.f64 x 2)) 2)
(pow.f64 x 2)
(/.f64 (*.f64 (pow.f64 x 2) 4) 4)
(pow.f64 x 2)
(/.f64 (*.f64 (pow.f64 x 2) 8) 8)
(pow.f64 x 2)
(/.f64 (pow.f64 (*.f64 x 4) 2) 16)
(pow.f64 x 2)
(/.f64 (.f64 2 (pow.f64 (.f64 x 4) 2)) 32)
(pow.f64 x 2)
(/.f64 (.f64 2 (.f64 2 (pow.f64 (*.f64 x 4) 2))) 64)
(pow.f64 x 2)
(/.f64 (.f64 2 (.f64 2 (.f64 2 (pow.f64 (.f64 x 4) 2)))) 128)
(pow.f64 x 2)
(/.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (pow.f64 (*.f64 x 4) 2))))) 256)
(pow.f64 x 2)
(/.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (pow.f64 (.f64 x 4) 2)))))) 512)
(pow.f64 x 2)
(/.f64 (+.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (pow.f64 (.f64 x 4) 2)))))) (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (pow.f64 (.f64 x 4) 2))))))) 1024)
(pow.f64 x 2)

localize11.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x)))
✓	0.5b	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))))

Compiler

Compiled 27 to 22 computations (18.5% saved)

series2.0ms (0%)

Counts

2 → 16

Calls

6 calls:

Time	Variable		Point	Expression
1.0ms	x	@	0	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))))
0.0ms	x	@	inf	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))))
0.0ms	x	@	-inf	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))))
0.0ms	x	@	0	(sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x)))
0.0ms	x	@	inf	(sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x)))

rewrite89.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

1902×	`rational.json-simplify-35`
1104×	`rational.json-1`
1104×	`rational.json-2`
1104×	`rational.json-4`
1104×	`rational.json-3`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	40
1	82	40
2	181	40
3	363	40
4	751	40
5	1910	40
6	4814	40

Stop Event

1×	node limit

Counts

2 → 56

Calls

Call 1

Inputs
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))))
(sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x)))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x)))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 -1 (neg.f64 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))) -2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 -2 (-.f64 1 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))) -2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (neg.f64 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))) -2)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 1/2 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))))) (*.f64 1/2 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/2 (*.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -1 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))) -1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 2 (*.f64 1/2 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 4 (/.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x)))) 4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x)))) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))) -1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x)))) 4) 1/4)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/4 (*.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x)))) 4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 1/2 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x)))) 4) 4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x)))) 2) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))) -1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x)))) 4) 4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x)))) 8) 8)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))) -1)) -2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x)))) 8)) 16)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))) -1) 4) -4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (*.f64 2 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))) -1))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 2 (*.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x)))) 8))) 32)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (neg.f64 (*.f64 2 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))) -1)))) 4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))) -1) 4)) -8)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (*.f64 2 (*.f64 2 (*.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x)))) 8))) (*.f64 2 (*.f64 2 (*.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x)))) 8)))) 64)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (*.f64 2 (neg.f64 (*.f64 2 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))) -1)))) (*.f64 2 (neg.f64 (*.f64 2 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))) -1))))) 8)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))) -1))))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 1/2 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x)))) (*.f64 1/2 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/2 (*.f64 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 2 (*.f64 1/2 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 4 (/.f64 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))) 4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))) 4) 1/4)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/4 (*.f64 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))) 4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 1/2 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))) 4) 4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))) 2) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))) 4) 4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))) 8) 8)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))) 8)) 16)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 2 (*.f64 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))) 8))) 32)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (*.f64 2 (*.f64 2 (*.f64 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))) 8))) (*.f64 2 (*.f64 2 (*.f64 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))) 8)))) 64)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))) 1)))))

simplify153.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

1546×	`rational.json-simplify-35`
1402×	`rational.json-simplify-61`
1064×	`rational.json-simplify-51`
1004×	`rational.json-simplify-1`
954×	`rational.json-simplify-48`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	135	2028
1	289	2028
2	714	2028
3	2169	2028
4	4029	2028
5	4739	2028
6	5080	2028
7	5645	2028
8	7087	2028

Stop Event

1×	node limit

Counts

72 → 86

Calls

Call 1

Inputs
(-.f64 1 (sqrt.f64 1/2))
(-.f64 (+.f64 1 (.f64 1/4 (/.f64 1 (.f64 (sqrt.f64 1/2) x)))) (sqrt.f64 1/2))
(-.f64 (+.f64 1 (+.f64 (.f64 1/4 (/.f64 1 (.f64 (sqrt.f64 1/2) x))) (.f64 1/32 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 x 2)))))) (sqrt.f64 1/2))
(-.f64 (+.f64 1 (+.f64 (.f64 1/128 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 1/2) 5) (pow.f64 x 3)))) (+.f64 (.f64 1/4 (/.f64 1 (.f64 (sqrt.f64 1/2) x))) (.f64 1/32 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 x 2))))))) (sqrt.f64 1/2))
(-.f64 1 (sqrt.f64 1/2))
(-.f64 (+.f64 1 (.f64 1/4 (/.f64 1 (.f64 (sqrt.f64 1/2) x)))) (sqrt.f64 1/2))
(-.f64 (+.f64 1 (+.f64 (.f64 1/4 (/.f64 1 (.f64 (sqrt.f64 1/2) x))) (.f64 1/32 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 x 2)))))) (sqrt.f64 1/2))
(-.f64 (+.f64 1 (+.f64 (.f64 1/128 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 1/2) 5) (pow.f64 x 3)))) (+.f64 (.f64 1/4 (/.f64 1 (.f64 (sqrt.f64 1/2) x))) (.f64 1/32 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 x 2))))))) (sqrt.f64 1/2))
(sqrt.f64 1/2)
(-.f64 (sqrt.f64 1/2) (.f64 1/4 (/.f64 1 (.f64 (sqrt.f64 1/2) x))))
(-.f64 (sqrt.f64 1/2) (+.f64 (.f64 1/4 (/.f64 1 (.f64 (sqrt.f64 1/2) x))) (.f64 1/32 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 x 2))))))
(-.f64 (sqrt.f64 1/2) (+.f64 (.f64 1/128 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 1/2) 5) (pow.f64 x 3)))) (+.f64 (.f64 1/4 (/.f64 1 (.f64 (sqrt.f64 1/2) x))) (.f64 1/32 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 x 2)))))))
(sqrt.f64 1/2)
(-.f64 (sqrt.f64 1/2) (.f64 1/4 (/.f64 1 (.f64 (sqrt.f64 1/2) x))))
(-.f64 (sqrt.f64 1/2) (+.f64 (.f64 1/4 (/.f64 1 (.f64 (sqrt.f64 1/2) x))) (.f64 1/32 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 x 2))))))
(-.f64 (sqrt.f64 1/2) (+.f64 (.f64 1/128 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 1/2) 5) (pow.f64 x 3)))) (+.f64 (.f64 1/4 (/.f64 1 (.f64 (sqrt.f64 1/2) x))) (.f64 1/32 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 x 2)))))))
(+.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x)))) 0)
(+.f64 0 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x)))))
(+.f64 -1 (neg.f64 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))) -2)))
(+.f64 -2 (-.f64 1 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))) -2)))
(+.f64 (neg.f64 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))) -2)) -1)
(+.f64 (.f64 1/2 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))))) (.f64 1/2 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))))))
(*.f64 1 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x)))))
(.f64 1/2 (.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x)))) 2))
(*.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x)))) 1)
(*.f64 -1 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))) -1))
(.f64 2 (.f64 1/2 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))))))
(*.f64 4 (/.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x)))) 4))
(.f64 (.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x)))) 2) 1/2)
(*.f64 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))) -1) -1)
(.f64 (.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x)))) 4) 1/4)
(.f64 1/4 (.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x)))) 4))
(.f64 (.f64 1/2 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))))) 2)
(*.f64 (/.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x)))) 4) 4)
(/.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x)))) 1)
(/.f64 (*.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x)))) 2) 2)
(/.f64 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))) -1) -1)
(/.f64 (*.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x)))) 4) 4)
(/.f64 (*.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x)))) 8) 8)
(/.f64 (*.f64 2 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))) -1)) -2)
(/.f64 (.f64 2 (.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x)))) 8)) 16)
(/.f64 (*.f64 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))) -1) 4) -4)
(/.f64 (neg.f64 (*.f64 2 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))) -1))) 2)
(/.f64 (.f64 2 (.f64 2 (*.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x)))) 8))) 32)
(/.f64 (.f64 2 (neg.f64 (.f64 2 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))) -1)))) 4)
(/.f64 (.f64 2 (.f64 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))) -1) 4)) -8)
(/.f64 (+.f64 (.f64 2 (.f64 2 (.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x)))) 8))) (.f64 2 (.f64 2 (.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x)))) 8)))) 64)
(/.f64 (+.f64 (.f64 2 (neg.f64 (.f64 2 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))) -1)))) (.f64 2 (neg.f64 (.f64 2 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))) -1))))) 8)
(pow.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x)))) 1)
(neg.f64 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))) -1))
(+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))) 0)
(+.f64 0 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))))
(+.f64 (.f64 1/2 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x)))) (.f64 1/2 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x)))))
(-.f64 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))) 0)
(*.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))))
(.f64 1/2 (.f64 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))) 2))
(*.f64 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))) 1)
(.f64 2 (.f64 1/2 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x)))))
(*.f64 4 (/.f64 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))) 4))
(.f64 (.f64 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))) 2) 1/2)
(.f64 (.f64 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))) 4) 1/4)
(.f64 1/4 (.f64 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))) 4))
(.f64 (.f64 1/2 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x)))) 2)
(*.f64 (/.f64 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))) 4) 4)
(/.f64 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))) 1)
(/.f64 (*.f64 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))) 2) 2)
(/.f64 (*.f64 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))) 4) 4)
(/.f64 (*.f64 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))) 8) 8)
(/.f64 (.f64 2 (.f64 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))) 8)) 16)
(/.f64 (.f64 2 (.f64 2 (*.f64 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))) 8))) 32)
(/.f64 (+.f64 (.f64 2 (.f64 2 (.f64 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))) 8))) (.f64 2 (.f64 2 (.f64 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))) 8)))) 64)
(pow.f64 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))) 1)

Outputs
(-.f64 1 (sqrt.f64 1/2))
(-.f64 (+.f64 1 (.f64 1/4 (/.f64 1 (.f64 (sqrt.f64 1/2) x)))) (sqrt.f64 1/2))
(+.f64 (.f64 1/4 (/.f64 1 (.f64 (sqrt.f64 1/2) x))) (-.f64 1 (sqrt.f64 1/2)))
(+.f64 (-.f64 1 (sqrt.f64 1/2)) (.f64 1/4 (/.f64 1 (.f64 (sqrt.f64 1/2) x))))
(+.f64 (-.f64 1 (sqrt.f64 1/2)) (*.f64 1/4 (/.f64 (/.f64 1 x) (sqrt.f64 1/2))))
(-.f64 (+.f64 1 (+.f64 (.f64 1/4 (/.f64 1 (.f64 (sqrt.f64 1/2) x))) (.f64 1/32 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 x 2)))))) (sqrt.f64 1/2))
(+.f64 (+.f64 (.f64 1/4 (/.f64 1 (.f64 (sqrt.f64 1/2) x))) (.f64 1/32 (/.f64 1 (.f64 (sqrt.f64 1/8) (pow.f64 x 2))))) (-.f64 1 (sqrt.f64 1/2)))
(+.f64 1 (-.f64 (+.f64 (.f64 1/4 (/.f64 1 (.f64 (sqrt.f64 1/2) x))) (*.f64 1/32 (/.f64 (/.f64 1 (pow.f64 x 2)) (sqrt.f64 1/8)))) (sqrt.f64 1/2)))
(+.f64 1 (+.f64 (.f64 1/4 (/.f64 (/.f64 1 x) (sqrt.f64 1/2))) (-.f64 (.f64 1/32 (/.f64 (/.f64 1 (pow.f64 x 2)) (sqrt.f64 1/8))) (sqrt.f64 1/2))))
(+.f64 (.f64 1/4 (/.f64 1 (.f64 (sqrt.f64 1/2) x))) (+.f64 (-.f64 1 (sqrt.f64 1/2)) (*.f64 1/32 (/.f64 (/.f64 1 (pow.f64 x 2)) (sqrt.f64 1/8)))))
(-.f64 (+.f64 1 (+.f64 (.f64 1/128 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 1/2) 5) (pow.f64 x 3)))) (+.f64 (.f64 1/4 (/.f64 1 (.f64 (sqrt.f64 1/2) x))) (.f64 1/32 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 x 2))))))) (sqrt.f64 1/2))
(+.f64 (+.f64 (.f64 1/4 (/.f64 1 (.f64 (sqrt.f64 1/2) x))) (+.f64 (.f64 1/32 (/.f64 1 (.f64 (sqrt.f64 1/8) (pow.f64 x 2)))) (.f64 1/128 (/.f64 1 (.f64 (sqrt.f64 1/32) (pow.f64 x 3)))))) (-.f64 1 (sqrt.f64 1/2)))
(+.f64 1 (-.f64 (+.f64 (.f64 1/4 (/.f64 1 (.f64 (sqrt.f64 1/2) x))) (+.f64 (.f64 1/32 (/.f64 (/.f64 1 (pow.f64 x 2)) (sqrt.f64 1/8))) (.f64 1/128 (/.f64 1 (*.f64 (sqrt.f64 1/32) (pow.f64 x 3)))))) (sqrt.f64 1/2)))
(+.f64 1 (+.f64 (+.f64 (.f64 1/4 (/.f64 (/.f64 1 x) (sqrt.f64 1/2))) (.f64 1/128 (/.f64 1 (.f64 (sqrt.f64 1/32) (pow.f64 x 3))))) (-.f64 (.f64 1/32 (/.f64 (/.f64 1 (pow.f64 x 2)) (sqrt.f64 1/8))) (sqrt.f64 1/2))))
(+.f64 1 (+.f64 (.f64 1/32 (/.f64 (/.f64 1 (pow.f64 x 2)) (sqrt.f64 1/8))) (+.f64 (-.f64 (.f64 1/4 (/.f64 (/.f64 1 x) (sqrt.f64 1/2))) (sqrt.f64 1/2)) (.f64 1/128 (/.f64 1 (.f64 (sqrt.f64 1/32) (pow.f64 x 3)))))))
(+.f64 1 (+.f64 (.f64 1/32 (/.f64 (/.f64 1 (pow.f64 x 2)) (sqrt.f64 1/8))) (+.f64 (.f64 1/4 (/.f64 1 (.f64 (sqrt.f64 1/2) x))) (-.f64 (.f64 1/128 (/.f64 1 (*.f64 (sqrt.f64 1/32) (pow.f64 x 3)))) (sqrt.f64 1/2)))))
(-.f64 1 (sqrt.f64 1/2))
(-.f64 (+.f64 1 (.f64 1/4 (/.f64 1 (.f64 (sqrt.f64 1/2) x)))) (sqrt.f64 1/2))
(+.f64 (.f64 1/4 (/.f64 1 (.f64 (sqrt.f64 1/2) x))) (-.f64 1 (sqrt.f64 1/2)))
(+.f64 (-.f64 1 (sqrt.f64 1/2)) (.f64 1/4 (/.f64 1 (.f64 (sqrt.f64 1/2) x))))
(+.f64 (-.f64 1 (sqrt.f64 1/2)) (*.f64 1/4 (/.f64 (/.f64 1 x) (sqrt.f64 1/2))))
(-.f64 (+.f64 1 (+.f64 (.f64 1/4 (/.f64 1 (.f64 (sqrt.f64 1/2) x))) (.f64 1/32 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 x 2)))))) (sqrt.f64 1/2))
(+.f64 (+.f64 (.f64 1/4 (/.f64 1 (.f64 (sqrt.f64 1/2) x))) (.f64 1/32 (/.f64 1 (.f64 (sqrt.f64 1/8) (pow.f64 x 2))))) (-.f64 1 (sqrt.f64 1/2)))
(+.f64 1 (-.f64 (+.f64 (.f64 1/4 (/.f64 1 (.f64 (sqrt.f64 1/2) x))) (*.f64 1/32 (/.f64 (/.f64 1 (pow.f64 x 2)) (sqrt.f64 1/8)))) (sqrt.f64 1/2)))
(+.f64 1 (+.f64 (.f64 1/4 (/.f64 (/.f64 1 x) (sqrt.f64 1/2))) (-.f64 (.f64 1/32 (/.f64 (/.f64 1 (pow.f64 x 2)) (sqrt.f64 1/8))) (sqrt.f64 1/2))))
(+.f64 (.f64 1/4 (/.f64 1 (.f64 (sqrt.f64 1/2) x))) (+.f64 (-.f64 1 (sqrt.f64 1/2)) (*.f64 1/32 (/.f64 (/.f64 1 (pow.f64 x 2)) (sqrt.f64 1/8)))))
(-.f64 (+.f64 1 (+.f64 (.f64 1/128 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 1/2) 5) (pow.f64 x 3)))) (+.f64 (.f64 1/4 (/.f64 1 (.f64 (sqrt.f64 1/2) x))) (.f64 1/32 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 x 2))))))) (sqrt.f64 1/2))
(+.f64 (+.f64 (.f64 1/4 (/.f64 1 (.f64 (sqrt.f64 1/2) x))) (+.f64 (.f64 1/32 (/.f64 1 (.f64 (sqrt.f64 1/8) (pow.f64 x 2)))) (.f64 1/128 (/.f64 1 (.f64 (sqrt.f64 1/32) (pow.f64 x 3)))))) (-.f64 1 (sqrt.f64 1/2)))
(+.f64 1 (-.f64 (+.f64 (.f64 1/4 (/.f64 1 (.f64 (sqrt.f64 1/2) x))) (+.f64 (.f64 1/32 (/.f64 (/.f64 1 (pow.f64 x 2)) (sqrt.f64 1/8))) (.f64 1/128 (/.f64 1 (*.f64 (sqrt.f64 1/32) (pow.f64 x 3)))))) (sqrt.f64 1/2)))
(+.f64 1 (+.f64 (+.f64 (.f64 1/4 (/.f64 (/.f64 1 x) (sqrt.f64 1/2))) (.f64 1/128 (/.f64 1 (.f64 (sqrt.f64 1/32) (pow.f64 x 3))))) (-.f64 (.f64 1/32 (/.f64 (/.f64 1 (pow.f64 x 2)) (sqrt.f64 1/8))) (sqrt.f64 1/2))))
(+.f64 1 (+.f64 (.f64 1/32 (/.f64 (/.f64 1 (pow.f64 x 2)) (sqrt.f64 1/8))) (+.f64 (-.f64 (.f64 1/4 (/.f64 (/.f64 1 x) (sqrt.f64 1/2))) (sqrt.f64 1/2)) (.f64 1/128 (/.f64 1 (.f64 (sqrt.f64 1/32) (pow.f64 x 3)))))))
(+.f64 1 (+.f64 (.f64 1/32 (/.f64 (/.f64 1 (pow.f64 x 2)) (sqrt.f64 1/8))) (+.f64 (.f64 1/4 (/.f64 1 (.f64 (sqrt.f64 1/2) x))) (-.f64 (.f64 1/128 (/.f64 1 (*.f64 (sqrt.f64 1/32) (pow.f64 x 3)))) (sqrt.f64 1/2)))))
(sqrt.f64 1/2)
(-.f64 (sqrt.f64 1/2) (.f64 1/4 (/.f64 1 (.f64 (sqrt.f64 1/2) x))))
(-.f64 (sqrt.f64 1/2) (*.f64 1/4 (/.f64 (/.f64 1 x) (sqrt.f64 1/2))))
(-.f64 (sqrt.f64 1/2) (+.f64 (.f64 1/4 (/.f64 1 (.f64 (sqrt.f64 1/2) x))) (.f64 1/32 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 x 2))))))
(-.f64 (sqrt.f64 1/2) (+.f64 (.f64 1/4 (/.f64 1 (.f64 (sqrt.f64 1/2) x))) (.f64 1/32 (/.f64 1 (.f64 (sqrt.f64 1/8) (pow.f64 x 2))))))
(-.f64 (sqrt.f64 1/2) (+.f64 (.f64 1/4 (/.f64 1 (.f64 (sqrt.f64 1/2) x))) (*.f64 1/32 (/.f64 (/.f64 1 (pow.f64 x 2)) (sqrt.f64 1/8)))))
(-.f64 (sqrt.f64 1/2) (+.f64 (.f64 1/4 (/.f64 (/.f64 1 x) (sqrt.f64 1/2))) (.f64 1/32 (/.f64 (/.f64 1 (pow.f64 x 2)) (sqrt.f64 1/8)))))
(-.f64 (sqrt.f64 1/2) (+.f64 (.f64 1/128 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 1/2) 5) (pow.f64 x 3)))) (+.f64 (.f64 1/4 (/.f64 1 (.f64 (sqrt.f64 1/2) x))) (.f64 1/32 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 x 2)))))))
(-.f64 (sqrt.f64 1/2) (+.f64 (.f64 1/4 (/.f64 1 (.f64 (sqrt.f64 1/2) x))) (+.f64 (.f64 1/32 (/.f64 1 (.f64 (sqrt.f64 1/8) (pow.f64 x 2)))) (.f64 1/128 (/.f64 1 (.f64 (sqrt.f64 1/32) (pow.f64 x 3)))))))
(-.f64 (sqrt.f64 1/2) (+.f64 (.f64 1/4 (/.f64 1 (.f64 (sqrt.f64 1/2) x))) (+.f64 (.f64 1/32 (/.f64 (/.f64 1 (pow.f64 x 2)) (sqrt.f64 1/8))) (.f64 1/128 (/.f64 1 (*.f64 (sqrt.f64 1/32) (pow.f64 x 3)))))))
(-.f64 (sqrt.f64 1/2) (+.f64 (.f64 1/4 (/.f64 (/.f64 1 x) (sqrt.f64 1/2))) (+.f64 (.f64 1/32 (/.f64 (/.f64 1 (pow.f64 x 2)) (sqrt.f64 1/8))) (.f64 1/128 (/.f64 1 (.f64 (sqrt.f64 1/32) (pow.f64 x 3)))))))
(-.f64 (sqrt.f64 1/2) (+.f64 (.f64 1/32 (/.f64 (/.f64 1 (pow.f64 x 2)) (sqrt.f64 1/8))) (+.f64 (.f64 1/4 (/.f64 1 (.f64 (sqrt.f64 1/2) x))) (.f64 1/128 (/.f64 1 (*.f64 (sqrt.f64 1/32) (pow.f64 x 3)))))))
(sqrt.f64 1/2)
(-.f64 (sqrt.f64 1/2) (.f64 1/4 (/.f64 1 (.f64 (sqrt.f64 1/2) x))))
(-.f64 (sqrt.f64 1/2) (*.f64 1/4 (/.f64 (/.f64 1 x) (sqrt.f64 1/2))))
(-.f64 (sqrt.f64 1/2) (+.f64 (.f64 1/4 (/.f64 1 (.f64 (sqrt.f64 1/2) x))) (.f64 1/32 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 x 2))))))
(-.f64 (sqrt.f64 1/2) (+.f64 (.f64 1/4 (/.f64 1 (.f64 (sqrt.f64 1/2) x))) (.f64 1/32 (/.f64 1 (.f64 (sqrt.f64 1/8) (pow.f64 x 2))))))
(-.f64 (sqrt.f64 1/2) (+.f64 (.f64 1/4 (/.f64 1 (.f64 (sqrt.f64 1/2) x))) (*.f64 1/32 (/.f64 (/.f64 1 (pow.f64 x 2)) (sqrt.f64 1/8)))))
(-.f64 (sqrt.f64 1/2) (+.f64 (.f64 1/4 (/.f64 (/.f64 1 x) (sqrt.f64 1/2))) (.f64 1/32 (/.f64 (/.f64 1 (pow.f64 x 2)) (sqrt.f64 1/8)))))
(-.f64 (sqrt.f64 1/2) (+.f64 (.f64 1/128 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 1/2) 5) (pow.f64 x 3)))) (+.f64 (.f64 1/4 (/.f64 1 (.f64 (sqrt.f64 1/2) x))) (.f64 1/32 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 x 2)))))))
(-.f64 (sqrt.f64 1/2) (+.f64 (.f64 1/4 (/.f64 1 (.f64 (sqrt.f64 1/2) x))) (+.f64 (.f64 1/32 (/.f64 1 (.f64 (sqrt.f64 1/8) (pow.f64 x 2)))) (.f64 1/128 (/.f64 1 (.f64 (sqrt.f64 1/32) (pow.f64 x 3)))))))
(-.f64 (sqrt.f64 1/2) (+.f64 (.f64 1/4 (/.f64 1 (.f64 (sqrt.f64 1/2) x))) (+.f64 (.f64 1/32 (/.f64 (/.f64 1 (pow.f64 x 2)) (sqrt.f64 1/8))) (.f64 1/128 (/.f64 1 (*.f64 (sqrt.f64 1/32) (pow.f64 x 3)))))))
(-.f64 (sqrt.f64 1/2) (+.f64 (.f64 1/4 (/.f64 (/.f64 1 x) (sqrt.f64 1/2))) (+.f64 (.f64 1/32 (/.f64 (/.f64 1 (pow.f64 x 2)) (sqrt.f64 1/8))) (.f64 1/128 (/.f64 1 (.f64 (sqrt.f64 1/32) (pow.f64 x 3)))))))
(-.f64 (sqrt.f64 1/2) (+.f64 (.f64 1/32 (/.f64 (/.f64 1 (pow.f64 x 2)) (sqrt.f64 1/8))) (+.f64 (.f64 1/4 (/.f64 1 (.f64 (sqrt.f64 1/2) x))) (.f64 1/128 (/.f64 1 (*.f64 (sqrt.f64 1/32) (pow.f64 x 3)))))))
(+.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x)))) 0)
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))))
(+.f64 0 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x)))))
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))))
(+.f64 -1 (neg.f64 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))) -2)))
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))))
(+.f64 -2 (-.f64 1 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))) -2)))
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))))
(+.f64 (neg.f64 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))) -2)) -1)
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))))
(+.f64 (.f64 1/2 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))))) (.f64 1/2 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))))))
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))))
(*.f64 1 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x)))))
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))))
(.f64 1/2 (.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x)))) 2))
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))))
(*.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x)))) 1)
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))))
(*.f64 -1 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))) -1))
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(.f64 2 (.f64 1/2 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))))))
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))))
(*.f64 4 (/.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x)))) 4))
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))))
(.f64 (.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x)))) 2) 1/2)
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))))
(*.f64 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))) -1) -1)
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(.f64 (.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x)))) 4) 1/4)
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(.f64 1/4 (.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x)))) 4))
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(/.f64 (*.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x)))) 2) 2)
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(/.f64 (.f64 2 (.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x)))) 8)) 16)
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(/.f64 (*.f64 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))) -1) 4) -4)
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(/.f64 (neg.f64 (*.f64 2 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))) -1))) 2)
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))))
(/.f64 (.f64 2 (.f64 2 (*.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x)))) 8))) 32)
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))))
(/.f64 (.f64 2 (neg.f64 (.f64 2 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))) -1)))) 4)
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))))
(/.f64 (.f64 2 (.f64 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))) -1) 4)) -8)
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(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))))
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(sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x)))
(+.f64 (.f64 1/2 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x)))) (.f64 1/2 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x)))))
(sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x)))
(-.f64 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))) 0)
(sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x)))
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(.f64 1/2 (.f64 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))) 2))
(sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x)))
(*.f64 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))) 1)
(sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x)))
(.f64 2 (.f64 1/2 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x)))))
(sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x)))
(*.f64 4 (/.f64 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))) 4))
(sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x)))
(.f64 (.f64 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))) 2) 1/2)
(sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x)))
(.f64 (.f64 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))) 4) 1/4)
(sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x)))
(.f64 1/4 (.f64 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))) 4))
(sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x)))
(.f64 (.f64 1/2 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x)))) 2)
(sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x)))
(*.f64 (/.f64 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))) 4) 4)
(sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x)))
(/.f64 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))) 1)
(sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x)))
(/.f64 (*.f64 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))) 2) 2)
(sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x)))
(/.f64 (*.f64 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))) 4) 4)
(sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x)))
(/.f64 (*.f64 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))) 8) 8)
(sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x)))
(/.f64 (.f64 2 (.f64 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))) 8)) 16)
(sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x)))
(/.f64 (.f64 2 (.f64 2 (*.f64 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))) 8))) 32)
(sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x)))
(/.f64 (+.f64 (.f64 2 (.f64 2 (.f64 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))) 8))) (.f64 2 (.f64 2 (.f64 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))) 8)))) 64)
(sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x)))
(pow.f64 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))) 1)
(sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x)))

localize12.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 x)))
✓	0.5b	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x))))

Compiler

Compiled 26 to 21 computations (19.2% saved)

series1.0ms (0%)

Counts

2 → 16

Calls

6 calls:

Time	Variable		Point	Expression
0.0ms	x	@	0	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x))))
0.0ms	x	@	inf	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x))))
0.0ms	x	@	0	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 x)))
0.0ms	x	@	inf	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 x)))
0.0ms	x	@	-inf	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 x)))

rewrite82.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

1226×	`rational.json-1`
1226×	`rational.json-2`
1226×	`rational.json-3`
1224×	`rational.json-4`
1208×	`exponential.json-3`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	40
1	77	40
2	176	40
3	370	40
4	755	40
5	2181	40
6	5289	40

Stop Event

1×	node limit

Counts

2 → 52

Calls

Call 1

Inputs
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x))))
(sqrt.f64 (+.f64 1/2 (/.f64 1/2 x)))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x)))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 -1 (neg.f64 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x))) -2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (neg.f64 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x))) -2)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 -2 (-.f64 1 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x))) -2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 1/2 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x))))) (*.f64 1/2 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/2 (*.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 2 (*.f64 1/2 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 4 (/.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x)))) 4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x)))) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x))) -1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -1 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x))) -1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x)))) 4) 1/4)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/4 (*.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x)))) 4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 1/2 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x))))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x)))) 4) 4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x)))) 2) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x))) -1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x)))) 4) 4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x))) -1)) -2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x)))) 8) 8)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x)))) 8)) 16)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x))) -1) 4) -4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (*.f64 2 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x))) -1))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 2 (*.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x)))) 8))) 32)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (neg.f64 (*.f64 2 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x))) -1)))) 4)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x))) -1))))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 1/2 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x)))) (*.f64 1/2 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/2 (*.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 2 (*.f64 1/2 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x))) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 4 (/.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x))) 4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x))) 4) 1/4)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/4 (*.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x))) 4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 1/2 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x))) 4) 4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x))) 2) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x))) 4) 4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x))) 8) 8)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x))) 8)) 16)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 2 (*.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x))) 8))) 32)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x))) 1)))))

simplify168.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

1462×	`rational.json-simplify-35`
1402×	`rational.json-simplify-61`
1216×	`rational.json-simplify-2`
854×	`rational.json-simplify-51`
812×	`rational.json-simplify-1`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	122	1942
1	264	1942
2	658	1942
3	1926	1942
4	3381	1942
5	3946	1942
6	4277	1942
7	4850	1942
8	6307	1942
9	7396	1942

Stop Event

1×	node limit

Counts

68 → 76

Calls

Call 1

Inputs
(-.f64 1 (sqrt.f64 1/2))
(-.f64 1 (+.f64 (sqrt.f64 1/2) (.f64 1/4 (/.f64 1 (.f64 (sqrt.f64 1/2) x)))))
(-.f64 (+.f64 1 (.f64 1/32 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 x 2))))) (+.f64 (sqrt.f64 1/2) (.f64 1/4 (/.f64 1 (.f64 (sqrt.f64 1/2) x)))))
(-.f64 (+.f64 1 (.f64 1/32 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 x 2))))) (+.f64 (sqrt.f64 1/2) (+.f64 (.f64 1/128 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 1/2) 5) (pow.f64 x 3)))) (.f64 1/4 (/.f64 1 (.f64 (sqrt.f64 1/2) x))))))
(-.f64 1 (sqrt.f64 1/2))
(-.f64 1 (+.f64 (sqrt.f64 1/2) (.f64 1/4 (/.f64 1 (.f64 (sqrt.f64 1/2) x)))))
(-.f64 (+.f64 1 (.f64 1/32 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 x 2))))) (+.f64 (sqrt.f64 1/2) (.f64 1/4 (/.f64 1 (.f64 (sqrt.f64 1/2) x)))))
(-.f64 (+.f64 1 (.f64 1/32 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 x 2))))) (+.f64 (sqrt.f64 1/2) (+.f64 (.f64 1/128 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 1/2) 5) (pow.f64 x 3)))) (.f64 1/4 (/.f64 1 (.f64 (sqrt.f64 1/2) x))))))
(sqrt.f64 1/2)
(+.f64 (sqrt.f64 1/2) (.f64 1/4 (/.f64 1 (.f64 (sqrt.f64 1/2) x))))
(-.f64 (+.f64 (sqrt.f64 1/2) (.f64 1/4 (/.f64 1 (.f64 (sqrt.f64 1/2) x)))) (.f64 1/32 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 x 2)))))
(-.f64 (+.f64 (sqrt.f64 1/2) (+.f64 (.f64 1/128 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 1/2) 5) (pow.f64 x 3)))) (.f64 1/4 (/.f64 1 (.f64 (sqrt.f64 1/2) x))))) (.f64 1/32 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 x 2)))))
(sqrt.f64 1/2)
(+.f64 (sqrt.f64 1/2) (.f64 1/4 (/.f64 1 (.f64 (sqrt.f64 1/2) x))))
(-.f64 (+.f64 (sqrt.f64 1/2) (.f64 1/4 (/.f64 1 (.f64 (sqrt.f64 1/2) x)))) (.f64 1/32 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 x 2)))))
(-.f64 (+.f64 (sqrt.f64 1/2) (+.f64 (.f64 1/128 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 1/2) 5) (pow.f64 x 3)))) (.f64 1/4 (/.f64 1 (.f64 (sqrt.f64 1/2) x))))) (.f64 1/32 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 x 2)))))
(+.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x)))) 0)
(+.f64 0 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x)))))
(+.f64 -1 (neg.f64 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x))) -2)))
(+.f64 (neg.f64 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x))) -2)) -1)
(+.f64 -2 (-.f64 1 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x))) -2)))
(+.f64 (.f64 1/2 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x))))) (.f64 1/2 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x))))))
(*.f64 1 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x)))))
(.f64 1/2 (.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x)))) 2))
(*.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x)))) 1)
(.f64 2 (.f64 1/2 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x))))))
(*.f64 4 (/.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x)))) 4))
(.f64 (.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x)))) 2) 1/2)
(*.f64 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x))) -1) -1)
(*.f64 -1 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x))) -1))
(.f64 (.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x)))) 4) 1/4)
(.f64 1/4 (.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x)))) 4))
(.f64 (.f64 1/2 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x))))) 2)
(*.f64 (/.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x)))) 4) 4)
(/.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x)))) 1)
(/.f64 (*.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x)))) 2) 2)
(/.f64 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x))) -1) -1)
(/.f64 (*.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x)))) 4) 4)
(/.f64 (*.f64 2 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x))) -1)) -2)
(/.f64 (*.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x)))) 8) 8)
(/.f64 (.f64 2 (.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x)))) 8)) 16)
(/.f64 (*.f64 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x))) -1) 4) -4)
(/.f64 (neg.f64 (*.f64 2 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x))) -1))) 2)
(/.f64 (.f64 2 (.f64 2 (*.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x)))) 8))) 32)
(/.f64 (.f64 2 (neg.f64 (.f64 2 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x))) -1)))) 4)
(pow.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x)))) 1)
(neg.f64 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x))) -1))
(+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x))) 0)
(+.f64 0 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x))))
(+.f64 (.f64 1/2 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x)))) (.f64 1/2 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x)))))
(-.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x))) 0)
(*.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x))))
(.f64 1/2 (.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x))) 2))
(*.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x))) 1)
(.f64 2 (.f64 1/2 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x)))))
(.f64 (.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x))) 2) 1/2)
(*.f64 4 (/.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x))) 4))
(.f64 (.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x))) 4) 1/4)
(.f64 1/4 (.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x))) 4))
(.f64 (.f64 1/2 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x)))) 2)
(*.f64 (/.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x))) 4) 4)
(/.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x))) 1)
(/.f64 (*.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x))) 2) 2)
(/.f64 (*.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x))) 4) 4)
(/.f64 (*.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x))) 8) 8)
(/.f64 (.f64 2 (.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x))) 8)) 16)
(/.f64 (.f64 2 (.f64 2 (*.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x))) 8))) 32)
(pow.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x))) 1)

Outputs
(-.f64 1 (sqrt.f64 1/2))
(-.f64 1 (+.f64 (sqrt.f64 1/2) (.f64 1/4 (/.f64 1 (.f64 (sqrt.f64 1/2) x)))))
(-.f64 1 (+.f64 (sqrt.f64 1/2) (*.f64 1/4 (/.f64 (/.f64 1 x) (sqrt.f64 1/2)))))
(-.f64 (+.f64 1 (.f64 1/32 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 x 2))))) (+.f64 (sqrt.f64 1/2) (.f64 1/4 (/.f64 1 (.f64 (sqrt.f64 1/2) x)))))
(-.f64 (+.f64 1 (.f64 1/32 (/.f64 (/.f64 1 (sqrt.f64 1/8)) (pow.f64 x 2)))) (+.f64 (sqrt.f64 1/2) (.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x)))))
(+.f64 1 (-.f64 (.f64 1/32 (/.f64 (/.f64 1 (sqrt.f64 1/8)) (pow.f64 x 2))) (+.f64 (sqrt.f64 1/2) (.f64 1/4 (/.f64 (/.f64 1 x) (sqrt.f64 1/2))))))
(+.f64 (-.f64 1 (+.f64 (sqrt.f64 1/2) (.f64 1/4 (/.f64 1 (.f64 (sqrt.f64 1/2) x))))) (*.f64 1/32 (/.f64 (/.f64 1 (sqrt.f64 1/8)) (pow.f64 x 2))))
(-.f64 (+.f64 1 (.f64 1/32 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 x 2))))) (+.f64 (sqrt.f64 1/2) (+.f64 (.f64 1/128 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 1/2) 5) (pow.f64 x 3)))) (.f64 1/4 (/.f64 1 (.f64 (sqrt.f64 1/2) x))))))
(-.f64 (+.f64 1 (.f64 1/32 (/.f64 (/.f64 1 (sqrt.f64 1/8)) (pow.f64 x 2)))) (+.f64 (sqrt.f64 1/2) (+.f64 (.f64 1/4 (/.f64 1 (.f64 (sqrt.f64 1/2) x))) (.f64 1/128 (/.f64 (/.f64 1 (sqrt.f64 1/32)) (pow.f64 x 3))))))
(-.f64 (+.f64 1 (.f64 1/32 (/.f64 (/.f64 1 (sqrt.f64 1/8)) (pow.f64 x 2)))) (+.f64 (+.f64 (sqrt.f64 1/2) (.f64 1/4 (/.f64 (/.f64 1 x) (sqrt.f64 1/2)))) (.f64 1/128 (/.f64 1 (.f64 (sqrt.f64 1/32) (pow.f64 x 3))))))
(-.f64 (+.f64 1 (.f64 1/32 (/.f64 (/.f64 1 (sqrt.f64 1/8)) (pow.f64 x 2)))) (+.f64 (sqrt.f64 1/2) (+.f64 (.f64 1/4 (/.f64 1 (.f64 (sqrt.f64 1/2) x))) (.f64 1/128 (/.f64 1 (*.f64 (sqrt.f64 1/32) (pow.f64 x 3)))))))
(-.f64 1 (sqrt.f64 1/2))
(-.f64 1 (+.f64 (sqrt.f64 1/2) (.f64 1/4 (/.f64 1 (.f64 (sqrt.f64 1/2) x)))))
(-.f64 1 (+.f64 (sqrt.f64 1/2) (*.f64 1/4 (/.f64 (/.f64 1 x) (sqrt.f64 1/2)))))
(-.f64 (+.f64 1 (.f64 1/32 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 x 2))))) (+.f64 (sqrt.f64 1/2) (.f64 1/4 (/.f64 1 (.f64 (sqrt.f64 1/2) x)))))
(-.f64 (+.f64 1 (.f64 1/32 (/.f64 (/.f64 1 (sqrt.f64 1/8)) (pow.f64 x 2)))) (+.f64 (sqrt.f64 1/2) (.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x)))))
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(+.f64 (-.f64 1 (+.f64 (sqrt.f64 1/2) (.f64 1/4 (/.f64 1 (.f64 (sqrt.f64 1/2) x))))) (*.f64 1/32 (/.f64 (/.f64 1 (sqrt.f64 1/8)) (pow.f64 x 2))))
(-.f64 (+.f64 1 (.f64 1/32 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 x 2))))) (+.f64 (sqrt.f64 1/2) (+.f64 (.f64 1/128 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 1/2) 5) (pow.f64 x 3)))) (.f64 1/4 (/.f64 1 (.f64 (sqrt.f64 1/2) x))))))
(-.f64 (+.f64 1 (.f64 1/32 (/.f64 (/.f64 1 (sqrt.f64 1/8)) (pow.f64 x 2)))) (+.f64 (sqrt.f64 1/2) (+.f64 (.f64 1/4 (/.f64 1 (.f64 (sqrt.f64 1/2) x))) (.f64 1/128 (/.f64 (/.f64 1 (sqrt.f64 1/32)) (pow.f64 x 3))))))
(-.f64 (+.f64 1 (.f64 1/32 (/.f64 (/.f64 1 (sqrt.f64 1/8)) (pow.f64 x 2)))) (+.f64 (+.f64 (sqrt.f64 1/2) (.f64 1/4 (/.f64 (/.f64 1 x) (sqrt.f64 1/2)))) (.f64 1/128 (/.f64 1 (.f64 (sqrt.f64 1/32) (pow.f64 x 3))))))
(-.f64 (+.f64 1 (.f64 1/32 (/.f64 (/.f64 1 (sqrt.f64 1/8)) (pow.f64 x 2)))) (+.f64 (sqrt.f64 1/2) (+.f64 (.f64 1/4 (/.f64 1 (.f64 (sqrt.f64 1/2) x))) (.f64 1/128 (/.f64 1 (*.f64 (sqrt.f64 1/32) (pow.f64 x 3)))))))
(sqrt.f64 1/2)
(+.f64 (sqrt.f64 1/2) (.f64 1/4 (/.f64 1 (.f64 (sqrt.f64 1/2) x))))
(+.f64 (sqrt.f64 1/2) (*.f64 1/4 (/.f64 (/.f64 1 x) (sqrt.f64 1/2))))
(-.f64 (+.f64 (sqrt.f64 1/2) (.f64 1/4 (/.f64 1 (.f64 (sqrt.f64 1/2) x)))) (.f64 1/32 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 x 2)))))
(+.f64 (.f64 1/4 (/.f64 1 (.f64 (sqrt.f64 1/2) x))) (-.f64 (sqrt.f64 1/2) (*.f64 1/32 (/.f64 (/.f64 1 (sqrt.f64 1/8)) (pow.f64 x 2)))))
(+.f64 (.f64 1/4 (/.f64 (/.f64 1 x) (sqrt.f64 1/2))) (-.f64 (sqrt.f64 1/2) (.f64 1/32 (/.f64 (/.f64 1 (sqrt.f64 1/8)) (pow.f64 x 2)))))
(-.f64 (+.f64 (sqrt.f64 1/2) (+.f64 (.f64 1/128 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 1/2) 5) (pow.f64 x 3)))) (.f64 1/4 (/.f64 1 (.f64 (sqrt.f64 1/2) x))))) (.f64 1/32 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 x 2)))))
(+.f64 (+.f64 (.f64 1/4 (/.f64 1 (.f64 (sqrt.f64 1/2) x))) (.f64 1/128 (/.f64 (/.f64 1 (sqrt.f64 1/32)) (pow.f64 x 3)))) (-.f64 (sqrt.f64 1/2) (.f64 1/32 (/.f64 (/.f64 1 (sqrt.f64 1/8)) (pow.f64 x 2)))))
(+.f64 (sqrt.f64 1/2) (-.f64 (+.f64 (.f64 1/4 (/.f64 1 (.f64 (sqrt.f64 1/2) x))) (.f64 1/128 (/.f64 (/.f64 1 (sqrt.f64 1/32)) (pow.f64 x 3)))) (.f64 1/32 (/.f64 (/.f64 1 (sqrt.f64 1/8)) (pow.f64 x 2)))))
(+.f64 (.f64 1/128 (/.f64 1 (.f64 (sqrt.f64 1/32) (pow.f64 x 3)))) (+.f64 (.f64 1/4 (/.f64 (/.f64 1 x) (sqrt.f64 1/2))) (-.f64 (sqrt.f64 1/2) (.f64 1/32 (/.f64 (/.f64 1 (sqrt.f64 1/8)) (pow.f64 x 2))))))
(+.f64 (.f64 1/4 (/.f64 1 (.f64 (sqrt.f64 1/2) x))) (+.f64 (.f64 1/128 (/.f64 1 (.f64 (sqrt.f64 1/32) (pow.f64 x 3)))) (-.f64 (sqrt.f64 1/2) (*.f64 1/32 (/.f64 (/.f64 1 (sqrt.f64 1/8)) (pow.f64 x 2))))))
(sqrt.f64 1/2)
(+.f64 (sqrt.f64 1/2) (.f64 1/4 (/.f64 1 (.f64 (sqrt.f64 1/2) x))))
(+.f64 (sqrt.f64 1/2) (*.f64 1/4 (/.f64 (/.f64 1 x) (sqrt.f64 1/2))))
(-.f64 (+.f64 (sqrt.f64 1/2) (.f64 1/4 (/.f64 1 (.f64 (sqrt.f64 1/2) x)))) (.f64 1/32 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 x 2)))))
(+.f64 (.f64 1/4 (/.f64 1 (.f64 (sqrt.f64 1/2) x))) (-.f64 (sqrt.f64 1/2) (*.f64 1/32 (/.f64 (/.f64 1 (sqrt.f64 1/8)) (pow.f64 x 2)))))
(+.f64 (.f64 1/4 (/.f64 (/.f64 1 x) (sqrt.f64 1/2))) (-.f64 (sqrt.f64 1/2) (.f64 1/32 (/.f64 (/.f64 1 (sqrt.f64 1/8)) (pow.f64 x 2)))))
(-.f64 (+.f64 (sqrt.f64 1/2) (+.f64 (.f64 1/128 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 1/2) 5) (pow.f64 x 3)))) (.f64 1/4 (/.f64 1 (.f64 (sqrt.f64 1/2) x))))) (.f64 1/32 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 x 2)))))
(+.f64 (+.f64 (.f64 1/4 (/.f64 1 (.f64 (sqrt.f64 1/2) x))) (.f64 1/128 (/.f64 (/.f64 1 (sqrt.f64 1/32)) (pow.f64 x 3)))) (-.f64 (sqrt.f64 1/2) (.f64 1/32 (/.f64 (/.f64 1 (sqrt.f64 1/8)) (pow.f64 x 2)))))
(+.f64 (sqrt.f64 1/2) (-.f64 (+.f64 (.f64 1/4 (/.f64 1 (.f64 (sqrt.f64 1/2) x))) (.f64 1/128 (/.f64 (/.f64 1 (sqrt.f64 1/32)) (pow.f64 x 3)))) (.f64 1/32 (/.f64 (/.f64 1 (sqrt.f64 1/8)) (pow.f64 x 2)))))
(+.f64 (.f64 1/128 (/.f64 1 (.f64 (sqrt.f64 1/32) (pow.f64 x 3)))) (+.f64 (.f64 1/4 (/.f64 (/.f64 1 x) (sqrt.f64 1/2))) (-.f64 (sqrt.f64 1/2) (.f64 1/32 (/.f64 (/.f64 1 (sqrt.f64 1/8)) (pow.f64 x 2))))))
(+.f64 (.f64 1/4 (/.f64 1 (.f64 (sqrt.f64 1/2) x))) (+.f64 (.f64 1/128 (/.f64 1 (.f64 (sqrt.f64 1/32) (pow.f64 x 3)))) (-.f64 (sqrt.f64 1/2) (*.f64 1/32 (/.f64 (/.f64 1 (sqrt.f64 1/8)) (pow.f64 x 2))))))
(+.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x)))) 0)
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x))))
(+.f64 0 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x)))))
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x))))
(+.f64 -1 (neg.f64 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x))) -2)))
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x))))
(+.f64 (neg.f64 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x))) -2)) -1)
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x))))
(+.f64 -2 (-.f64 1 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x))) -2)))
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x))))
(+.f64 (.f64 1/2 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x))))) (.f64 1/2 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x))))))
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x))))
(*.f64 1 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x)))))
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x))))
(.f64 1/2 (.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x)))) 2))
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x))))
(*.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x)))) 1)
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x))))
(.f64 2 (.f64 1/2 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x))))))
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x))))
(*.f64 4 (/.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x)))) 4))
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x))))
(.f64 (.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x)))) 2) 1/2)
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x))))
(*.f64 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x))) -1) -1)
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x))))
(*.f64 -1 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x))) -1))
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x))))
(.f64 (.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x)))) 4) 1/4)
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x))))
(.f64 1/4 (.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x)))) 4))
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x))))
(.f64 (.f64 1/2 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x))))) 2)
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x))))
(*.f64 (/.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x)))) 4) 4)
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x))))
(/.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x)))) 1)
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x))))
(/.f64 (*.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x)))) 2) 2)
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x))))
(/.f64 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x))) -1) -1)
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x))))
(/.f64 (*.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x)))) 4) 4)
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x))))
(/.f64 (*.f64 2 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x))) -1)) -2)
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x))))
(/.f64 (*.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x)))) 8) 8)
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x))))
(/.f64 (.f64 2 (.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x)))) 8)) 16)
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x))))
(/.f64 (*.f64 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x))) -1) 4) -4)
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x))))
(/.f64 (neg.f64 (*.f64 2 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x))) -1))) 2)
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x))))
(/.f64 (.f64 2 (.f64 2 (*.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x)))) 8))) 32)
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x))))
(/.f64 (.f64 2 (neg.f64 (.f64 2 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x))) -1)))) 4)
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x))))
(pow.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x)))) 1)
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x))))
(neg.f64 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x))) -1))
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x))))
(+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x))) 0)
(sqrt.f64 (+.f64 1/2 (/.f64 1/2 x)))
(+.f64 0 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x))))
(sqrt.f64 (+.f64 1/2 (/.f64 1/2 x)))
(+.f64 (.f64 1/2 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x)))) (.f64 1/2 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x)))))
(sqrt.f64 (+.f64 1/2 (/.f64 1/2 x)))
(-.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x))) 0)
(sqrt.f64 (+.f64 1/2 (/.f64 1/2 x)))
(*.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x))))
(sqrt.f64 (+.f64 1/2 (/.f64 1/2 x)))
(.f64 1/2 (.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x))) 2))
(sqrt.f64 (+.f64 1/2 (/.f64 1/2 x)))
(*.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x))) 1)
(sqrt.f64 (+.f64 1/2 (/.f64 1/2 x)))
(.f64 2 (.f64 1/2 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x)))))
(sqrt.f64 (+.f64 1/2 (/.f64 1/2 x)))
(.f64 (.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x))) 2) 1/2)
(sqrt.f64 (+.f64 1/2 (/.f64 1/2 x)))
(*.f64 4 (/.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x))) 4))
(sqrt.f64 (+.f64 1/2 (/.f64 1/2 x)))
(.f64 (.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x))) 4) 1/4)
(sqrt.f64 (+.f64 1/2 (/.f64 1/2 x)))
(.f64 1/4 (.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x))) 4))
(sqrt.f64 (+.f64 1/2 (/.f64 1/2 x)))
(.f64 (.f64 1/2 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x)))) 2)
(sqrt.f64 (+.f64 1/2 (/.f64 1/2 x)))
(*.f64 (/.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x))) 4) 4)
(sqrt.f64 (+.f64 1/2 (/.f64 1/2 x)))
(/.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x))) 1)
(sqrt.f64 (+.f64 1/2 (/.f64 1/2 x)))
(/.f64 (*.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x))) 2) 2)
(sqrt.f64 (+.f64 1/2 (/.f64 1/2 x)))
(/.f64 (*.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x))) 4) 4)
(sqrt.f64 (+.f64 1/2 (/.f64 1/2 x)))
(/.f64 (*.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x))) 8) 8)
(sqrt.f64 (+.f64 1/2 (/.f64 1/2 x)))
(/.f64 (.f64 2 (.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x))) 8)) 16)
(sqrt.f64 (+.f64 1/2 (/.f64 1/2 x)))
(/.f64 (.f64 2 (.f64 2 (*.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x))) 8))) 32)
(sqrt.f64 (+.f64 1/2 (/.f64 1/2 x)))
(pow.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x))) 1)
(sqrt.f64 (+.f64 1/2 (/.f64 1/2 x)))

localize13.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(pow.f64 x 2)
✓	0.1b	(*.f64 -11/128 (pow.f64 x 4))
✓	16.5b	(+.f64 (.f64 1/8 (pow.f64 x 2)) (.f64 -11/128 (pow.f64 x 4)))

Compiler

Compiled 33 to 26 computations (21.2% saved)

series2.0ms (0%)

Counts

2 → 3

Calls

6 calls:

Time	Variable		Point	Expression
0.0ms	x	@	inf	(+.f64 (.f64 1/8 (pow.f64 x 2)) (.f64 -11/128 (pow.f64 x 4)))
0.0ms	x	@	0	(+.f64 (.f64 1/8 (pow.f64 x 2)) (.f64 -11/128 (pow.f64 x 4)))
0.0ms	x	@	inf	(*.f64 -11/128 (pow.f64 x 4))
0.0ms	x	@	0	(*.f64 -11/128 (pow.f64 x 4))
0.0ms	x	@	-inf	(+.f64 (.f64 1/8 (pow.f64 x 2)) (.f64 -11/128 (pow.f64 x 4)))

rewrite183.0ms (1.6%)

Algorithm

1×	batch-egg-rewrite

Rules

1698×	`rational.json-simplify-35`
1644×	`rational.json-simplify-1`
1312×	`exponential.json-3`
1312×	`rational.json-1`
1312×	`rational.json-2`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	44
1	77	44
2	142	44
3	263	44
4	481	44
5	1094	44
6	2823	44
7	4807	44
8	5502	44
9	6787	44
10	7632	44
11	7632	44

Stop Event

1×	node limit

Counts

2 → 39

Calls

Call 1

Inputs
(+.f64 (.f64 1/8 (pow.f64 x 2)) (.f64 -11/128 (pow.f64 x 4)))
(*.f64 -11/128 (pow.f64 x 4))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 (*.f64 1/8 (pow.f64 x 2)) (*.f64 -11/128 (pow.f64 x 4))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/8 (*.f64 4 (+.f64 (*.f64 (pow.f64 x 4) -11/64) (*.f64 (pow.f64 x 2) 1/4))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 2 (+.f64 (*.f64 (pow.f64 x 4) -11/256) (*.f64 (pow.f64 x 2) 1/16)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 4 (*.f64 1/8 (+.f64 (*.f64 (pow.f64 x 4) -11/64) (*.f64 (pow.f64 x 2) 1/4))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (*.f64 1/8 (pow.f64 x 2)) (*.f64 -11/128 (pow.f64 x 4))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (+.f64 (*.f64 1/8 (pow.f64 x 2)) (*.f64 -11/128 (pow.f64 x 4))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (*.f64 (pow.f64 x 4) -11/64) (*.f64 (pow.f64 x 2) 1/4)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 8 (+.f64 (*.f64 (pow.f64 x 4) -11/256) (*.f64 (pow.f64 x 2) 1/16))) 1/4)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/4 (*.f64 8 (+.f64 (*.f64 (pow.f64 x 4) -11/256) (*.f64 (pow.f64 x 2) 1/16))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/4 (+.f64 (*.f64 (pow.f64 x 4) -11/32) (*.f64 (pow.f64 x 2) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 4 (+.f64 (*.f64 (pow.f64 x 4) -11/64) (*.f64 (pow.f64 x 2) 1/4))) 1/8)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/2 (+.f64 (*.f64 (pow.f64 x 4) -11/64) (*.f64 (pow.f64 x 2) 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (*.f64 (pow.f64 x 4) -11/256) (*.f64 (pow.f64 x 2) 1/16)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 1/8 (+.f64 (*.f64 (pow.f64 x 4) -11/64) (*.f64 (pow.f64 x 2) 1/4))) 4)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (*.f64 (pow.f64 x 4) -11/32) (*.f64 (pow.f64 x 2) 1/2)) 1/4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (*.f64 1/8 (pow.f64 x 2)) (*.f64 -11/128 (pow.f64 x 4))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (*.f64 (pow.f64 x 4) -11/64) (*.f64 (pow.f64 x 2) 1/4)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 8 (+.f64 (*.f64 (pow.f64 x 4) -11/256) (*.f64 (pow.f64 x 2) 1/16))) 4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 4 (+.f64 (*.f64 (pow.f64 x 4) -11/64) (*.f64 (pow.f64 x 2) 1/4))) 8)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 4 (+.f64 (*.f64 (pow.f64 x 4) -11/64) (*.f64 (pow.f64 x 2) 1/4)))) 16)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 2 (*.f64 4 (+.f64 (*.f64 (pow.f64 x 4) -11/64) (*.f64 (pow.f64 x 2) 1/4))))) 32)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 4 (+.f64 (*.f64 (pow.f64 x 4) -11/64) (*.f64 (pow.f64 x 2) 1/4)))))) 64)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 4 (+.f64 (*.f64 (pow.f64 x 4) -11/64) (*.f64 (pow.f64 x 2) 1/4))))))) 128)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 4 (+.f64 (*.f64 (pow.f64 x 4) -11/64) (*.f64 (pow.f64 x 2) 1/4)))))))) 256)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 (*.f64 1/8 (pow.f64 x 2)) (*.f64 -11/128 (pow.f64 x 4))) 1)))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 -11/128 (pow.f64 x 4)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 -11/128 (pow.f64 x 4)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (pow.f64 x 4) -11/256) (*.f64 (pow.f64 x 4) -11/256))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (*.f64 -11/128 (pow.f64 x 4)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 -11/128 (pow.f64 x 4)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (pow.f64 x 4) -11/64) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (pow.f64 x 4) -11/32) 4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (pow.f64 x 4) -11/16) 8)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 (pow.f64 x 4) -11/16)) 16)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 2 (*.f64 (pow.f64 x 4) -11/16))) 32)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 (pow.f64 x 4) -11/16)))) 64)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 (pow.f64 x 4) -11/16))))) 128)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 (pow.f64 x 4) -11/16)))))) 256)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 -11/128 (pow.f64 x 4)) 1)))))

simplify223.0ms (2%)

Algorithm

1×	egg-herbie

Rules

4152×	`rational.json-simplify-41`
2862×	`rational.json-simplify-43`
2188×	`rational.json-simplify-35`
1192×	`rational.json-simplify-2`
634×	`rational.json-simplify-1`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	89	996
1	199	996
2	372	996
3	838	996
4	2160	996
5	3039	996
6	3315	996
7	3489	996
8	3623	996
9	3734	996
10	3839	996
11	3941	996
12	4042	996
13	4143	996
14	4244	996
15	4244	996

Stop Event

1×	node limit

Counts

42 → 42

Calls

Call 1

Inputs
(*.f64 1/8 (pow.f64 x 2))
(*.f64 -11/128 (pow.f64 x 4))
(*.f64 -11/128 (pow.f64 x 4))
(-.f64 (+.f64 (.f64 1/8 (pow.f64 x 2)) (.f64 -11/128 (pow.f64 x 4))) 0)
(.f64 1/8 (.f64 4 (+.f64 (.f64 (pow.f64 x 4) -11/64) (.f64 (pow.f64 x 2) 1/4))))
(.f64 2 (+.f64 (.f64 (pow.f64 x 4) -11/256) (*.f64 (pow.f64 x 2) 1/16)))
(.f64 4 (.f64 1/8 (+.f64 (.f64 (pow.f64 x 4) -11/64) (.f64 (pow.f64 x 2) 1/4))))
(.f64 (+.f64 (.f64 1/8 (pow.f64 x 2)) (*.f64 -11/128 (pow.f64 x 4))) 1)
(.f64 1 (+.f64 (.f64 1/8 (pow.f64 x 2)) (*.f64 -11/128 (pow.f64 x 4))))
(.f64 (+.f64 (.f64 (pow.f64 x 4) -11/64) (*.f64 (pow.f64 x 2) 1/4)) 1/2)
(.f64 (.f64 8 (+.f64 (.f64 (pow.f64 x 4) -11/256) (.f64 (pow.f64 x 2) 1/16))) 1/4)
(.f64 1/4 (.f64 8 (+.f64 (.f64 (pow.f64 x 4) -11/256) (.f64 (pow.f64 x 2) 1/16))))
(.f64 1/4 (+.f64 (.f64 (pow.f64 x 4) -11/32) (*.f64 (pow.f64 x 2) 1/2)))
(.f64 (.f64 4 (+.f64 (.f64 (pow.f64 x 4) -11/64) (.f64 (pow.f64 x 2) 1/4))) 1/8)
(.f64 1/2 (+.f64 (.f64 (pow.f64 x 4) -11/64) (*.f64 (pow.f64 x 2) 1/4)))
(.f64 (+.f64 (.f64 (pow.f64 x 4) -11/256) (*.f64 (pow.f64 x 2) 1/16)) 2)
(.f64 (.f64 1/8 (+.f64 (.f64 (pow.f64 x 4) -11/64) (.f64 (pow.f64 x 2) 1/4))) 4)
(.f64 (+.f64 (.f64 (pow.f64 x 4) -11/32) (*.f64 (pow.f64 x 2) 1/2)) 1/4)
(/.f64 (+.f64 (.f64 1/8 (pow.f64 x 2)) (.f64 -11/128 (pow.f64 x 4))) 1)
(/.f64 (+.f64 (.f64 (pow.f64 x 4) -11/64) (.f64 (pow.f64 x 2) 1/4)) 2)
(/.f64 (.f64 8 (+.f64 (.f64 (pow.f64 x 4) -11/256) (*.f64 (pow.f64 x 2) 1/16))) 4)
(/.f64 (.f64 4 (+.f64 (.f64 (pow.f64 x 4) -11/64) (*.f64 (pow.f64 x 2) 1/4))) 8)
(/.f64 (.f64 2 (.f64 4 (+.f64 (.f64 (pow.f64 x 4) -11/64) (.f64 (pow.f64 x 2) 1/4)))) 16)
(/.f64 (.f64 2 (.f64 2 (.f64 4 (+.f64 (.f64 (pow.f64 x 4) -11/64) (*.f64 (pow.f64 x 2) 1/4))))) 32)
(/.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 4 (+.f64 (.f64 (pow.f64 x 4) -11/64) (.f64 (pow.f64 x 2) 1/4)))))) 64)
(/.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 4 (+.f64 (.f64 (pow.f64 x 4) -11/64) (*.f64 (pow.f64 x 2) 1/4))))))) 128)
(/.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 4 (+.f64 (.f64 (pow.f64 x 4) -11/64) (.f64 (pow.f64 x 2) 1/4)))))))) 256)
(pow.f64 (+.f64 (.f64 1/8 (pow.f64 x 2)) (.f64 -11/128 (pow.f64 x 4))) 1)
(+.f64 (*.f64 -11/128 (pow.f64 x 4)) 0)
(+.f64 0 (*.f64 -11/128 (pow.f64 x 4)))
(+.f64 (.f64 (pow.f64 x 4) -11/256) (.f64 (pow.f64 x 4) -11/256))
(-.f64 (*.f64 -11/128 (pow.f64 x 4)) 0)
(/.f64 (*.f64 -11/128 (pow.f64 x 4)) 1)
(/.f64 (*.f64 (pow.f64 x 4) -11/64) 2)
(/.f64 (*.f64 (pow.f64 x 4) -11/32) 4)
(/.f64 (*.f64 (pow.f64 x 4) -11/16) 8)
(/.f64 (.f64 2 (.f64 (pow.f64 x 4) -11/16)) 16)
(/.f64 (.f64 2 (.f64 2 (*.f64 (pow.f64 x 4) -11/16))) 32)
(/.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 (pow.f64 x 4) -11/16)))) 64)
(/.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (*.f64 (pow.f64 x 4) -11/16))))) 128)
(/.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 (pow.f64 x 4) -11/16)))))) 256)
(pow.f64 (*.f64 -11/128 (pow.f64 x 4)) 1)

Outputs
(*.f64 1/8 (pow.f64 x 2))
(*.f64 -11/128 (pow.f64 x 4))
(*.f64 -11/128 (pow.f64 x 4))
(-.f64 (+.f64 (.f64 1/8 (pow.f64 x 2)) (.f64 -11/128 (pow.f64 x 4))) 0)
(+.f64 (.f64 1/8 (pow.f64 x 2)) (.f64 -11/128 (pow.f64 x 4)))
(.f64 1/8 (.f64 4 (+.f64 (.f64 (pow.f64 x 4) -11/64) (.f64 (pow.f64 x 2) 1/4))))
(+.f64 (.f64 1/8 (pow.f64 x 2)) (.f64 -11/128 (pow.f64 x 4)))
(.f64 2 (+.f64 (.f64 (pow.f64 x 4) -11/256) (*.f64 (pow.f64 x 2) 1/16)))
(+.f64 (.f64 1/8 (pow.f64 x 2)) (.f64 -11/128 (pow.f64 x 4)))
(.f64 4 (.f64 1/8 (+.f64 (.f64 (pow.f64 x 4) -11/64) (.f64 (pow.f64 x 2) 1/4))))
(+.f64 (.f64 1/8 (pow.f64 x 2)) (.f64 -11/128 (pow.f64 x 4)))
(.f64 (+.f64 (.f64 1/8 (pow.f64 x 2)) (*.f64 -11/128 (pow.f64 x 4))) 1)
(+.f64 (.f64 1/8 (pow.f64 x 2)) (.f64 -11/128 (pow.f64 x 4)))
(.f64 1 (+.f64 (.f64 1/8 (pow.f64 x 2)) (*.f64 -11/128 (pow.f64 x 4))))
(+.f64 (.f64 1/8 (pow.f64 x 2)) (.f64 -11/128 (pow.f64 x 4)))
(.f64 (+.f64 (.f64 (pow.f64 x 4) -11/64) (*.f64 (pow.f64 x 2) 1/4)) 1/2)
(+.f64 (.f64 1/8 (pow.f64 x 2)) (.f64 -11/128 (pow.f64 x 4)))
(.f64 (.f64 8 (+.f64 (.f64 (pow.f64 x 4) -11/256) (.f64 (pow.f64 x 2) 1/16))) 1/4)
(+.f64 (.f64 1/8 (pow.f64 x 2)) (.f64 -11/128 (pow.f64 x 4)))
(.f64 1/4 (.f64 8 (+.f64 (.f64 (pow.f64 x 4) -11/256) (.f64 (pow.f64 x 2) 1/16))))
(+.f64 (.f64 1/8 (pow.f64 x 2)) (.f64 -11/128 (pow.f64 x 4)))
(.f64 1/4 (+.f64 (.f64 (pow.f64 x 4) -11/32) (*.f64 (pow.f64 x 2) 1/2)))
(+.f64 (.f64 1/8 (pow.f64 x 2)) (.f64 -11/128 (pow.f64 x 4)))
(.f64 (.f64 4 (+.f64 (.f64 (pow.f64 x 4) -11/64) (.f64 (pow.f64 x 2) 1/4))) 1/8)
(+.f64 (.f64 1/8 (pow.f64 x 2)) (.f64 -11/128 (pow.f64 x 4)))
(.f64 1/2 (+.f64 (.f64 (pow.f64 x 4) -11/64) (*.f64 (pow.f64 x 2) 1/4)))
(+.f64 (.f64 1/8 (pow.f64 x 2)) (.f64 -11/128 (pow.f64 x 4)))
(.f64 (+.f64 (.f64 (pow.f64 x 4) -11/256) (*.f64 (pow.f64 x 2) 1/16)) 2)
(+.f64 (.f64 1/8 (pow.f64 x 2)) (.f64 -11/128 (pow.f64 x 4)))
(.f64 (.f64 1/8 (+.f64 (.f64 (pow.f64 x 4) -11/64) (.f64 (pow.f64 x 2) 1/4))) 4)
(+.f64 (.f64 1/8 (pow.f64 x 2)) (.f64 -11/128 (pow.f64 x 4)))
(.f64 (+.f64 (.f64 (pow.f64 x 4) -11/32) (*.f64 (pow.f64 x 2) 1/2)) 1/4)
(+.f64 (.f64 1/8 (pow.f64 x 2)) (.f64 -11/128 (pow.f64 x 4)))
(/.f64 (+.f64 (.f64 1/8 (pow.f64 x 2)) (.f64 -11/128 (pow.f64 x 4))) 1)
(+.f64 (.f64 1/8 (pow.f64 x 2)) (.f64 -11/128 (pow.f64 x 4)))
(/.f64 (+.f64 (.f64 (pow.f64 x 4) -11/64) (.f64 (pow.f64 x 2) 1/4)) 2)
(+.f64 (.f64 1/8 (pow.f64 x 2)) (.f64 -11/128 (pow.f64 x 4)))
(/.f64 (.f64 8 (+.f64 (.f64 (pow.f64 x 4) -11/256) (*.f64 (pow.f64 x 2) 1/16))) 4)
(+.f64 (.f64 1/8 (pow.f64 x 2)) (.f64 -11/128 (pow.f64 x 4)))
(/.f64 (.f64 4 (+.f64 (.f64 (pow.f64 x 4) -11/64) (*.f64 (pow.f64 x 2) 1/4))) 8)
(+.f64 (.f64 1/8 (pow.f64 x 2)) (.f64 -11/128 (pow.f64 x 4)))
(/.f64 (.f64 2 (.f64 4 (+.f64 (.f64 (pow.f64 x 4) -11/64) (.f64 (pow.f64 x 2) 1/4)))) 16)
(+.f64 (.f64 1/8 (pow.f64 x 2)) (.f64 -11/128 (pow.f64 x 4)))
(/.f64 (.f64 2 (.f64 2 (.f64 4 (+.f64 (.f64 (pow.f64 x 4) -11/64) (*.f64 (pow.f64 x 2) 1/4))))) 32)
(+.f64 (.f64 1/8 (pow.f64 x 2)) (.f64 -11/128 (pow.f64 x 4)))
(/.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 4 (+.f64 (.f64 (pow.f64 x 4) -11/64) (.f64 (pow.f64 x 2) 1/4)))))) 64)
(+.f64 (.f64 1/8 (pow.f64 x 2)) (.f64 -11/128 (pow.f64 x 4)))
(/.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 4 (+.f64 (.f64 (pow.f64 x 4) -11/64) (*.f64 (pow.f64 x 2) 1/4))))))) 128)
(+.f64 (.f64 1/8 (pow.f64 x 2)) (.f64 -11/128 (pow.f64 x 4)))
(/.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 4 (+.f64 (.f64 (pow.f64 x 4) -11/64) (.f64 (pow.f64 x 2) 1/4)))))))) 256)
(+.f64 (.f64 1/8 (pow.f64 x 2)) (.f64 -11/128 (pow.f64 x 4)))
(pow.f64 (+.f64 (.f64 1/8 (pow.f64 x 2)) (.f64 -11/128 (pow.f64 x 4))) 1)
(+.f64 (.f64 1/8 (pow.f64 x 2)) (.f64 -11/128 (pow.f64 x 4)))
(+.f64 (*.f64 -11/128 (pow.f64 x 4)) 0)
(*.f64 -11/128 (pow.f64 x 4))
(+.f64 0 (*.f64 -11/128 (pow.f64 x 4)))
(*.f64 -11/128 (pow.f64 x 4))
(+.f64 (.f64 (pow.f64 x 4) -11/256) (.f64 (pow.f64 x 4) -11/256))
(*.f64 -11/128 (pow.f64 x 4))
(-.f64 (*.f64 -11/128 (pow.f64 x 4)) 0)
(*.f64 -11/128 (pow.f64 x 4))
(/.f64 (*.f64 -11/128 (pow.f64 x 4)) 1)
(*.f64 -11/128 (pow.f64 x 4))
(/.f64 (*.f64 (pow.f64 x 4) -11/64) 2)
(*.f64 -11/128 (pow.f64 x 4))
(/.f64 (*.f64 (pow.f64 x 4) -11/32) 4)
(*.f64 -11/128 (pow.f64 x 4))
(/.f64 (*.f64 (pow.f64 x 4) -11/16) 8)
(*.f64 -11/128 (pow.f64 x 4))
(/.f64 (.f64 2 (.f64 (pow.f64 x 4) -11/16)) 16)
(*.f64 -11/128 (pow.f64 x 4))
(/.f64 (.f64 2 (.f64 2 (*.f64 (pow.f64 x 4) -11/16))) 32)
(*.f64 -11/128 (pow.f64 x 4))
(/.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 (pow.f64 x 4) -11/16)))) 64)
(*.f64 -11/128 (pow.f64 x 4))
(/.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (*.f64 (pow.f64 x 4) -11/16))))) 128)
(*.f64 -11/128 (pow.f64 x 4))
(/.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 (pow.f64 x 4) -11/16)))))) 256)
(*.f64 -11/128 (pow.f64 x 4))
(pow.f64 (*.f64 -11/128 (pow.f64 x 4)) 1)
(*.f64 -11/128 (pow.f64 x 4))

localize14.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (-.f64 1 (sqrt.f64 1/2)) (*.f64 1/2 (/.f64 (sqrt.f64 1/2) x)))
	0.4b	(/.f64 (sqrt.f64 1/2) x)
	1.0b	(-.f64 1 (sqrt.f64 1/2))

Compiler

Compiled 31 to 27 computations (12.9% saved)

series1.0ms (0%)

Counts

1 → 12

Calls

3 calls:

Time

Variable

Point

Expression

0.0ms

(+.f64 (-.f64 1 (sqrt.f64 1/2)) (*.f64 1/2 (/.f64 (sqrt.f64 1/2) x)))

0.0ms

-inf

(+.f64 (-.f64 1 (sqrt.f64 1/2)) (*.f64 1/2 (/.f64 (sqrt.f64 1/2) x)))

0.0ms

inf

(+.f64 (-.f64 1 (sqrt.f64 1/2)) (*.f64 1/2 (/.f64 (sqrt.f64 1/2) x)))

rewrite81.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

1550×	`rational.json-1`
1550×	`rational.json-2`
1550×	`rational.json-4`
1550×	`rational.json-3`
1544×	`exponential.json-3`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	33
1	82	33
2	185	33
3	405	33
4	1013	33
5	4253	33

Stop Event

1×	node limit

Counts

1 → 19

Calls

Call 1

Inputs
(+.f64 (-.f64 1 (sqrt.f64 1/2)) (*.f64 1/2 (/.f64 (sqrt.f64 1/2) x)))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 (-.f64 1 (sqrt.f64 1/2)) (*.f64 (sqrt.f64 1/2) (/.f64 1/2 x))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (+.f64 (-.f64 1 (sqrt.f64 1/2)) (*.f64 (sqrt.f64 1/2) (/.f64 1/2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/2 (*.f64 (+.f64 (-.f64 1 (sqrt.f64 1/2)) (*.f64 (sqrt.f64 1/2) (/.f64 1/2 x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/2 (+.f64 (/.f64 (sqrt.f64 1/2) x) (*.f64 (-.f64 1 (sqrt.f64 1/2)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (-.f64 1 (sqrt.f64 1/2)) (*.f64 (sqrt.f64 1/2) (/.f64 1/2 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 2 (*.f64 1/2 (+.f64 (-.f64 1 (sqrt.f64 1/2)) (*.f64 (sqrt.f64 1/2) (/.f64 1/2 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 4 (/.f64 (+.f64 (-.f64 1 (sqrt.f64 1/2)) (*.f64 (sqrt.f64 1/2) (/.f64 1/2 x))) 4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (+.f64 (-.f64 1 (sqrt.f64 1/2)) (*.f64 (sqrt.f64 1/2) (/.f64 1/2 x))) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (+.f64 (-.f64 1 (sqrt.f64 1/2)) (*.f64 (sqrt.f64 1/2) (/.f64 1/2 x))) 4) 1/4)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/4 (*.f64 (+.f64 (-.f64 1 (sqrt.f64 1/2)) (*.f64 (sqrt.f64 1/2) (/.f64 1/2 x))) 4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 1/2 (+.f64 (-.f64 1 (sqrt.f64 1/2)) (*.f64 (sqrt.f64 1/2) (/.f64 1/2 x)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (+.f64 (-.f64 1 (sqrt.f64 1/2)) (*.f64 (sqrt.f64 1/2) (/.f64 1/2 x))) 4) 4)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (/.f64 (sqrt.f64 1/2) x) (*.f64 (-.f64 1 (sqrt.f64 1/2)) 2)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (-.f64 1 (sqrt.f64 1/2)) (*.f64 (sqrt.f64 1/2) (/.f64 1/2 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (+.f64 (-.f64 1 (sqrt.f64 1/2)) (*.f64 (sqrt.f64 1/2) (/.f64 1/2 x))) 2) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (+.f64 (-.f64 1 (sqrt.f64 1/2)) (*.f64 (sqrt.f64 1/2) (/.f64 1/2 x))) 4) 4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 (+.f64 (-.f64 1 (sqrt.f64 1/2)) (*.f64 (sqrt.f64 1/2) (/.f64 1/2 x))) 4)) 8)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (*.f64 2 (*.f64 (+.f64 (-.f64 1 (sqrt.f64 1/2)) (*.f64 (sqrt.f64 1/2) (/.f64 1/2 x))) 4)) (*.f64 2 (*.f64 (+.f64 (-.f64 1 (sqrt.f64 1/2)) (*.f64 (sqrt.f64 1/2) (/.f64 1/2 x))) 4))) 16)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 (-.f64 1 (sqrt.f64 1/2)) (*.f64 (sqrt.f64 1/2) (/.f64 1/2 x))) 1)))))

simplify184.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

1504×	`rational.json-simplify-46`
1106×	`rational.json-simplify-1`
1054×	`rational.json-simplify-35`
970×	`rational.json-simplify-2`
872×	`rational.json-simplify-19`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	48	975
1	90	975
2	266	975
3	593	975
4	1285	975
5	2517	975
6	3236	975
7	3305	975
8	3368	975
9	3477	975
10	3857	975
11	5463	975
12	7795	975

Stop Event

1×	node limit

Counts

31 → 24

Calls

Call 1

Inputs
(*.f64 1/2 (/.f64 (sqrt.f64 1/2) x))
(-.f64 (+.f64 1 (*.f64 1/2 (/.f64 (sqrt.f64 1/2) x))) (sqrt.f64 1/2))
(-.f64 (+.f64 1 (*.f64 1/2 (/.f64 (sqrt.f64 1/2) x))) (sqrt.f64 1/2))
(-.f64 (+.f64 1 (*.f64 1/2 (/.f64 (sqrt.f64 1/2) x))) (sqrt.f64 1/2))
(-.f64 1 (sqrt.f64 1/2))
(-.f64 (+.f64 1 (*.f64 1/2 (/.f64 (sqrt.f64 1/2) x))) (sqrt.f64 1/2))
(-.f64 (+.f64 1 (*.f64 1/2 (/.f64 (sqrt.f64 1/2) x))) (sqrt.f64 1/2))
(-.f64 (+.f64 1 (*.f64 1/2 (/.f64 (sqrt.f64 1/2) x))) (sqrt.f64 1/2))
(-.f64 1 (sqrt.f64 1/2))
(-.f64 (+.f64 1 (*.f64 1/2 (/.f64 (sqrt.f64 1/2) x))) (sqrt.f64 1/2))
(-.f64 (+.f64 1 (*.f64 1/2 (/.f64 (sqrt.f64 1/2) x))) (sqrt.f64 1/2))
(-.f64 (+.f64 1 (*.f64 1/2 (/.f64 (sqrt.f64 1/2) x))) (sqrt.f64 1/2))
(-.f64 (+.f64 (-.f64 1 (sqrt.f64 1/2)) (*.f64 (sqrt.f64 1/2) (/.f64 1/2 x))) 0)
(.f64 1 (+.f64 (-.f64 1 (sqrt.f64 1/2)) (.f64 (sqrt.f64 1/2) (/.f64 1/2 x))))
(.f64 1/2 (.f64 (+.f64 (-.f64 1 (sqrt.f64 1/2)) (*.f64 (sqrt.f64 1/2) (/.f64 1/2 x))) 2))
(.f64 1/2 (+.f64 (/.f64 (sqrt.f64 1/2) x) (.f64 (-.f64 1 (sqrt.f64 1/2)) 2)))
(.f64 (+.f64 (-.f64 1 (sqrt.f64 1/2)) (.f64 (sqrt.f64 1/2) (/.f64 1/2 x))) 1)
(.f64 2 (.f64 1/2 (+.f64 (-.f64 1 (sqrt.f64 1/2)) (*.f64 (sqrt.f64 1/2) (/.f64 1/2 x)))))
(.f64 4 (/.f64 (+.f64 (-.f64 1 (sqrt.f64 1/2)) (.f64 (sqrt.f64 1/2) (/.f64 1/2 x))) 4))
(.f64 (.f64 (+.f64 (-.f64 1 (sqrt.f64 1/2)) (*.f64 (sqrt.f64 1/2) (/.f64 1/2 x))) 2) 1/2)
(.f64 (.f64 (+.f64 (-.f64 1 (sqrt.f64 1/2)) (*.f64 (sqrt.f64 1/2) (/.f64 1/2 x))) 4) 1/4)
(.f64 1/4 (.f64 (+.f64 (-.f64 1 (sqrt.f64 1/2)) (*.f64 (sqrt.f64 1/2) (/.f64 1/2 x))) 4))
(.f64 (.f64 1/2 (+.f64 (-.f64 1 (sqrt.f64 1/2)) (*.f64 (sqrt.f64 1/2) (/.f64 1/2 x)))) 2)
(.f64 (/.f64 (+.f64 (-.f64 1 (sqrt.f64 1/2)) (.f64 (sqrt.f64 1/2) (/.f64 1/2 x))) 4) 4)
(.f64 (+.f64 (/.f64 (sqrt.f64 1/2) x) (.f64 (-.f64 1 (sqrt.f64 1/2)) 2)) 1/2)
(/.f64 (+.f64 (-.f64 1 (sqrt.f64 1/2)) (*.f64 (sqrt.f64 1/2) (/.f64 1/2 x))) 1)
(/.f64 (.f64 (+.f64 (-.f64 1 (sqrt.f64 1/2)) (.f64 (sqrt.f64 1/2) (/.f64 1/2 x))) 2) 2)
(/.f64 (.f64 (+.f64 (-.f64 1 (sqrt.f64 1/2)) (.f64 (sqrt.f64 1/2) (/.f64 1/2 x))) 4) 4)
(/.f64 (.f64 2 (.f64 (+.f64 (-.f64 1 (sqrt.f64 1/2)) (*.f64 (sqrt.f64 1/2) (/.f64 1/2 x))) 4)) 8)
(/.f64 (+.f64 (.f64 2 (.f64 (+.f64 (-.f64 1 (sqrt.f64 1/2)) (.f64 (sqrt.f64 1/2) (/.f64 1/2 x))) 4)) (.f64 2 (.f64 (+.f64 (-.f64 1 (sqrt.f64 1/2)) (.f64 (sqrt.f64 1/2) (/.f64 1/2 x))) 4))) 16)
(pow.f64 (+.f64 (-.f64 1 (sqrt.f64 1/2)) (*.f64 (sqrt.f64 1/2) (/.f64 1/2 x))) 1)

Outputs
(*.f64 1/2 (/.f64 (sqrt.f64 1/2) x))
(-.f64 (+.f64 1 (*.f64 1/2 (/.f64 (sqrt.f64 1/2) x))) (sqrt.f64 1/2))
(+.f64 (*.f64 1/2 (/.f64 (sqrt.f64 1/2) x)) (-.f64 1 (sqrt.f64 1/2)))
(-.f64 (+.f64 1 (*.f64 1/2 (/.f64 (sqrt.f64 1/2) x))) (sqrt.f64 1/2))
(+.f64 (*.f64 1/2 (/.f64 (sqrt.f64 1/2) x)) (-.f64 1 (sqrt.f64 1/2)))
(-.f64 (+.f64 1 (*.f64 1/2 (/.f64 (sqrt.f64 1/2) x))) (sqrt.f64 1/2))
(+.f64 (*.f64 1/2 (/.f64 (sqrt.f64 1/2) x)) (-.f64 1 (sqrt.f64 1/2)))
(-.f64 1 (sqrt.f64 1/2))
(-.f64 (+.f64 1 (*.f64 1/2 (/.f64 (sqrt.f64 1/2) x))) (sqrt.f64 1/2))
(+.f64 (*.f64 1/2 (/.f64 (sqrt.f64 1/2) x)) (-.f64 1 (sqrt.f64 1/2)))
(-.f64 (+.f64 1 (*.f64 1/2 (/.f64 (sqrt.f64 1/2) x))) (sqrt.f64 1/2))
(+.f64 (*.f64 1/2 (/.f64 (sqrt.f64 1/2) x)) (-.f64 1 (sqrt.f64 1/2)))
(-.f64 (+.f64 1 (*.f64 1/2 (/.f64 (sqrt.f64 1/2) x))) (sqrt.f64 1/2))
(+.f64 (*.f64 1/2 (/.f64 (sqrt.f64 1/2) x)) (-.f64 1 (sqrt.f64 1/2)))
(-.f64 1 (sqrt.f64 1/2))
(-.f64 (+.f64 1 (*.f64 1/2 (/.f64 (sqrt.f64 1/2) x))) (sqrt.f64 1/2))
(+.f64 (*.f64 1/2 (/.f64 (sqrt.f64 1/2) x)) (-.f64 1 (sqrt.f64 1/2)))
(-.f64 (+.f64 1 (*.f64 1/2 (/.f64 (sqrt.f64 1/2) x))) (sqrt.f64 1/2))
(+.f64 (*.f64 1/2 (/.f64 (sqrt.f64 1/2) x)) (-.f64 1 (sqrt.f64 1/2)))
(-.f64 (+.f64 1 (*.f64 1/2 (/.f64 (sqrt.f64 1/2) x))) (sqrt.f64 1/2))
(+.f64 (*.f64 1/2 (/.f64 (sqrt.f64 1/2) x)) (-.f64 1 (sqrt.f64 1/2)))
(-.f64 (+.f64 (-.f64 1 (sqrt.f64 1/2)) (*.f64 (sqrt.f64 1/2) (/.f64 1/2 x))) 0)
(+.f64 (-.f64 1 (sqrt.f64 1/2)) (*.f64 (sqrt.f64 1/2) (/.f64 1/2 x)))
(.f64 1 (+.f64 (-.f64 1 (sqrt.f64 1/2)) (.f64 (sqrt.f64 1/2) (/.f64 1/2 x))))
(+.f64 (-.f64 1 (sqrt.f64 1/2)) (*.f64 (sqrt.f64 1/2) (/.f64 1/2 x)))
(.f64 1/2 (.f64 (+.f64 (-.f64 1 (sqrt.f64 1/2)) (*.f64 (sqrt.f64 1/2) (/.f64 1/2 x))) 2))
(+.f64 (-.f64 1 (sqrt.f64 1/2)) (*.f64 (sqrt.f64 1/2) (/.f64 1/2 x)))
(.f64 1/2 (+.f64 (/.f64 (sqrt.f64 1/2) x) (.f64 (-.f64 1 (sqrt.f64 1/2)) 2)))
(.f64 (+.f64 (-.f64 1 (sqrt.f64 1/2)) (.f64 (sqrt.f64 1/2) (/.f64 1/2 x))) 1)
(+.f64 (-.f64 1 (sqrt.f64 1/2)) (*.f64 (sqrt.f64 1/2) (/.f64 1/2 x)))
(.f64 2 (.f64 1/2 (+.f64 (-.f64 1 (sqrt.f64 1/2)) (*.f64 (sqrt.f64 1/2) (/.f64 1/2 x)))))
(+.f64 (-.f64 1 (sqrt.f64 1/2)) (*.f64 (sqrt.f64 1/2) (/.f64 1/2 x)))
(.f64 4 (/.f64 (+.f64 (-.f64 1 (sqrt.f64 1/2)) (.f64 (sqrt.f64 1/2) (/.f64 1/2 x))) 4))
(+.f64 (-.f64 1 (sqrt.f64 1/2)) (*.f64 (sqrt.f64 1/2) (/.f64 1/2 x)))
(.f64 (.f64 (+.f64 (-.f64 1 (sqrt.f64 1/2)) (*.f64 (sqrt.f64 1/2) (/.f64 1/2 x))) 2) 1/2)
(+.f64 (-.f64 1 (sqrt.f64 1/2)) (*.f64 (sqrt.f64 1/2) (/.f64 1/2 x)))
(.f64 (.f64 (+.f64 (-.f64 1 (sqrt.f64 1/2)) (*.f64 (sqrt.f64 1/2) (/.f64 1/2 x))) 4) 1/4)
(+.f64 (-.f64 1 (sqrt.f64 1/2)) (*.f64 (sqrt.f64 1/2) (/.f64 1/2 x)))
(.f64 1/4 (.f64 (+.f64 (-.f64 1 (sqrt.f64 1/2)) (*.f64 (sqrt.f64 1/2) (/.f64 1/2 x))) 4))
(+.f64 (-.f64 1 (sqrt.f64 1/2)) (*.f64 (sqrt.f64 1/2) (/.f64 1/2 x)))
(.f64 (.f64 1/2 (+.f64 (-.f64 1 (sqrt.f64 1/2)) (*.f64 (sqrt.f64 1/2) (/.f64 1/2 x)))) 2)
(+.f64 (-.f64 1 (sqrt.f64 1/2)) (*.f64 (sqrt.f64 1/2) (/.f64 1/2 x)))
(.f64 (/.f64 (+.f64 (-.f64 1 (sqrt.f64 1/2)) (.f64 (sqrt.f64 1/2) (/.f64 1/2 x))) 4) 4)
(+.f64 (-.f64 1 (sqrt.f64 1/2)) (*.f64 (sqrt.f64 1/2) (/.f64 1/2 x)))
(.f64 (+.f64 (/.f64 (sqrt.f64 1/2) x) (.f64 (-.f64 1 (sqrt.f64 1/2)) 2)) 1/2)
(.f64 1/2 (+.f64 (/.f64 (sqrt.f64 1/2) x) (.f64 (-.f64 1 (sqrt.f64 1/2)) 2)))
(/.f64 (+.f64 (-.f64 1 (sqrt.f64 1/2)) (*.f64 (sqrt.f64 1/2) (/.f64 1/2 x))) 1)
(+.f64 (-.f64 1 (sqrt.f64 1/2)) (*.f64 (sqrt.f64 1/2) (/.f64 1/2 x)))
(/.f64 (.f64 (+.f64 (-.f64 1 (sqrt.f64 1/2)) (.f64 (sqrt.f64 1/2) (/.f64 1/2 x))) 2) 2)
(+.f64 (-.f64 1 (sqrt.f64 1/2)) (*.f64 (sqrt.f64 1/2) (/.f64 1/2 x)))
(/.f64 (.f64 (+.f64 (-.f64 1 (sqrt.f64 1/2)) (.f64 (sqrt.f64 1/2) (/.f64 1/2 x))) 4) 4)
(+.f64 (-.f64 1 (sqrt.f64 1/2)) (*.f64 (sqrt.f64 1/2) (/.f64 1/2 x)))
(/.f64 (.f64 2 (.f64 (+.f64 (-.f64 1 (sqrt.f64 1/2)) (*.f64 (sqrt.f64 1/2) (/.f64 1/2 x))) 4)) 8)
(+.f64 (-.f64 1 (sqrt.f64 1/2)) (*.f64 (sqrt.f64 1/2) (/.f64 1/2 x)))
(/.f64 (+.f64 (.f64 2 (.f64 (+.f64 (-.f64 1 (sqrt.f64 1/2)) (.f64 (sqrt.f64 1/2) (/.f64 1/2 x))) 4)) (.f64 2 (.f64 (+.f64 (-.f64 1 (sqrt.f64 1/2)) (.f64 (sqrt.f64 1/2) (/.f64 1/2 x))) 4))) 16)
(+.f64 (-.f64 1 (sqrt.f64 1/2)) (*.f64 (sqrt.f64 1/2) (/.f64 1/2 x)))
(pow.f64 (+.f64 (-.f64 1 (sqrt.f64 1/2)) (*.f64 (sqrt.f64 1/2) (/.f64 1/2 x))) 1)
(+.f64 (-.f64 1 (sqrt.f64 1/2)) (*.f64 (sqrt.f64 1/2) (/.f64 1/2 x)))

eval131.0ms (1.2%)

Compiler: Compiled 5982 to 5435 computations (9.1% saved)

prune56.0ms (0.5%)

Pruning

10 alts after pruning (2 fresh and 8 done)

	Pruned	Kept	Total
New	391	0	391
Fresh	0	2	2
Picked	0	1	1
Done	0	7	7
Total	391	10	401

Error

0.5b

Counts

401 → 10

Alt Table

Click to see full alt table

Status	Error	Program
✓	14.7b	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
✓	32.5b	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x))))
✓	32.5b	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))))
✓	31.8b	(-.f64 1 (sqrt.f64 1/2))
✓	32.2b	(+.f64 (-.f64 1 (sqrt.f64 1/2)) (*.f64 1/2 (/.f64 (sqrt.f64 1/2) x)))
▶	32.3b	(+.f64 (.f64 1/2 (/.f64 (sqrt.f64 1/2) x)) (+.f64 (.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (-.f64 1 (sqrt.f64 1/2))))
✓	31.9b	(+.f64 (.f64 1/8 (pow.f64 x 2)) (.f64 -11/128 (pow.f64 x 4)))
✓	32.3b	(+.f64 (.f64 -1/2 (/.f64 (sqrt.f64 1/2) x)) (+.f64 1 (-.f64 (.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (sqrt.f64 1/2))))
✓	31.4b	(*.f64 1/8 (pow.f64 x 2))
	45.6b	0

Compiler

Compiled 108 to 97 computations (10.2% saved)

localize30.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (.f64 1/2 (/.f64 (sqrt.f64 1/2) x)) (+.f64 (.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (-.f64 1 (sqrt.f64 1/2))))
	0.2b	(/.f64 (sqrt.f64 1/2) (pow.f64 x 2))
	0.4b	(/.f64 (sqrt.f64 1/2) x)
	1.0b	(-.f64 1 (sqrt.f64 1/2))

Compiler

Compiled 72 to 63 computations (12.5% saved)

series0.0ms (0%)

Counts

1 → 12

Calls

3 calls:

Time

Variable

Point

Expression

0.0ms

(+.f64 (*.f64 1/2 (/.f64 (sqrt.f64 1/2) x)) (+.f64 (*.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (-.f64 1 (sqrt.f64 1/2))))

0.0ms

inf

(+.f64 (*.f64 1/2 (/.f64 (sqrt.f64 1/2) x)) (+.f64 (*.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (-.f64 1 (sqrt.f64 1/2))))

0.0ms

-inf

(+.f64 (*.f64 1/2 (/.f64 (sqrt.f64 1/2) x)) (+.f64 (*.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (-.f64 1 (sqrt.f64 1/2))))

rewrite74.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

1558×	`rational.json-1`
1558×	`rational.json-2`
1558×	`rational.json-4`
1558×	`rational.json-3`
1548×	`exponential.json-3`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	17	61
1	123	61
2	266	61
3	615	61
4	1666	57
5	4688	57

Stop Event

1×	node limit

Counts

1 → 15

Calls

Call 1

Inputs
(+.f64 (.f64 1/2 (/.f64 (sqrt.f64 1/2) x)) (+.f64 (.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (-.f64 1 (sqrt.f64 1/2))))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 (-.f64 1 (sqrt.f64 1/2)) (*.f64 (sqrt.f64 1/2) (+.f64 (*.f64 1/8 (/.f64 1 (pow.f64 x 2))) (/.f64 1/2 x)))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/2 (*.f64 2 (+.f64 (-.f64 1 (sqrt.f64 1/2)) (*.f64 (sqrt.f64 1/2) (+.f64 (*.f64 1/8 (/.f64 1 (pow.f64 x 2))) (/.f64 1/2 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/2 (+.f64 (/.f64 (sqrt.f64 1/2) x) (*.f64 2 (+.f64 (*.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (-.f64 1 (sqrt.f64 1/2))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 2 (/.f64 (+.f64 (-.f64 1 (sqrt.f64 1/2)) (*.f64 (sqrt.f64 1/2) (+.f64 (*.f64 1/8 (/.f64 1 (pow.f64 x 2))) (/.f64 1/2 x)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 2 (*.f64 (/.f64 (+.f64 (-.f64 1 (sqrt.f64 1/2)) (*.f64 (sqrt.f64 1/2) (+.f64 (*.f64 1/8 (/.f64 1 (pow.f64 x 2))) (/.f64 1/2 x)))) 2) 1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (+.f64 (-.f64 1 (sqrt.f64 1/2)) (*.f64 (sqrt.f64 1/2) (+.f64 (*.f64 1/8 (/.f64 1 (pow.f64 x 2))) (/.f64 1/2 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (-.f64 1 (sqrt.f64 1/2)) (*.f64 (sqrt.f64 1/2) (+.f64 (*.f64 1/8 (/.f64 1 (pow.f64 x 2))) (/.f64 1/2 x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 2 (+.f64 (-.f64 1 (sqrt.f64 1/2)) (*.f64 (sqrt.f64 1/2) (+.f64 (*.f64 1/8 (/.f64 1 (pow.f64 x 2))) (/.f64 1/2 x))))) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (+.f64 (-.f64 1 (sqrt.f64 1/2)) (*.f64 (sqrt.f64 1/2) (+.f64 (*.f64 1/8 (/.f64 1 (pow.f64 x 2))) (/.f64 1/2 x)))) 2) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (-.f64 1 (sqrt.f64 1/2)) (*.f64 (sqrt.f64 1/2) (+.f64 (*.f64 1/8 (/.f64 1 (pow.f64 x 2))) (/.f64 1/2 x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (+.f64 (-.f64 1 (sqrt.f64 1/2)) (*.f64 (sqrt.f64 1/2) (+.f64 (*.f64 1/8 (/.f64 1 (pow.f64 x 2))) (/.f64 1/2 x))))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (+.f64 (-.f64 1 (sqrt.f64 1/2)) (*.f64 (sqrt.f64 1/2) (+.f64 (*.f64 1/8 (/.f64 1 (pow.f64 x 2))) (/.f64 1/2 x)))) 4) 4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 (+.f64 (-.f64 1 (sqrt.f64 1/2)) (*.f64 (sqrt.f64 1/2) (+.f64 (*.f64 1/8 (/.f64 1 (pow.f64 x 2))) (/.f64 1/2 x)))) 4)) 8)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 2 (*.f64 (+.f64 (-.f64 1 (sqrt.f64 1/2)) (*.f64 (sqrt.f64 1/2) (+.f64 (*.f64 1/8 (/.f64 1 (pow.f64 x 2))) (/.f64 1/2 x)))) 4))) 16)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 (-.f64 1 (sqrt.f64 1/2)) (*.f64 (sqrt.f64 1/2) (+.f64 (*.f64 1/8 (/.f64 1 (pow.f64 x 2))) (/.f64 1/2 x)))) 1)))))

simplify754.0ms (6.6%)

Algorithm

1×	egg-herbie

Rules

4212×	`rational.json-simplify-51`
2424×	`rational.json-simplify-35`
1186×	`rational.json-simplify-1`
1090×	`rational.json-simplify-49`
1070×	`rational.json-simplify-2`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	54	1387
1	119	1387
2	215	1387
3	498	1387
4	1255	1387
5	2392	1387
6	3020	1387
7	3078	1387
8	3129	1387
9	3167	1387
10	3200	1387
11	3233	1387
12	3266	1387
13	3299	1387
14	3332	1387
15	3365	1387
16	3398	1387
17	3431	1387
18	3464	1387
19	3497	1387
20	4185	1387
21	4348	1387
22	4402	1387
23	4453	1387
24	4503	1387
25	4553	1387
26	4732	1387
27	4782	1387
28	4832	1387
29	4882	1387
30	4932	1387
31	4932	1387
32	4982	1387
33	5032	1387
34	5082	1387
35	5132	1387
36	7942	1387

Stop Event

1×	node limit

Counts

27 → 24

Calls

Call 1

Inputs
(*.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2)))
(+.f64 (.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (.f64 1/2 (/.f64 (sqrt.f64 1/2) x)))
(-.f64 (+.f64 1 (+.f64 (.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (.f64 1/2 (/.f64 (sqrt.f64 1/2) x)))) (sqrt.f64 1/2))
(-.f64 (+.f64 1 (+.f64 (.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (.f64 1/2 (/.f64 (sqrt.f64 1/2) x)))) (sqrt.f64 1/2))
(-.f64 1 (sqrt.f64 1/2))
(-.f64 (+.f64 1 (*.f64 1/2 (/.f64 (sqrt.f64 1/2) x))) (sqrt.f64 1/2))
(-.f64 (+.f64 1 (+.f64 (.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (.f64 1/2 (/.f64 (sqrt.f64 1/2) x)))) (sqrt.f64 1/2))
(-.f64 (+.f64 1 (+.f64 (.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (.f64 1/2 (/.f64 (sqrt.f64 1/2) x)))) (sqrt.f64 1/2))
(-.f64 1 (sqrt.f64 1/2))
(-.f64 (+.f64 1 (*.f64 1/2 (/.f64 (sqrt.f64 1/2) x))) (sqrt.f64 1/2))
(-.f64 (+.f64 1 (+.f64 (.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (.f64 1/2 (/.f64 (sqrt.f64 1/2) x)))) (sqrt.f64 1/2))
(-.f64 (+.f64 1 (+.f64 (.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (.f64 1/2 (/.f64 (sqrt.f64 1/2) x)))) (sqrt.f64 1/2))
(-.f64 (+.f64 (-.f64 1 (sqrt.f64 1/2)) (.f64 (sqrt.f64 1/2) (+.f64 (.f64 1/8 (/.f64 1 (pow.f64 x 2))) (/.f64 1/2 x)))) 0)
(.f64 1/2 (.f64 2 (+.f64 (-.f64 1 (sqrt.f64 1/2)) (.f64 (sqrt.f64 1/2) (+.f64 (.f64 1/8 (/.f64 1 (pow.f64 x 2))) (/.f64 1/2 x))))))
(.f64 1/2 (+.f64 (/.f64 (sqrt.f64 1/2) x) (.f64 2 (+.f64 (*.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (-.f64 1 (sqrt.f64 1/2))))))
(.f64 2 (/.f64 (+.f64 (-.f64 1 (sqrt.f64 1/2)) (.f64 (sqrt.f64 1/2) (+.f64 (*.f64 1/8 (/.f64 1 (pow.f64 x 2))) (/.f64 1/2 x)))) 2))
(.f64 2 (.f64 (/.f64 (+.f64 (-.f64 1 (sqrt.f64 1/2)) (.f64 (sqrt.f64 1/2) (+.f64 (.f64 1/8 (/.f64 1 (pow.f64 x 2))) (/.f64 1/2 x)))) 2) 1))
(.f64 1 (+.f64 (-.f64 1 (sqrt.f64 1/2)) (.f64 (sqrt.f64 1/2) (+.f64 (*.f64 1/8 (/.f64 1 (pow.f64 x 2))) (/.f64 1/2 x)))))
(.f64 (+.f64 (-.f64 1 (sqrt.f64 1/2)) (.f64 (sqrt.f64 1/2) (+.f64 (*.f64 1/8 (/.f64 1 (pow.f64 x 2))) (/.f64 1/2 x)))) 1)
(.f64 (.f64 2 (+.f64 (-.f64 1 (sqrt.f64 1/2)) (.f64 (sqrt.f64 1/2) (+.f64 (.f64 1/8 (/.f64 1 (pow.f64 x 2))) (/.f64 1/2 x))))) 1/2)
(.f64 (/.f64 (+.f64 (-.f64 1 (sqrt.f64 1/2)) (.f64 (sqrt.f64 1/2) (+.f64 (*.f64 1/8 (/.f64 1 (pow.f64 x 2))) (/.f64 1/2 x)))) 2) 2)
(/.f64 (+.f64 (-.f64 1 (sqrt.f64 1/2)) (.f64 (sqrt.f64 1/2) (+.f64 (.f64 1/8 (/.f64 1 (pow.f64 x 2))) (/.f64 1/2 x)))) 1)
(/.f64 (.f64 2 (+.f64 (-.f64 1 (sqrt.f64 1/2)) (.f64 (sqrt.f64 1/2) (+.f64 (*.f64 1/8 (/.f64 1 (pow.f64 x 2))) (/.f64 1/2 x))))) 2)
(/.f64 (.f64 (+.f64 (-.f64 1 (sqrt.f64 1/2)) (.f64 (sqrt.f64 1/2) (+.f64 (*.f64 1/8 (/.f64 1 (pow.f64 x 2))) (/.f64 1/2 x)))) 4) 4)
(/.f64 (.f64 2 (.f64 (+.f64 (-.f64 1 (sqrt.f64 1/2)) (.f64 (sqrt.f64 1/2) (+.f64 (.f64 1/8 (/.f64 1 (pow.f64 x 2))) (/.f64 1/2 x)))) 4)) 8)
(/.f64 (.f64 2 (.f64 2 (.f64 (+.f64 (-.f64 1 (sqrt.f64 1/2)) (.f64 (sqrt.f64 1/2) (+.f64 (*.f64 1/8 (/.f64 1 (pow.f64 x 2))) (/.f64 1/2 x)))) 4))) 16)
(pow.f64 (+.f64 (-.f64 1 (sqrt.f64 1/2)) (.f64 (sqrt.f64 1/2) (+.f64 (.f64 1/8 (/.f64 1 (pow.f64 x 2))) (/.f64 1/2 x)))) 1)

Outputs
(*.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2)))
(+.f64 (.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (.f64 1/2 (/.f64 (sqrt.f64 1/2) x)))
(-.f64 (+.f64 1 (+.f64 (.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (.f64 1/2 (/.f64 (sqrt.f64 1/2) x)))) (sqrt.f64 1/2))
(+.f64 (+.f64 (.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (.f64 1/2 (/.f64 (sqrt.f64 1/2) x))) (-.f64 1 (sqrt.f64 1/2)))
(+.f64 (.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (+.f64 (.f64 1/2 (/.f64 (sqrt.f64 1/2) x)) (-.f64 1 (sqrt.f64 1/2))))
(-.f64 (+.f64 1 (+.f64 (.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (.f64 1/2 (/.f64 (sqrt.f64 1/2) x)))) (sqrt.f64 1/2))
(+.f64 (+.f64 (.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (.f64 1/2 (/.f64 (sqrt.f64 1/2) x))) (-.f64 1 (sqrt.f64 1/2)))
(+.f64 (.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (+.f64 (.f64 1/2 (/.f64 (sqrt.f64 1/2) x)) (-.f64 1 (sqrt.f64 1/2))))
(-.f64 1 (sqrt.f64 1/2))
(-.f64 (+.f64 1 (*.f64 1/2 (/.f64 (sqrt.f64 1/2) x))) (sqrt.f64 1/2))
(+.f64 (*.f64 1/2 (/.f64 (sqrt.f64 1/2) x)) (-.f64 1 (sqrt.f64 1/2)))
(-.f64 (+.f64 1 (+.f64 (.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (.f64 1/2 (/.f64 (sqrt.f64 1/2) x)))) (sqrt.f64 1/2))
(+.f64 (+.f64 (.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (.f64 1/2 (/.f64 (sqrt.f64 1/2) x))) (-.f64 1 (sqrt.f64 1/2)))
(+.f64 (.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (+.f64 (.f64 1/2 (/.f64 (sqrt.f64 1/2) x)) (-.f64 1 (sqrt.f64 1/2))))
(-.f64 (+.f64 1 (+.f64 (.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (.f64 1/2 (/.f64 (sqrt.f64 1/2) x)))) (sqrt.f64 1/2))
(+.f64 (+.f64 (.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (.f64 1/2 (/.f64 (sqrt.f64 1/2) x))) (-.f64 1 (sqrt.f64 1/2)))
(+.f64 (.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (+.f64 (.f64 1/2 (/.f64 (sqrt.f64 1/2) x)) (-.f64 1 (sqrt.f64 1/2))))
(-.f64 1 (sqrt.f64 1/2))
(-.f64 (+.f64 1 (*.f64 1/2 (/.f64 (sqrt.f64 1/2) x))) (sqrt.f64 1/2))
(+.f64 (*.f64 1/2 (/.f64 (sqrt.f64 1/2) x)) (-.f64 1 (sqrt.f64 1/2)))
(-.f64 (+.f64 1 (+.f64 (.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (.f64 1/2 (/.f64 (sqrt.f64 1/2) x)))) (sqrt.f64 1/2))
(+.f64 (+.f64 (.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (.f64 1/2 (/.f64 (sqrt.f64 1/2) x))) (-.f64 1 (sqrt.f64 1/2)))
(+.f64 (.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (+.f64 (.f64 1/2 (/.f64 (sqrt.f64 1/2) x)) (-.f64 1 (sqrt.f64 1/2))))
(-.f64 (+.f64 1 (+.f64 (.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (.f64 1/2 (/.f64 (sqrt.f64 1/2) x)))) (sqrt.f64 1/2))
(+.f64 (+.f64 (.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (.f64 1/2 (/.f64 (sqrt.f64 1/2) x))) (-.f64 1 (sqrt.f64 1/2)))
(+.f64 (.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (+.f64 (.f64 1/2 (/.f64 (sqrt.f64 1/2) x)) (-.f64 1 (sqrt.f64 1/2))))
(-.f64 (+.f64 (-.f64 1 (sqrt.f64 1/2)) (.f64 (sqrt.f64 1/2) (+.f64 (.f64 1/8 (/.f64 1 (pow.f64 x 2))) (/.f64 1/2 x)))) 0)
(+.f64 (-.f64 1 (sqrt.f64 1/2)) (.f64 (sqrt.f64 1/2) (+.f64 (.f64 1/8 (/.f64 1 (pow.f64 x 2))) (/.f64 1/2 x))))
(.f64 1/2 (.f64 2 (+.f64 (-.f64 1 (sqrt.f64 1/2)) (.f64 (sqrt.f64 1/2) (+.f64 (.f64 1/8 (/.f64 1 (pow.f64 x 2))) (/.f64 1/2 x))))))
(+.f64 (-.f64 1 (sqrt.f64 1/2)) (.f64 (sqrt.f64 1/2) (+.f64 (.f64 1/8 (/.f64 1 (pow.f64 x 2))) (/.f64 1/2 x))))
(.f64 1/2 (+.f64 (/.f64 (sqrt.f64 1/2) x) (.f64 2 (+.f64 (*.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (-.f64 1 (sqrt.f64 1/2))))))
(.f64 2 (/.f64 (+.f64 (-.f64 1 (sqrt.f64 1/2)) (.f64 (sqrt.f64 1/2) (+.f64 (*.f64 1/8 (/.f64 1 (pow.f64 x 2))) (/.f64 1/2 x)))) 2))
(+.f64 (-.f64 1 (sqrt.f64 1/2)) (.f64 (sqrt.f64 1/2) (+.f64 (.f64 1/8 (/.f64 1 (pow.f64 x 2))) (/.f64 1/2 x))))
(.f64 2 (.f64 (/.f64 (+.f64 (-.f64 1 (sqrt.f64 1/2)) (.f64 (sqrt.f64 1/2) (+.f64 (.f64 1/8 (/.f64 1 (pow.f64 x 2))) (/.f64 1/2 x)))) 2) 1))
(+.f64 (-.f64 1 (sqrt.f64 1/2)) (.f64 (sqrt.f64 1/2) (+.f64 (.f64 1/8 (/.f64 1 (pow.f64 x 2))) (/.f64 1/2 x))))
(.f64 1 (+.f64 (-.f64 1 (sqrt.f64 1/2)) (.f64 (sqrt.f64 1/2) (+.f64 (*.f64 1/8 (/.f64 1 (pow.f64 x 2))) (/.f64 1/2 x)))))
(+.f64 (-.f64 1 (sqrt.f64 1/2)) (.f64 (sqrt.f64 1/2) (+.f64 (.f64 1/8 (/.f64 1 (pow.f64 x 2))) (/.f64 1/2 x))))
(.f64 (+.f64 (-.f64 1 (sqrt.f64 1/2)) (.f64 (sqrt.f64 1/2) (+.f64 (*.f64 1/8 (/.f64 1 (pow.f64 x 2))) (/.f64 1/2 x)))) 1)
(+.f64 (-.f64 1 (sqrt.f64 1/2)) (.f64 (sqrt.f64 1/2) (+.f64 (.f64 1/8 (/.f64 1 (pow.f64 x 2))) (/.f64 1/2 x))))
(.f64 (.f64 2 (+.f64 (-.f64 1 (sqrt.f64 1/2)) (.f64 (sqrt.f64 1/2) (+.f64 (.f64 1/8 (/.f64 1 (pow.f64 x 2))) (/.f64 1/2 x))))) 1/2)
(+.f64 (-.f64 1 (sqrt.f64 1/2)) (.f64 (sqrt.f64 1/2) (+.f64 (.f64 1/8 (/.f64 1 (pow.f64 x 2))) (/.f64 1/2 x))))
(.f64 (/.f64 (+.f64 (-.f64 1 (sqrt.f64 1/2)) (.f64 (sqrt.f64 1/2) (+.f64 (*.f64 1/8 (/.f64 1 (pow.f64 x 2))) (/.f64 1/2 x)))) 2) 2)
(+.f64 (-.f64 1 (sqrt.f64 1/2)) (.f64 (sqrt.f64 1/2) (+.f64 (.f64 1/8 (/.f64 1 (pow.f64 x 2))) (/.f64 1/2 x))))
(/.f64 (+.f64 (-.f64 1 (sqrt.f64 1/2)) (.f64 (sqrt.f64 1/2) (+.f64 (.f64 1/8 (/.f64 1 (pow.f64 x 2))) (/.f64 1/2 x)))) 1)
(+.f64 (-.f64 1 (sqrt.f64 1/2)) (.f64 (sqrt.f64 1/2) (+.f64 (.f64 1/8 (/.f64 1 (pow.f64 x 2))) (/.f64 1/2 x))))
(/.f64 (.f64 2 (+.f64 (-.f64 1 (sqrt.f64 1/2)) (.f64 (sqrt.f64 1/2) (+.f64 (*.f64 1/8 (/.f64 1 (pow.f64 x 2))) (/.f64 1/2 x))))) 2)
(+.f64 (-.f64 1 (sqrt.f64 1/2)) (.f64 (sqrt.f64 1/2) (+.f64 (.f64 1/8 (/.f64 1 (pow.f64 x 2))) (/.f64 1/2 x))))
(/.f64 (.f64 (+.f64 (-.f64 1 (sqrt.f64 1/2)) (.f64 (sqrt.f64 1/2) (+.f64 (*.f64 1/8 (/.f64 1 (pow.f64 x 2))) (/.f64 1/2 x)))) 4) 4)
(+.f64 (-.f64 1 (sqrt.f64 1/2)) (.f64 (sqrt.f64 1/2) (+.f64 (.f64 1/8 (/.f64 1 (pow.f64 x 2))) (/.f64 1/2 x))))
(/.f64 (.f64 2 (.f64 (+.f64 (-.f64 1 (sqrt.f64 1/2)) (.f64 (sqrt.f64 1/2) (+.f64 (.f64 1/8 (/.f64 1 (pow.f64 x 2))) (/.f64 1/2 x)))) 4)) 8)
(+.f64 (-.f64 1 (sqrt.f64 1/2)) (.f64 (sqrt.f64 1/2) (+.f64 (.f64 1/8 (/.f64 1 (pow.f64 x 2))) (/.f64 1/2 x))))
(/.f64 (.f64 2 (.f64 2 (.f64 (+.f64 (-.f64 1 (sqrt.f64 1/2)) (.f64 (sqrt.f64 1/2) (+.f64 (*.f64 1/8 (/.f64 1 (pow.f64 x 2))) (/.f64 1/2 x)))) 4))) 16)
(+.f64 (-.f64 1 (sqrt.f64 1/2)) (.f64 (sqrt.f64 1/2) (+.f64 (.f64 1/8 (/.f64 1 (pow.f64 x 2))) (/.f64 1/2 x))))
(pow.f64 (+.f64 (-.f64 1 (sqrt.f64 1/2)) (.f64 (sqrt.f64 1/2) (+.f64 (.f64 1/8 (/.f64 1 (pow.f64 x 2))) (/.f64 1/2 x)))) 1)
(+.f64 (-.f64 1 (sqrt.f64 1/2)) (.f64 (sqrt.f64 1/2) (+.f64 (.f64 1/8 (/.f64 1 (pow.f64 x 2))) (/.f64 1/2 x))))

eval78.0ms (0.7%)

Compiler: Compiled 3917 to 3575 computations (8.7% saved)

prune101.0ms (0.9%)

Pruning

10 alts after pruning (1 fresh and 9 done)

	Pruned	Kept	Total
New	164	0	164
Fresh	0	1	1
Picked	0	1	1
Done	0	8	8
Total	164	10	174

Error

0.5b

Counts

174 → 10

Alt Table

Click to see full alt table

Status	Error	Program
✓	14.7b	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
✓	32.5b	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x))))
✓	32.5b	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))))
✓	31.8b	(-.f64 1 (sqrt.f64 1/2))
✓	32.2b	(+.f64 (-.f64 1 (sqrt.f64 1/2)) (*.f64 1/2 (/.f64 (sqrt.f64 1/2) x)))
✓	32.3b	(+.f64 (.f64 1/2 (/.f64 (sqrt.f64 1/2) x)) (+.f64 (.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (-.f64 1 (sqrt.f64 1/2))))
✓	31.9b	(+.f64 (.f64 1/8 (pow.f64 x 2)) (.f64 -11/128 (pow.f64 x 4)))
✓	32.3b	(+.f64 (.f64 -1/2 (/.f64 (sqrt.f64 1/2) x)) (+.f64 1 (-.f64 (.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (sqrt.f64 1/2))))
✓	31.4b	(*.f64 1/8 (pow.f64 x 2))
	45.6b	0

Compiler

Compiled 108 to 97 computations (10.2% saved)

regimes272.0ms (2.4%)

Counts

16 → 2

Calls

Call 1

Inputs
0
(-.f64 1 (sqrt.f64 1/2))
(*.f64 1/8 (pow.f64 x 2))
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))))
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x))))
(-.f64 1 (sqrt.f64 (*.f64 1/2 (+.f64 1 (/.f64 1 x)))))
(-.f64 1 (sqrt.f64 (*.f64 1/2 (-.f64 1 (/.f64 1 x)))))
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
(+.f64 (.f64 1/8 (pow.f64 x 2)) (.f64 -11/128 (pow.f64 x 4)))
(+.f64 (-.f64 1 (sqrt.f64 1/2)) (*.f64 1/2 (/.f64 (sqrt.f64 1/2) x)))
(-.f64 -1 (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -2))
(-.f64 1 (sqrt.f64 (*.f64 1/2 (+.f64 1 (/.f64 1 (hypot.f64 1 x))))))
(.f64 1/4 (.f64 (sqrt.f64 1/2) (/.f64 (pow.f64 x 2) (sqrt.f64 2))))
(+.f64 (.f64 -1/2 (/.f64 (sqrt.f64 1/2) x)) (+.f64 1 (-.f64 (.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (sqrt.f64 1/2))))
(+.f64 (.f64 1/2 (/.f64 (sqrt.f64 1/2) x)) (+.f64 (.f64 1/8 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (-.f64 1 (sqrt.f64 1/2))))
(+.f64 (.f64 1/4 (.f64 (sqrt.f64 1/2) (/.f64 (pow.f64 x 2) (sqrt.f64 2)))) (.f64 -1/2 (.f64 (*.f64 (sqrt.f64 1/2) (pow.f64 x 4)) (/.f64 (-.f64 3/8 (pow.f64 (/.f64 -1/4 (sqrt.f64 2)) 2)) (sqrt.f64 2)))))

Outputs
(+.f64 (.f64 1/8 (pow.f64 x 2)) (.f64 -11/128 (pow.f64 x 4)))
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))

Calls

7 calls:

212.0ms	(+.f64 1 (/.f64 1 (hypot.f64 1 x)))
22.0ms	x
12.0ms	(/.f64 1 (hypot.f64 1 x))
9.0ms	(hypot.f64 1 x)
4.0ms	(-.f64 1 (sqrt.f64 (*.f64 1/2 (+.f64 1 (/.f64 1 (hypot.f64 1 x))))))

Results

Error	Segments	Branch
0.5b	3	`x`
0.5b	2	`(-.f64 1 (sqrt.f64 (*.f64 1/2 (+.f64 1 (/.f64 1 (hypot.f64 1 x))))))`
0.5b	2	`(sqrt.f64 (*.f64 1/2 (+.f64 1 (/.f64 1 (hypot.f64 1 x)))))`
0.5b	2	`(*.f64 1/2 (+.f64 1 (/.f64 1 (hypot.f64 1 x))))`
0.5b	2	`(+.f64 1 (/.f64 1 (hypot.f64 1 x)))`
0.5b	2	`(/.f64 1 (hypot.f64 1 x))`
0.5b	2	`(hypot.f64 1 x)`

Compiler

Compiled 240 to 215 computations (10.4% saved)

bsearch0.0ms (0%)

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	1.000000001693296	360.81934864074196

Compiler

Compiled 17 to 15 computations (11.8% saved)

regimes21.0ms (0.2%)

Counts

8 → 3

Calls

Call 1

Inputs
0
(-.f64 1 (sqrt.f64 1/2))
(*.f64 1/8 (pow.f64 x 2))
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))))
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x))))
(-.f64 1 (sqrt.f64 (*.f64 1/2 (+.f64 1 (/.f64 1 x)))))
(-.f64 1 (sqrt.f64 (*.f64 1/2 (-.f64 1 (/.f64 1 x)))))
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))

Outputs
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
(*.f64 1/8 (pow.f64 x 2))
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x))))

Calls

2 calls:

14.0ms	x
5.0ms	(hypot.f64 1 x)

Results

Error	Segments	Branch
0.8b	3	`x`
0.8b	2	`(hypot.f64 1 x)`

Compiler

Compiled 63 to 55 computations (12.7% saved)

bsearch38.0ms (0.3%)

Algorithm

2×	binary-search

Steps

Time	Left	Right
19.0ms	7.580508083094249e-6	1522170.581393448
19.0ms	-360.81796290308125	-5.819443283954906e-5

Results

34.0ms

304×

body

256

valid

Compiler

Compiled 358 to 318 computations (11.2% saved)

regimes16.0ms (0.1%)

Counts

7 → 3

Calls

Call 1

Inputs
0
(-.f64 1 (sqrt.f64 1/2))
(*.f64 1/8 (pow.f64 x 2))
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))))
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x))))
(-.f64 1 (sqrt.f64 (*.f64 1/2 (+.f64 1 (/.f64 1 x)))))
(-.f64 1 (sqrt.f64 (*.f64 1/2 (-.f64 1 (/.f64 1 x)))))

Outputs
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))))
(*.f64 1/8 (pow.f64 x 2))
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x))))

Calls

1 calls:

14.0ms

Results

Error	Segments	Branch
0.9b	3	`x`

Compiler

Compiled 49 to 43 computations (12.2% saved)

bsearch38.0ms (0.3%)

Algorithm

2×	binary-search

Steps

Time	Left	Right
19.0ms	7.580508083094249e-6	1522170.581393448
19.0ms	-360.81796290308125	-5.819443283954906e-5

Results

33.0ms

304×

body

256

valid

Compiler

Compiled 340 to 300 computations (11.8% saved)

regimes85.0ms (0.7%)

Counts

4 → 3

Calls

Call 1

Inputs
0
(-.f64 1 (sqrt.f64 1/2))
(*.f64 1/8 (pow.f64 x 2))
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))))

Outputs
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))))
(*.f64 1/8 (pow.f64 x 2))
(-.f64 1 (sqrt.f64 1/2))

Calls

1 calls:

83.0ms

Results

Error	Segments	Branch
1.2b	3	`x`

Compiler

Compiled 21 to 18 computations (14.3% saved)

bsearch133.0ms (1.2%)

Algorithm

2×	binary-search

Steps

Time	Left	Right
115.0ms	7.580508083094249e-6	1522170.581393448
18.0ms	-360.81796290308125	-5.819443283954906e-5

Results

129.0ms

304×

body

256

valid

Compiler

Compiled 300 to 270 computations (10% saved)

regimes111.0ms (1%)

Counts

3 → 3

Calls

Call 1

Inputs
0
(-.f64 1 (sqrt.f64 1/2))
(*.f64 1/8 (pow.f64 x 2))

Outputs
(-.f64 1 (sqrt.f64 1/2))
(*.f64 1/8 (pow.f64 x 2))
(-.f64 1 (sqrt.f64 1/2))

Calls

1 calls:

110.0ms

Results

Error	Segments	Branch
1.4b	3	`x`

Compiler

Compiled 13 to 11 computations (15.4% saved)

bsearch37.0ms (0.3%)

Algorithm

2×	binary-search

Steps

Time	Left	Right
20.0ms	7.580508083094249e-6	1522170.581393448
17.0ms	-360.81796290308125	-5.819443283954906e-5

Results

33.0ms

304×

body

256

valid

Compiler

Compiled 264 to 243 computations (8% saved)

regimes9.0ms (0.1%)

Accuracy

Total -46.4b remaining (-298.9%)

Threshold costs -46.4b (-298.9%)

Counts

2 → 3

Calls

Call 1

Inputs
0
(-.f64 1 (sqrt.f64 1/2))

Outputs
(-.f64 1 (sqrt.f64 1/2))
0
(-.f64 1 (sqrt.f64 1/2))

Calls

1 calls:

8.0ms

Results

Error	Segments	Branch
15.5b	3	`x`

Compiler

Compiled 8 to 7 computations (12.5% saved)

bsearch161.0ms (1.4%)

Algorithm

2×	binary-search

Steps

Time	Left	Right
74.0ms	6.718509491171711e-81	9.015625214125557e-75
87.0ms	-8.278430860683106e-70	-3.829953368812128e-80

Results

157.0ms

304×

body

1024

valid

Compiler

Compiled 188 to 186 computations (1.1% saved)

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	59	395

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

Inputs
(if (<=.f64 (hypot.f64 1 x) 2) (+.f64 (.f64 1/8 (pow.f64 x 2)) (.f64 -11/128 (pow.f64 x 4))) (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
(if (<=.f64 x -8264141345021879/73786976294838206464) (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) (if (<=.f64 x 5/4) (*.f64 1/8 (pow.f64 x 2)) (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x))))))
(if (<=.f64 x -5/4) (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x)))) (if (<=.f64 x 5/4) (*.f64 1/8 (pow.f64 x 2)) (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x))))))
(if (<=.f64 x -5/4) (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x)))) (if (<=.f64 x 3422735716801577/2251799813685248) (*.f64 1/8 (pow.f64 x 2)) (-.f64 1 (sqrt.f64 1/2))))
(if (<=.f64 x -3/2) (-.f64 1 (sqrt.f64 1/2)) (if (<=.f64 x 3422735716801577/2251799813685248) (*.f64 1/8 (pow.f64 x 2)) (-.f64 1 (sqrt.f64 1/2))))
(if (<=.f64 x -5736293309357913/260740604970814219042361048116400404614587954389239840081425977517360806369707098391474864128) (-.f64 1 (sqrt.f64 1/2)) (if (<=.f64 x 5736293309357913/260740604970814219042361048116400404614587954389239840081425977517360806369707098391474864128) 0 (-.f64 1 (sqrt.f64 1/2))))
0

Outputs
(if (<=.f64 (hypot.f64 1 x) 2) (+.f64 (.f64 1/8 (pow.f64 x 2)) (.f64 -11/128 (pow.f64 x 4))) (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
(if (<=.f64 x -8264141345021879/73786976294838206464) (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) (if (<=.f64 x 5/4) (*.f64 1/8 (pow.f64 x 2)) (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x))))))
(if (<=.f64 x -5/4) (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x)))) (if (<=.f64 x 5/4) (*.f64 1/8 (pow.f64 x 2)) (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x))))))
(if (<=.f64 x -5/4) (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x)))) (if (<=.f64 x 3422735716801577/2251799813685248) (*.f64 1/8 (pow.f64 x 2)) (-.f64 1 (sqrt.f64 1/2))))
(if (<=.f64 x -3/2) (-.f64 1 (sqrt.f64 1/2)) (if (<=.f64 x 3422735716801577/2251799813685248) (*.f64 1/8 (pow.f64 x 2)) (-.f64 1 (sqrt.f64 1/2))))
(if (<=.f64 x -5736293309357913/260740604970814219042361048116400404614587954389239840081425977517360806369707098391474864128) (-.f64 1 (sqrt.f64 1/2)) (if (<=.f64 x 5736293309357913/260740604970814219042361048116400404614587954389239840081425977517360806369707098391474864128) 0 (-.f64 1 (sqrt.f64 1/2))))
0

Compiler

Compiled 158 to 135 computations (14.6% saved)

soundness236.0ms (2.1%)

Algorithm

2×	egg-herbie

Rules

1472×	`rational.json-simplify-35`
1472×	`rational.json-simplify-35`
1092×	`rational.json-simplify-46`
1092×	`rational.json-simplify-46`
1090×	`rational.json-simplify-2`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	395	5858
1	938	5822
2	2466	5804
3	5517	5774
0	395	5858
1	938	5822
2	2466	5804
3	5517	5774

Stop Event

1×	node limit
1×	node limit

Compiler

Compiled 46 to 42 computations (8.7% saved)

end136.0ms (1.2%)

Compiler: Compiled 152 to 129 computations (15.1% saved)

Details

analyze0.0ms (0%)

sample2.5s (21.7%)

preprocess707.0ms (6.2%)

simplify708.0ms (6.2%)

eval0.0ms (0%)

prune1.0ms (0%)

localize20.0ms (0.2%)

series4.0ms (0%)

rewrite95.0ms (0.8%)

simplify119.0ms (1%)

eval129.0ms (1.1%)

prune50.0ms (0.4%)

localize16.0ms (0.1%)

series3.0ms (0%)

rewrite96.0ms (0.8%)

simplify149.0ms (1.3%)

localize4.0ms (0%)

series0.0ms (0%)

rewrite238.0ms (2.1%)

simplify206.0ms (1.8%)

localize15.0ms (0.1%)

series2.0ms (0%)

rewrite71.0ms (0.6%)

simplify359.0ms (3.1%)

localize20.0ms (0.2%)

series1.0ms (0%)

rewrite87.0ms (0.8%)

simplify199.0ms (1.7%)

localize55.0ms (0.5%)

series3.0ms (0%)

rewrite199.0ms (1.7%)

simplify128.0ms (1.1%)

eval334.0ms (2.9%)

prune153.0ms (1.3%)

localize5.0ms (0%)

series1.0ms (0%)

rewrite246.0ms (2.2%)

simplify765.0ms (6.7%)

localize11.0ms (0.1%)

series2.0ms (0%)

rewrite89.0ms (0.8%)

simplify153.0ms (1.3%)

localize12.0ms (0.1%)

series1.0ms (0%)

rewrite82.0ms (0.7%)

simplify168.0ms (1.5%)

localize13.0ms (0.1%)

series2.0ms (0%)

rewrite183.0ms (1.6%)

simplify223.0ms (2%)

localize14.0ms (0.1%)

series1.0ms (0%)

rewrite81.0ms (0.7%)

simplify184.0ms (1.6%)

eval131.0ms (1.2%)

prune56.0ms (0.5%)

localize30.0ms (0.3%)

series0.0ms (0%)

rewrite74.0ms (0.6%)

simplify754.0ms (6.6%)

eval78.0ms (0.7%)

prune101.0ms (0.9%)

regimes272.0ms (2.4%)

bsearch0.0ms (0%)

regimes21.0ms (0.2%)

bsearch38.0ms (0.3%)

regimes16.0ms (0.1%)

bsearch38.0ms (0.3%)

regimes85.0ms (0.7%)

bsearch133.0ms (1.2%)

regimes111.0ms (1%)

bsearch37.0ms (0.3%)

regimes9.0ms (0.1%)

bsearch161.0ms (1.4%)

simplify7.0ms (0.1%)

soundness236.0ms (2.1%)

end136.0ms (1.2%)

Profiling