Details

analyze75.0ms (1.5%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	99.9%	0.1%	0%	0%	0%	0
0%	0%	99.9%	0.1%	0%	0%	0%	1
0%	0%	99.9%	0.1%	0%	0%	0%	2
0%	0%	99.9%	0.1%	0%	0%	0%	3
0%	0%	99.9%	0.1%	0%	0%	0%	4
0%	0%	99.9%	0.1%	0%	0%	0%	5
0%	0%	99.9%	0.1%	0%	0%	0%	6
40.6%	40.6%	59.3%	0.1%	0%	0%	0%	7
46%	45.3%	53.1%	0.1%	1.6%	0%	0%	8
65.3%	63.2%	33.6%	0.1%	3.1%	0%	0%	9
69.5%	66%	28.9%	0.1%	5.1%	0%	0%	10
80.9%	75.1%	17.8%	0.1%	7%	0%	0%	11
83.6%	76.6%	15%	0.1%	8.3%	0%	0%	12

Compiler

Compiled 10 to 6 computations (40% saved)

sample1.4s (27.5%)

Results

1.4s	8256×	body	256	valid
31.0ms	419×	body	256	infinite

Bogosity

preprocess1.3s (24.4%)

Algorithm

2×	egg-herbie

Rules

20338×	`rational.json-simplify-41`
2300×	`rational.json-simplify-1`
648×	`rational.json-simplify-35`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	38
1	16	38
2	29	38
3	58	38
4	149	38
5	433	38
6	582	38
7	587	38
8	592	38
9	597	38
10	602	38
11	607	38
12	612	38
13	617	38
14	622	38
15	627	38
16	632	38
17	637	38
18	642	38
19	647	38
20	652	38
21	2230	38
22	2235	38
23	2240	38
24	2245	38
25	2250	38
26	2255	38
27	3121	38
28	3126	38
29	3131	38
30	3136	38
31	3141	38
32	3146	38
33	3151	38
34	3156	38
35	3161	38
36	3166	38
37	3171	38
38	3176	38
39	3181	38
40	3186	38
41	3191	38
42	3196	38
43	3201	38
44	3206	38
45	3211	38
46	3216	38
47	3221	38
48	3226	38
49	3231	38
50	3236	38
51	3241	38
52	3246	38
53	3251	38
54	3256	38
55	3261	38
56	3266	38
57	3271	38
58	3276	38
59	3281	38
60	3286	38
61	3291	38
62	3296	38
63	3301	38
64	3306	38
65	3311	38
66	3316	38
67	3321	38
68	3326	38
69	3331	38
70	3336	38
71	3341	38
72	3346	38
73	3351	38
74	3356	38
75	3361	38
76	3366	38
77	3371	38
78	3376	38
79	3381	38
80	3386	38
81	3391	38
82	3396	38
83	3401	38
84	3406	38
85	3411	38
86	3416	38
87	3421	38
88	3426	38
89	3431	38
90	3436	38
91	3441	38
92	3446	38
93	3451	38
94	3456	38
95	3461	38
96	3466	38
97	3471	38
98	3476	38
99	3481	38
100	3486	38
101	3491	38
102	3496	38
103	3501	38
104	3506	38
105	3511	38
106	3516	38
107	3521	38
108	3526	38
109	3531	38
110	3536	38
111	3541	38
112	3546	38
113	3551	38
114	3556	38
115	3561	38
116	3566	38
117	3571	38
118	3576	38
119	3581	38
120	3586	38
121	3591	38
122	3596	38
123	3601	38
124	3606	38
125	3611	38
126	3616	38
127	3621	38
128	3626	38
129	3631	38
130	3636	38
131	3641	38
132	3646	38
133	3651	38
134	3656	38
135	3661	38
136	3666	38
137	3671	38
138	3676	38
139	3681	38
140	3686	38
141	3691	38
142	3696	38
143	3701	38
144	3706	38
145	3711	38
146	3716	38
147	3721	38
148	3726	38
149	3731	38
150	3736	38
151	3741	38
152	3746	38
153	3751	38
154	3756	38
155	3761	38
156	3766	38
157	3771	38
158	3776	38
159	3781	38
160	3786	38
161	3791	38
0	2	2

Stop Event

1×	saturated
1×	node limit

Calls

Call 1

Inputs
0
1

Outputs
0
1

Call 2

Inputs
(/.f64 (+.f64 x y) (+.f64 y y))
(/.f64 (+.f64 y x) (+.f64 x x))

Outputs
(/.f64 (+.f64 x y) (+.f64 y y))
(/.f64 (+.f64 y x) (+.f64 x x))
(/.f64 (+.f64 x y) (+.f64 x x))

Compiler

Compiled 11 to 7 computations (36.4% saved)

simplify1.5s (28.8%)

Algorithm

1×	egg-herbie

Rules

18662×	`rational.json-simplify-41`
1726×	`rational.json-simplify-1`
324×	`rational.json-simplify-35`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	19
1	11	19
2	20	19
3	42	19
4	112	19
5	332	19
6	444	19
7	447	19
8	450	19
9	453	19
10	456	19
11	1607	19
12	1610	19
13	1613	19
14	1616	19
15	1619	19
16	1622	19
17	2268	19
18	2271	19
19	2274	19
20	2277	19
21	2280	19
22	2283	19
23	2286	19
24	2289	19
25	2292	19
26	2295	19
27	2298	19
28	2301	19
29	2304	19
30	2307	19
31	2310	19
32	2313	19
33	2316	19
34	2319	19
35	2322	19
36	2325	19
37	2328	19
38	2331	19
39	2334	19
40	2337	19
41	2340	19
42	2343	19
43	2346	19
44	2349	19
45	2352	19
46	2355	19
47	2358	19
48	2361	19
49	2364	19
50	2367	19
51	2370	19
52	2373	19
53	2376	19
54	2379	19
55	2382	19
56	2385	19
57	2388	19
58	2391	19
59	2394	19
60	2397	19
61	2400	19
62	2403	19
63	2406	19
64	2409	19
65	2412	19
66	2415	19
67	2418	19
68	2421	19
69	2424	19
70	2427	19
71	2430	19
72	2433	19
73	2436	19
74	2439	19
75	2442	19
76	2445	19
77	2448	19
78	2451	19
79	2454	19
80	2457	19
81	2460	19
82	2463	19
83	2466	19
84	2469	19
85	2472	19
86	2475	19
87	2478	19
88	2481	19
89	2484	19
90	2487	19
91	2490	19
92	2493	19
93	2496	19
94	2499	19
95	2502	19
96	2505	19
97	2508	19
98	2511	19
99	2514	19
100	2517	19
101	2520	19
102	2523	19
103	2526	19
104	2529	19
105	2532	19
106	2535	19
107	2538	19
108	2541	19
109	2544	19
110	2547	19
111	2550	19
112	2553	19
113	2556	19
114	2559	19
115	2562	19
116	2565	19
117	2568	19
118	2571	19
119	2574	19
120	2577	19
121	2580	19
122	2583	19
123	2586	19
124	2589	19
125	2592	19
126	2595	19
127	2598	19
128	2601	19
129	2604	19
130	2607	19
131	2610	19
132	2613	19
133	2616	19
134	2619	19
135	2622	19
136	2625	19
137	2628	19
138	2631	19
139	2634	19
140	2637	19
141	2640	19
142	2643	19
143	2646	19
144	2649	19
145	2652	19
146	2655	19
147	2658	19
148	2661	19
149	2664	19
150	2667	19
151	2670	19
152	2673	19
153	2676	19
154	2679	19
155	2682	19
156	2685	19
157	2688	19
158	2691	19
159	2694	19
160	2697	19
161	2700	19

Stop Event

1×	node limit

Counts

1 → 1

Calls

Call 1

Inputs
(/.f64 (+.f64 x y) (+.f64 y y))

Outputs
(/.f64 (+.f64 x y) (+.f64 y y))

eval0.0ms (0%)

Compiler: Compiled 9 to 5 computations (44.4% 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

0.0b

Counts

2 → 1

Alt Table

Click to see full alt table

Status	Error	Program
▶	0.0b	(/.f64 (+.f64 x y) (+.f64 y y))

Compiler

Compiled 9 to 5 computations (44.4% saved)

localize6.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (+.f64 x y) (+.f64 y y))

Compiler

Compiled 17 to 5 computations (70.6% saved)

series3.0ms (0.1%)

Counts

1 → 24

Calls

6 calls:

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

rewrite86.0ms (1.7%)

Algorithm

1×	batch-egg-rewrite

Rules

1550×	`rational.json-1`
1550×	`rational.json-2`
1550×	`rational.json-4`
1550×	`rational.json-3`
1540×	`exponential.json-3`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	19
1	48	19
2	132	19
3	352	19
4	972	19
5	4162	19

Stop Event

1×	node limit

Counts

1 → 82

Calls

Call 1

Inputs
(/.f64 (+.f64 x y) (+.f64 y y))

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

Outputs

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

simplify164.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

1286×	`rational.json-simplify-2`
960×	`rational.json-simplify-41`
808×	`rational.json-simplify-35`
806×	`rational.json-simplify-44`
710×	`rational.json-simplify-47`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	161	2374
1	354	2314
2	962	2278
3	3981	2278
4	6628	2278

Stop Event

1×	node limit

Counts

106 → 101

Calls

Call 1

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

eval20.0ms (0.4%)

Compiler: Compiled 1455 to 649 computations (55.4% saved)

prune17.0ms (0.3%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	98	3	101
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	99	3	102

Error

Counts

102 → 3

Alt Table

Click to see full alt table

Status	Error	Program
▶	0.0b	(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
▶	36.3b	(*.f64 1/2 (/.f64 x y))
	26.7b	1/2

Compiler

Compiled 19 to 15 computations (21.1% saved)

localize5.0ms (0.1%)

Compiler: Compiled 13 to 6 computations (53.8% saved)

localize8.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))

Compiler

Compiled 20 to 10 computations (50% saved)

series2.0ms (0%)

Counts

1 → 6

Calls

6 calls:

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

rewrite83.0ms (1.6%)

Algorithm

1×	batch-egg-rewrite

Rules

1464×	`rational.json-1`
1464×	`rational.json-2`
1464×	`rational.json-4`
1464×	`rational.json-3`
1458×	`exponential.json-3`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	19
1	55	19
2	135	19
3	330	19
4	884	19
5	3939	19

Stop Event

1×	node limit

Counts

1 → 19

Calls

Call 1

Inputs
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))

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

Outputs

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

simplify409.0ms (7.9%)

Algorithm

1×	egg-herbie

Rules

2264×	`rational.json-simplify-2`
2012×	`rational.json-simplify-1`
1900×	`rational.json-simplify-48`
1494×	`rational.json-simplify-49`
1298×	`rational.json-simplify-35`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	427
1	87	427
2	162	427
3	322	427
4	718	427
5	1875	427
6	3091	427
7	3521	427
8	3819	427
9	4060	427
10	4252	427
11	5108	427
12	5603	427
13	5946	427
14	5981	427
15	6011	427
16	6040	427
17	6069	427
18	6110	427
19	6268	427
20	6396	427
21	6474	427
22	7293	427
23	7928	427

Stop Event

1×	node limit

Counts

25 → 24

Calls

Call 1

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

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

eval5.0ms (0.1%)

Compiler: Compiled 236 to 157 computations (33.5% saved)

prune4.0ms (0.1%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	24	0	24
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	24	3	27

Error

Counts

27 → 3

Alt Table

Click to see full alt table

Status	Error	Program
✓	0.0b	(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
✓	36.3b	(*.f64 1/2 (/.f64 x y))
	26.7b	1/2

Compiler

Compiled 19 to 15 computations (21.1% saved)

eval0.0ms (0%)

Compiler: Compiled 2 to 2 computations (0% saved)

prune2.0ms (0%)

Pruning

3 alts after pruning (1 fresh and 2 done)

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

Error

Counts

3 → 3

Alt Table

Click to see full alt table

Status	Error	Program
✓	0.0b	(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
✓	36.3b	(*.f64 1/2 (/.f64 x y))
	26.7b	1/2

Compiler

Compiled 19 to 15 computations (21.1% saved)

eval0.0ms (0%)

Compiler: Compiled 2 to 2 computations (0% saved)

prune1.0ms (0%)

Pruning

3 alts after pruning (1 fresh and 2 done)

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

Error

Counts

3 → 3

Alt Table

Click to see full alt table

Status	Error	Program
✓	0.0b	(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
✓	36.3b	(*.f64 1/2 (/.f64 x y))
	26.7b	1/2

Compiler

Compiled 19 to 15 computations (21.1% saved)

regimes12.0ms (0.2%)

Counts

4 → 1

Calls

Call 1

Inputs
1/2
(*.f64 1/2 (/.f64 x y))
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(/.f64 (+.f64 x y) (+.f64 y y))

Outputs
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))

Calls

3 calls:

4.0ms	x
4.0ms	y
3.0ms	(/.f64 (+.f64 x y) (+.f64 y y))

Results

Error	Segments	Branch
0.0b	1	`x`
0.0b	1	`y`
0.0b	1	`(/.f64 (+.f64 x y) (+.f64 y y))`

Compiler

Compiled 37 to 22 computations (40.5% saved)

regimes30.0ms (0.6%)

Accuracy

Total -46.4b remaining (-303.9%)

Threshold costs -46.4b (-303.9%)

Counts

2 → 3

Calls

Call 1

Inputs
1/2
(*.f64 1/2 (/.f64 x y))

Outputs
(*.f64 1/2 (/.f64 x y))
1/2
(*.f64 1/2 (/.f64 x y))

Calls

2 calls:

19.0ms	y
10.0ms	x

Results

Error	Segments	Branch
15.3b	3	`x`
15.7b	7	`y`

Compiler

Compiled 14 to 10 computations (28.6% saved)

bsearch29.0ms (0.6%)

Algorithm

2×	binary-search

Steps

Time	Left	Right
14.0ms	26114569646275.875	3.512147734111435e+21
14.0ms	-1.3685046716692822e+75	-3.4128979057768245e+71

Results

23.0ms	272×	body	256	valid
2.0ms	15×	body	256	infinite

Compiler

Compiled 218 to 179 computations (17.9% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	65

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

Inputs

(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))

(if (<=.f64 x -102000000000000004860393895242070033426731512823033231390225449522816876544) (*.f64 1/2 (/.f64 x y)) (if (<=.f64 x 34000000000000000000) 1/2 (*.f64 1/2 (/.f64 x y))))

1/2

Outputs

(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))

(if (<=.f64 x -102000000000000004860393895242070033426731512823033231390225449522816876544) (*.f64 1/2 (/.f64 x y)) (if (<=.f64 x 34000000000000000000) 1/2 (*.f64 1/2 (/.f64 x y))))

1/2

Compiler

Compiled 33 to 24 computations (27.3% saved)

soundness0.0ms (0%)

end30.0ms (0.6%)

Compiler: Compiled 29 to 19 computations (34.5% saved)

Details

analyze75.0ms (1.5%)

sample1.4s (27.5%)

preprocess1.3s (24.4%)

simplify1.5s (28.8%)

eval0.0ms (0%)

prune1.0ms (0%)

localize6.0ms (0.1%)

series3.0ms (0.1%)

rewrite86.0ms (1.7%)

simplify164.0ms (3.2%)

eval20.0ms (0.4%)

prune17.0ms (0.3%)

localize5.0ms (0.1%)

localize8.0ms (0.2%)

series2.0ms (0%)

rewrite83.0ms (1.6%)

simplify409.0ms (7.9%)

eval5.0ms (0.1%)

prune4.0ms (0.1%)

eval0.0ms (0%)

prune2.0ms (0%)

eval0.0ms (0%)

prune1.0ms (0%)

regimes12.0ms (0.2%)

regimes30.0ms (0.6%)

bsearch29.0ms (0.6%)

simplify2.0ms (0%)

soundness0.0ms (0%)

end30.0ms (0.6%)

Profiling