Details

sample147.0ms

Algorithm

intervals

Results

102.0ms	184×	body	1280	valid
11.0ms	282×	body	80	valid
10.0ms	42×	body	640	valid
2.0ms	11×	body	320	valid
1.0ms	12×	body	160	valid

simplify8.0s

Counts

1 → 1

Iterations

Useful iterations: 3 (22.0ms)

Iter	Nodes	Cost
0	7	262
1	14	262
2	26	262
3	40	193
4	49	193
5	53	193
6	60	193
7	73	193
8	94	193
9	152	193
10	243	193
11	330	193
12	385	193
13	449	193
14	515	193
15	581	193
16	645	193
17	710	193
18	773	193
19	837	193
20	901	193
21	966	193
22	1029	193
23	1093	193
24	1157	193
25	1222	193
26	1285	193
27	1349	193
28	1413	193
29	1478	193
30	1541	193
31	1605	193
32	1669	193
33	1734	193
34	1797	193
35	1861	193
36	1925	193
37	1990	193
38	2053	193
39	2117	193
40	2181	193
41	2246	193
42	2309	193
43	2373	193
44	2437	193
45	2502	193
46	2565	193
47	2629	193
48	2693	193
49	2758	193
50	2821	193
51	2885	193
52	2949	193
53	3014	193
54	3077	193
55	3141	193
56	3205	193
57	3270	193
58	3333	193
59	3397	193
60	3461	193
61	3526	193
62	3589	193
63	3653	193
64	3717	193
65	3782	193
66	3845	193
67	3909	193
68	3973	193
69	4038	193
70	4101	193
71	4165	193
72	4229	193
73	4294	193
74	4357	193
75	4421	193
76	4485	193
77	4550	193
78	4613	193
79	4677	193
80	4741	193
81	4806	193
82	4869	193
83	4933	193
84	4997	193
done	5001	193

prune10.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 26.9b

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b	(- (exp x) 2.0)
3.4b	(+ (- (exp x) 2.0) (exp (- x)))

rewrite74.0ms

Algorithm

rewrite-expression-head

Rules

25×	`*-un-lft-identity`
20×	`add-sqr-sqrt`
18×	`prod-diff`
16×	`add-cube-cbrt`
11×	`associate-+l+`
9×	`add-log-exp`
5×	`fma-def`
4×	`frac-add`
3×	`flip3--` `fma-neg` `flip--` `distribute-lft-out--`
2×	`neg-sub0` `exp-neg` `expm1-log1p-u` `pow1` `sum-log` `sub-neg` `add-cbrt-cube` `exp-diff` `diff-log` `add-exp-log` `log1p-expm1-u` `distribute-lft-out` `difference-of-squares`
1×	`+-commutative` `flip3-+` `associate-+l-` `flip-+`

Counts

2 → 65

Calls

2 calls:

18.0ms	(- (exp x) 2.0)
52.0ms	(+ (- (exp x) 2.0) (exp (- x)))

series94.0ms

Counts

2 → 6

Calls

2 calls:

23.0ms	(- (exp x) 2.0)
71.0ms	(+ (- (exp x) 2.0) (exp (- x)))

simplify3.2s

Counts

71 → 71

Iterations

Useful iterations: done (3.1s)

Iter	Nodes	Cost
0	124	23353
1	295	19434
2	857	16631
3	3022	16478
done	5000	16398

prune360.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* x x) x)
0.1b	(* (* x x) x)
0.1b	(* (* (* x x) x) (* (* x x) x))
0.1b	(* (* x x) (* x x))

rewrite188.0ms

Algorithm

rewrite-expression-head

Rules

695×	`pow1`
326×	`pow-prod-up`
221×	`pow-plus`
120×	`pow-prod-down`
112×	`pow-sqr`
70×	`pow2`
62×	`add-cbrt-cube` `add-exp-log`
41×	`prod-exp` `cbrt-unprod`
24×	`pow3`
8×	`add-sqr-sqrt` `associate-r`
6×	`*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `associate-l` `*-commutative` `log1p-expm1-u` `add-log-exp`
3×	`unswap-sqr`
2×	`swap-sqr`

Counts

4 → 318

Calls

4 calls:

14.0ms	(* (* x x) x)
15.0ms	(* (* x x) x)
99.0ms	(* (* (* x x) x) (* (* x x) x))
40.0ms	(* (* x x) (* x x))

series252.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(* (* x x) x)
59.0ms	(* (* x x) x)
72.0ms	(* (* (* x x) x) (* (* x x) x))
63.0ms	(* (* x x) (* x x))

simplify7.5s

Counts

330 → 330

Iterations

Useful iterations: 3 (2.3s)

Iter	Nodes	Cost
0	113	40375
1	348	18190
2	808	16093
3	4224	15578
done	5001	15578

prune457.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize66.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (exp x) 2.0)
0.0b	(- (exp x) 2.0)
0.0b	(exp (fma x -2 (- x)))
4.3b	(fma (* (- (exp x) 2.0) (- (exp x) 2.0)) (- (exp x) 2.0) (exp (fma x -2 (- x))))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt` `*-un-lft-identity`
19×	`add-cube-cbrt`
18×	`prod-diff`
9×	`add-log-exp`
6×	`fma-neg`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u`
3×	`exp-prod`
2×	`sub-neg` `flip3--` `diff-log` `fma-udef` `flip--` `distribute-lft-out--` `difference-of-squares`
1×	`exp-sum` `rem-exp-log`

Counts

4 → 80

Calls

4 calls:

19.0ms	(- (exp x) 2.0)
18.0ms	(- (exp x) 2.0)
4.0ms	(exp (fma x -2 (- x)))
1.0ms	(fma (* (- (exp x) 2.0) (- (exp x) 2.0)) (- (exp x) 2.0) (exp (fma x -2 (- x))))

series245.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(- (exp x) 2.0)
21.0ms	(- (exp x) 2.0)
23.0ms	(exp (fma x -2 (- x)))
186.0ms	(fma (* (- (exp x) 2.0) (- (exp x) 2.0)) (- (exp x) 2.0) (exp (fma x -2 (- x))))

simplify124.0ms

Iterations

Useful iterations: 0 (20.0ms)

Iter	Nodes	Cost
0	128	28158