Details

sample148.0ms

Algorithm

intervals

Results

98.0ms	181×	body	1280	valid
13.0ms	276×	body	80	valid
12.0ms	37×	body	640	valid
4.0ms	20×	body	320	valid
1.0ms	11×	body	160	valid

simplify2.6s

Counts

1 → 1

Iterations

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

prune11.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 28.5b

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b	(- (exp x) 2.0)
4.1b	(+ (- (exp x) 2.0) (exp (- x)))

rewrite70.0ms

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:

9.0ms	(- (exp x) 2.0)
59.0ms	(+ (- (exp x) 2.0) (exp (- x)))

series91.0ms

Counts

2 → 6

Calls

2 calls:

22.0ms	(- (exp x) 2.0)
69.0ms	(+ (- (exp x) 2.0) (exp (- x)))

simplify2.3s

Counts

71 → 71

Iterations

Iter	Nodes
done	5000
3	3022
2	857
1	295
0	124

prune292.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize33.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma 1/12 (* (* x x) (* x x)) (* x x))
0.1b	(* (* (* x x) (* x x)) (* x x))
0.1b	(* (* x x) (* x x))
0.1b	(* (* x x) (* x x))

rewrite296.0ms

Algorithm

rewrite-expression-head

Rules

891×	`pow1`
378×	`pow-prod-up`
190×	`pow-prod-down`
163×	`pow-plus`
159×	`pow-sqr`
102×	`pow2`
69×	`add-cbrt-cube` `add-exp-log`
47×	`prod-exp` `cbrt-unprod`
4×	`add-sqr-sqrt` `expm1-log1p-u` `*-un-lft-identity` `add-cube-cbrt` `log1p-expm1-u` `add-log-exp`
3×	`associate-r` `associate-l` `*-commutative` `unswap-sqr`
2×	`swap-sqr`
1×	`pow3` `fma-udef`

Counts

4 → 350

Calls

4 calls:

1.0ms	(fma 1/12 (* (* x x) (* x x)) (* x x))
192.0ms	(* (* (* x x) (* x x)) (* x x))
35.0ms	(* (* x x) (* x x))
26.0ms	(* (* x x) (* x x))

series290.0ms

Counts

4 → 12

Calls

4 calls:

122.0ms	(fma 1/12 (* (* x x) (* x x)) (* x x))
50.0ms	(* (* (* x x) (* x x)) (* x x))
54.0ms	(* (* x x) (* x x))
64.0ms	(* (* x x) (* x x))

simplify3.2s

Counts

362 → 362

Iterations

Iter	Nodes
done	5000
3	2370
2	806
1	334
0	129

prune413.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* (* x x) (* x x)) (* x x))
0.1b	(* (* x x) (* x x))
0.1b	(* (* x x) (* x x))
1.2b	(log (exp (* (* (* x x) (* x x)) (* x x))))

rewrite214.0ms

Algorithm

rewrite-expression-head

Rules

892×	`pow1`
378×	`pow-prod-up`
190×	`pow-prod-down`
163×	`pow-plus`
159×	`pow-sqr`
102×	`pow2`
69×	`add-cbrt-cube` `add-exp-log`
47×	`prod-exp` `cbrt-unprod`
5×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`log-prod` `associate-r` `associate-l` `log-pow` `*-commutative` `unswap-sqr`
2×	`swap-sqr`
1×	`exp-prod` `exp-to-pow` `rem-log-exp` `pow3`

Counts

4 → 356

Calls

4 calls:

103.0ms	(* (* (* x x) (* x x)) (* x x))
46.0ms	(* (* x x) (* x x))
23.0ms	(* (* x x) (* x x))
7.0ms	(log (exp (* (* (* x x) (* x x)) (* x x))))

series207.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(* (* (* x x) (* x x)) (* x x))
37.0ms	(* (* x x) (* x x))
47.0ms	(* (* x x) (* x x))
62.0ms	(log (exp (* (* (* x x) (* x x)) (* x x))))

simplify4.4s

Counts

368 → 368

Iterations

Iter	Nodes
done	5000
4	3392
3	890
2	468
1	304
0	132

prune476.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize59.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma (+ (exp x) 2.0) 2.0 (* (exp x) (exp x)))
0.0b	(exp (fma x 2 x))
0.0b	(* (exp x) (exp x))
4.4b	(+ (/ (- (exp (fma x 2 x)) (* (* 2.0 2.0) 2.0)) (fma (+ (exp x) 2.0) 2.0 (* (exp x) (exp x)))) (exp (- x)))

rewrite101.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt` `*-un-lft-identity`
22×	`add-cube-cbrt`
21×	`exp-prod`
13×	`fma-def`
11×	`pow1`
9×	`times-frac`
7×	`add-log-exp`
6×	`add-cbrt-cube`
4×	`expm1-log1p-u` `pow-prod-down` `add-exp-log` `pow-sqr` `pow-prod-up` `log1p-expm1-u`
3×	`swap-sqr` `associate-r` `associate-l`
2×	`frac-add` `fma-udef`
1×	`pow2` `neg-sub0` `exp-neg` `+-commutative` `sum-log` `flip3-+` `pow-plus` `exp-diff` `div-sub` `exp-sum` `prod-exp` `*-commutative` `associate-+l-` `cbrt-unprod` `flip-+` `div-inv` `distribute-lft-out` `unswap-sqr` `rem-exp-log`

Counts

4 → 90

Calls

4 calls:

0.0ms	(fma (+ (exp x) 2.0) 2.0 (* (exp x) (exp x)))
3.0ms	(exp (fma x 2 x))
19.0ms	(* (exp x) (exp x))
74.0ms	(+ (/ (- (exp (fma x 2 x)) (* (* 2.0 2.0) 2.0)) (fma (+ (exp x) 2.0) 2.0 (* (exp x) (exp x)))) (exp (- x)))

series386.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(fma (+ (exp x) 2.0) 2.0 (* (exp x) (exp x)))
23.0ms	(exp (fma x 2 x))
23.0ms	(* (exp x) (exp x))
275.0ms	(+ (/ (- (exp (fma x 2 x)) (* (* 2.0 2.0) 2.0)) (fma (+ (exp x) 2.0) 2.0 (* (exp x) (exp x)))) (exp (- x)))

simplify3.0s

Counts

102 → 102

Iterations

Iter	Nodes
done	5009
3	3785
2	1031
1	366
0	155

prune743.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

regimes66.0ms

Accuracy

0% (0.6b remaining)

Error of 0.6b against oracle of 0.1b and baseline of 0.6b

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	9
1	9
0	8

end0.0ms

sample5.2s

Algorithm

intervals

Results

3.3s	5705×	body	1280	valid
881.0ms	8184×	body	80	valid
355.0ms	1195×	body	640	valid
176.0ms	612×	body	320	valid
128.0ms	321×	body	160	valid