Details

sample267.0ms

Algorithm

intervals

Results

186.0ms	191×	body	1280	valid
23.0ms	318×	body	80	valid
12.0ms	30×	body	640	valid
4.0ms	18×	body	320	valid
2.0ms	11×	body	160	valid

simplify7.0s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
85	4970
84	4918
83	4846
82	4794
81	4721
80	4669
79	4597
78	4545
77	4472
76	4420
75	4348
74	4296
73	4223
72	4171
71	4099
70	4047
69	3974
68	3922
67	3850
66	3798
65	3725
64	3673
63	3601
62	3549
61	3476
60	3424
59	3352
58	3300
57	3227
56	3175
55	3103
54	3051
53	2978
52	2926
51	2854
50	2802
49	2729
48	2677
47	2605
46	2553
45	2480
44	2428
43	2356
42	2304
41	2231
40	2179
39	2107
38	2055
37	1982
36	1930
35	1858
34	1806
33	1733
32	1681
31	1609
30	1557
29	1484
28	1432
27	1360
26	1308
25	1235
24	1183
23	1111
22	1059
21	986
20	934
19	862
18	810
17	737
16	685
15	613
14	561
13	488
12	436
11	364
10	266
9	155
8	94
7	73
6	60
5	53
4	49
3	40
2	26
1	14
0	7

prune70.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 30.9b

localize24.0ms

Local error

Found 2 expressions with local error:

0.0b	(- (exp x) 2.0)
3.8b	(+ (- (exp x) 2.0) (exp (- x)))

rewrite153.0ms

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×	`pow1` `add-exp-log` `neg-sub0` `exp-neg` `expm1-log1p-u` `sub-neg` `exp-diff` `diff-log` `sum-log` `add-cbrt-cube` `log1p-expm1-u` `distribute-lft-out` `difference-of-squares`
1×	`+-commutative` `associate-+l-` `flip3-+` `flip-+`

Counts

2 → 65

Calls

2 calls:

25.0ms	(- (exp x) 2.0)
123.0ms	(+ (- (exp x) 2.0) (exp (- x)))

series140.0ms

Counts

2 → 6

Calls

2 calls:

23.0ms	(- (exp x) 2.0)
116.0ms	(+ (- (exp x) 2.0) (exp (- x)))

simplify7.1s

Counts

71 → 71

Iterations

Iter	Nodes
done	5000
3	2995
2	868
1	296
0	124

prune538.0ms

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)) (fma 1/360 (* (* x x) (* (* 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))

rewrite657.0ms

Algorithm

rewrite-expression-head

Rules

848×	`pow1`
370×	`pow-prod-up`
175×	`pow-prod-down`
153×	`pow-sqr`
140×	`pow-plus`
99×	`pow2`
69×	`add-exp-log` `add-cbrt-cube`
47×	`prod-exp` `cbrt-unprod`
4×	`add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `log1p-expm1-u` `add-log-exp`
3×	`associate-r` `associate-l` `*-commutative` `unswap-sqr`
2×	`swap-sqr`
1×	`cube-unmult` `fma-udef`

Counts

4 → 333

Calls

4 calls:

1.0ms	(fma 1/12 (* (* x x) (* x x)) (fma 1/360 (* (* x x) (* (* x x) (* x x))) (* x x)))
464.0ms	(* (* x x) (* (* x x) (* x x)))
60.0ms	(* (* x x) (* x x))
66.0ms	(* (* x x) (* x x))

series889.0ms

Counts

4 → 12

Calls

4 calls:

317.0ms	(fma 1/12 (* (* x x) (* x x)) (fma 1/360 (* (* x x) (* (* x x) (* x x))) (* x x)))
425.0ms	(* (* x x) (* (* x x) (* x x)))
75.0ms	(* (* x x) (* x x))
61.0ms	(* (* x x) (* x x))

simplify9.0s

Counts

345 → 345

Iterations

Iter	Nodes
done	5004
3	2422
2	756
1	345
0	136

prune743.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize90.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* x x) (* x x))
0.1b	(* (* x x) (* x x))
26.9b	(sqrt (fma 1/12 (* (* x x) (* x x)) (fma 1/360 (* (* x x) (* (* x x) (* x x))) (* x x))))
26.9b	(sqrt (fma 1/12 (* (* x x) (* x x)) (fma 1/360 (* (* x x) (* (* x x) (* x x))) (* x x))))

rewrite156.0ms

Algorithm

rewrite-expression-head

Rules

228×	`pow1`
72×	`pow-prod-up`
46×	`pow-prod-down`
44×	`pow-sqr`
36×	`pow-plus`
28×	`add-exp-log` `add-cbrt-cube`
26×	`pow2`
16×	`prod-exp` `cbrt-unprod`
8×	`add-sqr-sqrt`
6×	`add-cube-cbrt` `*-un-lft-identity` `sqrt-prod`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `swap-sqr` `associate-r` `associate-l` `*-commutative` `unswap-sqr`

Counts

4 → 160

Calls

4 calls:

60.0ms	(* (* x x) (* x x))
72.0ms	(* (* x x) (* x x))
5.0ms	(sqrt (fma 1/12 (* (* x x) (* x x)) (fma 1/360 (* (* x x) (* (* x x) (* x x))) (* x x))))
4.0ms	(sqrt (fma 1/12 (* (* x x) (* x x)) (fma 1/360 (* (* x x) (* (* x x) (* x x))) (* x x))))

series1.2s

Counts

4 → 12

Calls

4 calls:

299.0ms	(* (* x x) (* x x))
60.0ms	(* (* x x) (* x x))
195.0ms	(sqrt (fma 1/12 (* (* x x) (* x x)) (fma 1/360 (* (* x x) (* (* x x) (* x x))) (* x x))))
638.0ms	(sqrt (fma 1/12 (* (* x x) (* x x)) (fma 1/360 (* (* x x) (* (* x x) (* x x))) (* x x))))

simplify7.0s

Counts

172 → 172

Iterations

Iter	Nodes
done	5001
3	1301
2	491
1	220
0	93

prune2.2s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize110.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (- (exp x) 2.0) (- (exp x) 2.0))
0.1b	(* (exp (- x)) (exp (- x)))
0.1b	(exp (fma 2 (- x) (- x)))
5.4b	(fma (* (- (exp x) 2.0) (- (exp x) 2.0)) (- (exp x) 2.0) (exp (fma 2 (- x) (- x))))

rewrite584.0ms

Algorithm

rewrite-expression-head

Rules

79×	`exp-prod`
71×	`*-un-lft-identity`
55×	`add-sqr-sqrt`
43×	`add-cube-cbrt`
24×	`distribute-rgt-neg-in`
20×	`distribute-lft-neg-in`
18×	`pow1` `prod-diff`
16×	`pow-prod-down`
14×	`pow-sqr` `pow-prod-up`
11×	`distribute-rgt-in` `distribute-lft-in`
10×	`swap-sqr`
8×	`frac-times` `neg-mul-1` `associate-r` `associate-l` `add-cbrt-cube`
7×	`exp-neg`
6×	`add-exp-log` `neg-sub0` `flip3--` `exp-diff` `flip--` `distribute-lft-out--`
5×	`add-log-exp`
4×	`expm1-log1p-u` `associate-r/` `associate-l/` `log1p-expm1-u` `difference-of-squares`
2×	`pow2` `sub-neg` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod` `fma-udef` `unswap-sqr`
1×	`exp-sum` `un-div-inv` `rem-exp-log`

Counts

4 → 163

Calls

4 calls:

227.0ms	(* (- (exp x) 2.0) (- (exp x) 2.0))
294.0ms	(* (exp (- x)) (exp (- x)))
4.0ms	(exp (fma 2 (- x) (- x)))
1.0ms	(fma (* (- (exp x) 2.0) (- (exp x) 2.0)) (- (exp x) 2.0) (exp (fma 2 (- x) (- x))))

series595.0ms

Counts

4 → 12

Calls

4 calls:

74.0ms	(* (- (exp x) 2.0) (- (exp x) 2.0))
29.0ms	(* (exp (- x)) (exp (- x)))
27.0ms	(exp (fma 2 (- x) (- x)))
456.0ms	(fma (* (- (exp x) 2.0) (- (exp x) 2.0)) (- (exp x) 2.0) (exp (fma 2 (- x) (- x))))

simplify3.8s

Counts

175 → 175

Iterations

Iter	Nodes
done	5004
2	1759
1	628
0	269

prune1.3s

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0.0b

regimes102.0ms

Accuracy

0% (0.5b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	9
1	9
0	8

end0.0ms

sample9.8s

Algorithm

intervals

Results

7.1s	5625×	body	1280	valid
1.0s	1212×	body	640	valid
806.0ms	7957×	body	80	valid
192.0ms	335×	body	160	valid
176.0ms	651×	body	320	valid