Details

sample242.0ms

Algorithm

intervals

Results

101.0ms	94×	body	1280	valid
66.0ms	29×	body	2560	valid
42.0ms	56×	body	640	valid
12.0ms	26×	body	320	valid
7.0ms	44×	body	80	valid
2.0ms	7×	body	160	valid

simplify4.0ms

Counts

1 → 1

Iterations

Iter	Nodes
3	10
2	10
1	9
0	6

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.1b

localize64.0ms

Local error

Found 2 expressions with local error:

1.6b	(- (sin (+ x eps)) (sin x))
4.1b	(sin (+ x eps))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt` `*-un-lft-identity` `add-log-exp`
2×	`pow1` `add-cbrt-cube` `sin-sum` `add-exp-log` `add-cube-cbrt` `insert-posit16`
1×	`sub-neg` `flip3--` `diff-log` `diff-sin` `associate--l+` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 26

Calls

2 calls:

40.0ms	(- (sin (+ x eps)) (sin x))
7.0ms	(sin (+ x eps))

series98.0ms

Counts

2 → 6

Calls

2 calls:

70.0ms	(- (sin (+ x eps)) (sin x))
28.0ms	(sin (+ x eps))

simplify1.5s

Counts

32 → 32

Iterations

Iter	Nodes
5	3374
4	1441
3	637
2	294
1	137
0	65

prune122.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.4b

localize42.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ x (+ x eps))
0.2b	(* (sin (/ eps 2)) (cos (/ (+ x (+ x eps)) 2)))
4.1b	(cos (/ (+ x (+ x eps)) 2))

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

10×	`*-un-lft-identity`
8×	`add-log-exp`
7×	`add-sqr-sqrt`
5×	`pow1` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
3×	`sum-log` `associate-r` `associate-l` `insert-posit16` `distribute-lft-out`
1×	`+-commutative` `associate-+r+` `flip3-+` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `sin-cos-mult` `unswap-sqr`

Counts

3 → 44

Calls

3 calls:

25.0ms	(+ x (+ x eps))
25.0ms	(* (sin (/ eps 2)) (cos (/ (+ x (+ x eps)) 2)))
20.0ms	(cos (/ (+ x (+ x eps)) 2))

series138.0ms

Counts

3 → 9

Calls

3 calls:

27.0ms	(+ x (+ x eps))
71.0ms	(* (sin (/ eps 2)) (cos (/ (+ x (+ x eps)) 2)))
39.0ms	(cos (/ (+ x (+ x eps)) 2))

simplify5.0s

Counts

53 → 53

Iterations

Iter	Nodes
4	7454
3	1757
2	596
1	221
0	94

prune308.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.3b

localize67.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (cos (/ (+ x (+ x eps)) 2)))
4.1b	(cos (/ (+ x (+ x eps)) 2))
4.1b	(cos (/ (+ x (+ x eps)) 2))
4.1b	(cos (/ (+ x (+ x eps)) 2))

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

5×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `add-log-exp`
3×	`cbrt-prod`
1×	`pow1/3`

Counts

4 → 36

Calls

4 calls:

1.0ms	(cbrt (cos (/ (+ x (+ x eps)) 2)))
20.0ms	(cos (/ (+ x (+ x eps)) 2))
29.0ms	(cos (/ (+ x (+ x eps)) 2))
22.0ms	(cos (/ (+ x (+ x eps)) 2))

series205.0ms

Counts

4 → 12

Calls

4 calls:

109.0ms	(cbrt (cos (/ (+ x (+ x eps)) 2)))
31.0ms	(cos (/ (+ x (+ x eps)) 2))
30.0ms	(cos (/ (+ x (+ x eps)) 2))
35.0ms	(cos (/ (+ x (+ x eps)) 2))

simplify1.5s

Counts

48 → 48

Iterations

Iter	Nodes
6	2069
5	1011
4	589
3	314
2	157
1	89
0	44

prune372.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.3b

localize53.0ms

Local error

Found 4 expressions with local error:

4.1b	(cos (/ (+ x (+ x eps)) 2))
4.1b	(cos (/ (+ x (+ x eps)) 2))
4.1b	(cos (/ (+ x (+ x eps)) 2))
4.1b	(cos (/ (+ x (+ x eps)) 2))

rewrite81.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `insert-posit16` `add-log-exp`

Counts

4 → 32

Calls

4 calls:

19.0ms	(cos (/ (+ x (+ x eps)) 2))
22.0ms	(cos (/ (+ x (+ x eps)) 2))
19.0ms	(cos (/ (+ x (+ x eps)) 2))
20.0ms	(cos (/ (+ x (+ x eps)) 2))

series119.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(cos (/ (+ x (+ x eps)) 2))
35.0ms	(cos (/ (+ x (+ x eps)) 2))
30.0ms	(cos (/ (+ x (+ x eps)) 2))
27.0ms	(cos (/ (+ x (+ x eps)) 2))

simplify1.9s

Counts

44 → 44

Iterations

Iter	Nodes
9	2889
8	1502
7	748
6	527
5	355
4	251
3	165
2	92
1	57
0	27

prune398.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 0.3b

regimes210.0ms

Accuracy

99.6% (0.1b remaining)

Error of 0.4b against oracle of 0.3b and baseline of 15.4b

bsearch332.0ms

Steps

Iters	Range		Point
10	3.395948864018026e-11	318690.85562629136	1.9528216764299977e-08
11	-0.030639508246526274	-2.729201958508851e-30	-8.778095247816633e-09

simplify10.0ms

Iterations

Iter	Nodes
2	35
1	35
0	25

end0.0ms

sample8.0s

Algorithm

intervals

Results

4.3s	3237×	body	1280	valid
1.5s	1892×	body	640	valid
1.1s	640×	body	2560	valid
449.0ms	759×	body	320	valid
190.0ms	1099×	body	80	valid
175.0ms	373×	body	160	valid