Details

sample260.0ms

Algorithm

intervals

Results

96.0ms	94×	body	1280	valid
67.0ms	56×	body	640	valid
60.0ms	29×	body	2560	valid
13.0ms	26×	body	320	valid
8.0ms	44×	body	80	valid
2.0ms	7×	body	160	valid

simplify9.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	10
2	10
1	9
0	6

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.1b

localize13.0ms

Local error

Found 2 expressions with local error:

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

rewrite85.0ms

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:

77.0ms	(- (sin (+ x eps)) (sin x))
8.0ms	(sin (+ x eps))

series92.0ms

Counts

2 → 6

Calls

2 calls:

60.0ms	(- (sin (+ x eps)) (sin x))
32.0ms	(sin (+ x eps))

simplify1.3s

Counts

32 → 32

Iterations

Iter	Nodes
done	2009
5	2009
4	1723
3	751
2	308
1	137
0	65

prune330.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.4b

localize46.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ x (+ x eps))
0.2b	(* (sin (* 1/2 eps)) (cos (/ (+ x (+ x eps)) 2)))
4.1b	(cos (/ (+ x (+ x eps)) 2))

rewrite64.0ms

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:

11.0ms	(+ x (+ x eps))
29.0ms	(* (sin (* 1/2 eps)) (cos (/ (+ x (+ x eps)) 2)))
24.0ms	(cos (/ (+ x (+ x eps)) 2))

series143.0ms

Counts

3 → 9

Calls

3 calls:

26.0ms	(+ x (+ x eps))
76.0ms	(* (sin (* 1/2 eps)) (cos (/ (+ x (+ x eps)) 2)))
41.0ms	(cos (/ (+ x (+ x eps)) 2))

simplify994.0ms

Counts

53 → 53

Iterations

Iter	Nodes
done	2005
3	2005
2	654
1	221
0	92

prune505.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.3b

localize77.0ms

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))

rewrite451.0ms

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:

2.0ms	(cbrt (cos (/ (+ x (+ x eps)) 2)))
373.0ms	(cos (/ (+ x (+ x eps)) 2))
39.0ms	(cos (/ (+ x (+ x eps)) 2))
37.0ms	(cos (/ (+ x (+ x eps)) 2))

series233.0ms

Counts

4 → 12

Calls

4 calls:

123.0ms	(cbrt (cos (/ (+ x (+ x eps)) 2)))
47.0ms	(cos (/ (+ x (+ x eps)) 2))
25.0ms	(cos (/ (+ x (+ x eps)) 2))
38.0ms	(cos (/ (+ x (+ x eps)) 2))

simplify1.3s

Counts

48 → 48

Iterations

Iter	Nodes
done	2011
5	2011
4	1626
3	543
2	186
1	91
0	44

prune771.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.3b

localize67.0ms

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))

rewrite129.0ms

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:

20.0ms	(cos (/ (+ x (+ x eps)) 2))
27.0ms	(cos (/ (+ x (+ x eps)) 2))
38.0ms	(cos (/ (+ x (+ x eps)) 2))
43.0ms	(cos (/ (+ x (+ x eps)) 2))

series148.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(cos (/ (+ x (+ x eps)) 2))
30.0ms	(cos (/ (+ x (+ x eps)) 2))
39.0ms	(cos (/ (+ x (+ x eps)) 2))
41.0ms	(cos (/ (+ x (+ x eps)) 2))

simplify1.2s

Counts

44 → 44

Iterations

Iter	Nodes
done	2047
6	2047
5	1466
4	628
3	279
2	99
1	59
0	27

prune683.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 0.3b

regimes168.0ms

Accuracy

99.6% (0.1b remaining)

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

bsearch271.0ms

Steps

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

simplify7.0ms

Iterations

Iter	Nodes
done	37
1	37
0	26

end0.0ms

sample7.9s

Algorithm

intervals

Results

3.6s	3237×	body	1280	valid
2.1s	1892×	body	640	valid
1.1s	640×	body	2560	valid
487.0ms	759×	body	320	valid
212.0ms	1099×	body	80	valid
147.0ms	373×	body	160	valid