Details

sample233.0ms

Algorithm

intervals

Results

118.0ms	112×	body	1280	valid
46.0ms	17×	body	2560	valid
33.0ms	49×	body	640	valid
10.0ms	20×	body	320	valid
8.0ms	23×	body	160	valid
5.0ms	35×	body	80	valid

simplify8.0ms

Counts

1 → 1

Iterations

Iter	Nodes
3	10
2	10
1	9
0	6

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.1b

localize28.0ms

Local error

Found 2 expressions with local error:

2.0b	(- (sin (+ x eps)) (sin x))
2.2b	(sin (+ x eps))

rewrite63.0ms

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:

30.0ms	(- (sin (+ x eps)) (sin x))
33.0ms	(sin (+ x eps))

series65.0ms

Counts

2 → 6

Calls

2 calls:

45.0ms	(- (sin (+ x eps)) (sin x))
19.0ms	(sin (+ x eps))

simplify1.4s

Counts

32 → 32

Iterations

Iter	Nodes
5	3343
4	1447
3	634
2	296
1	137
0	65

prune312.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.2b

localize24.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ x (+ x eps))
0.3b	(* (sin (/ eps 2)) (cos (/ (+ x (+ x eps)) 2)))
2.3b	(cos (/ (+ x (+ x eps)) 2))

rewrite69.0ms

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:

22.0ms	(+ x (+ x eps))
18.0ms	(* (sin (/ eps 2)) (cos (/ (+ x (+ x eps)) 2)))
28.0ms	(cos (/ (+ x (+ x eps)) 2))

series152.0ms

Counts

3 → 9

Calls

3 calls:

24.0ms	(+ x (+ x eps))
86.0ms	(* (sin (/ eps 2)) (cos (/ (+ x (+ x eps)) 2)))
42.0ms	(cos (/ (+ x (+ x eps)) 2))

simplify3.8s

Counts

53 → 53

Iterations

Iter	Nodes
4	6965
3	1694
2	567
1	224
0	94

prune629.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.2b

localize62.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (cos (/ (+ x (+ x eps)) 2)))
2.3b	(cos (/ (+ x (+ x eps)) 2))
2.3b	(cos (/ (+ x (+ x eps)) 2))
2.3b	(cos (/ (+ x (+ x eps)) 2))

rewrite113.0ms

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)))
36.0ms	(cos (/ (+ x (+ x eps)) 2))
42.0ms	(cos (/ (+ x (+ x eps)) 2))
32.0ms	(cos (/ (+ x (+ x eps)) 2))

series207.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(cbrt (cos (/ (+ x (+ x eps)) 2)))
34.0ms	(cos (/ (+ x (+ x eps)) 2))
42.0ms	(cos (/ (+ x (+ x eps)) 2))
35.0ms	(cos (/ (+ x (+ x eps)) 2))

simplify3.0s

Counts

48 → 48

Iterations

Iter	Nodes
7	5204
6	1964
5	979
4	579
3	316
2	160
1	91
0	44

prune609.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.2b

localize72.0ms

Local error

Found 4 expressions with local error:

2.3b	(cos (/ (+ x (+ x eps)) 2))
2.3b	(cos (/ (+ x (+ x eps)) 2))
2.3b	(cos (/ (+ x (+ x eps)) 2))
2.3b	(cos (/ (+ x (+ x eps)) 2))

rewrite91.0ms

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:

18.0ms	(cos (/ (+ x (+ x eps)) 2))
25.0ms	(cos (/ (+ x (+ x eps)) 2))
19.0ms	(cos (/ (+ x (+ x eps)) 2))
29.0ms	(cos (/ (+ x (+ x eps)) 2))

series101.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(cos (/ (+ x (+ x eps)) 2))
25.0ms	(cos (/ (+ x (+ x eps)) 2))
27.0ms	(cos (/ (+ x (+ x eps)) 2))
24.0ms	(cos (/ (+ x (+ x eps)) 2))

simplify1.2s

Counts

44 → 44

Iterations

Iter	Nodes
9	2443
8	1335
7	709
6	496
5	342
4	247
3	164
2	95
1	59
0	27

prune509.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.2b

regimes136.0ms

Accuracy

99.6% (0.1b remaining)

Error of 0.4b against oracle of 0.3b and baseline of 15.3b

bsearch208.0ms

Steps

Iters	Range		Point
10	1.897422751335727e-16	1.7533327294420356e-05	1.323043055488758e-08
11	-511.55301347613675	-1.7758424453292816e-19	-7.873478750891084e-09

simplify6.0ms

Iterations

Iter	Nodes
2	35
1	35
0	27

end0.0ms

sample5.6s

Algorithm

intervals

Results

3.2s	3306×	body	1280	valid
864.0ms	630×	body	2560	valid
814.0ms	1898×	body	640	valid
315.0ms	756×	body	320	valid
127.0ms	352×	body	160	valid
98.0ms	1058×	body	80	valid