Details

sample247.0ms

Algorithm

intervals

Results

119.0ms	115×	body	1280	valid
44.0ms	28×	body	320	valid
34.0ms	50×	body	640	valid
25.0ms	14×	body	2560	valid
5.0ms	34×	body	80	valid
4.0ms	15×	body	160	valid

simplify14.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	10
2	10
1	9
0	6

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.5b

localize27.0ms

Local error

Found 2 expressions with local error:

1.8b	(sin (+ x eps))
2.0b	(- (sin (+ x eps)) (sin x))

rewrite69.0ms

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:

13.0ms	(sin (+ x eps))
55.0ms	(- (sin (+ x eps)) (sin x))

series95.0ms

Counts

2 → 6

Calls

2 calls:

23.0ms	(sin (+ x eps))
72.0ms	(- (sin (+ x eps)) (sin x))

simplify2.9s

Counts

32 → 32

Iterations

Iter	Nodes
done	5016
5	4587
4	1727
3	752
2	305
1	136
0	65

prune162.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.6b

localize24.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ x (+ eps x))
0.2b	(* (cos (/ (+ x (+ eps x)) 2)) (sin (* eps 1/2)))
2.1b	(cos (/ (+ x (+ eps x)) 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-+` `unswap-sqr`

Counts

3 → 43

Calls

3 calls:

11.0ms	(+ x (+ eps x))
30.0ms	(* (cos (/ (+ x (+ eps x)) 2)) (sin (* eps 1/2)))
24.0ms	(cos (/ (+ x (+ eps x)) 2))

series180.0ms

Counts

3 → 9

Calls

3 calls:

35.0ms	(+ x (+ eps x))
113.0ms	(* (cos (/ (+ x (+ eps x)) 2)) (sin (* eps 1/2)))
33.0ms	(cos (/ (+ x (+ eps x)) 2))

simplify1.9s

Counts

52 → 52

Iterations

Iter	Nodes
done	5002
3	2448
2	603
1	211
0	89

prune290.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.6b

localize63.0ms

Local error

Found 4 expressions with local error:

0.7b	(cbrt (* (cos (/ (+ x (+ eps x)) 2)) (sin (* eps 1/2))))
2.1b	(cos (/ (+ x (+ eps x)) 2))
2.1b	(cos (/ (+ x (+ eps x)) 2))
2.1b	(cos (/ (+ x (+ eps x)) 2))

rewrite112.0ms

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`
1×	`cbrt-prod` `pow1/3`

Counts

4 → 34

Calls

4 calls:

9.0ms	(cbrt (* (cos (/ (+ x (+ eps x)) 2)) (sin (* eps 1/2))))
39.0ms	(cos (/ (+ x (+ eps x)) 2))
43.0ms	(cos (/ (+ x (+ eps x)) 2))
19.0ms	(cos (/ (+ x (+ eps x)) 2))

series290.0ms

Counts

4 → 12

Calls

4 calls:

202.0ms	(cbrt (* (cos (/ (+ x (+ eps x)) 2)) (sin (* eps 1/2))))
26.0ms	(cos (/ (+ x (+ eps x)) 2))
37.0ms	(cos (/ (+ x (+ eps x)) 2))
26.0ms	(cos (/ (+ x (+ eps x)) 2))

simplify2.7s

Counts

46 → 46

Iterations

Iter	Nodes
done	5002
4	2854
3	799
2	246
1	132
0	64

prune394.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.6b

localize58.0ms

Local error

Found 4 expressions with local error:

0.7b	(cbrt (* (cos (/ (+ x (+ eps x)) 2)) (sin (* eps 1/2))))
2.1b	(cos (/ (+ x (+ eps x)) 2))
2.1b	(cos (/ (+ x (+ eps x)) 2))
2.1b	(cos (/ (+ x (+ eps x)) 2))

rewrite94.0ms

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`
1×	`cbrt-prod` `pow1/3`

Counts

4 → 34

Calls

4 calls:

16.0ms	(cbrt (* (cos (/ (+ x (+ eps x)) 2)) (sin (* eps 1/2))))
37.0ms	(cos (/ (+ x (+ eps x)) 2))
22.0ms	(cos (/ (+ x (+ eps x)) 2))
19.0ms	(cos (/ (+ x (+ eps x)) 2))

series245.0ms

Counts

4 → 12

Calls

4 calls:

152.0ms	(cbrt (* (cos (/ (+ x (+ eps x)) 2)) (sin (* eps 1/2))))
35.0ms	(cos (/ (+ x (+ eps x)) 2))
28.0ms	(cos (/ (+ x (+ eps x)) 2))
30.0ms	(cos (/ (+ x (+ eps x)) 2))

simplify3.0s

Counts

46 → 46

Iterations

Iter	Nodes
done	5002
4	2854
3	799
2	246
1	132
0	64

prune315.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 0.6b

regimes153.0ms

Accuracy

98.3% (0.3b remaining)

Error of 0.6b against oracle of 0.4b and baseline of 15.3b

bsearch208.0ms

Steps

Iters	Range		Point
8	6.0329627772416755e-24	1.9249297628844816e-20	1.8942327691411048e-20
9	-5.984165099293203e-09	-2.0017119239229129e-16	-5.893930927518443e-09

simplify9.0ms

Iterations

Iter	Nodes
done	37
1	37
0	26

end0.0ms

sample7.2s

Algorithm

intervals

Results

4.1s	3310×	body	1280	valid
1.3s	1858×	body	640	valid
1.0s	618×	body	2560	valid
287.0ms	764×	body	320	valid
207.0ms	1111×	body	80	valid
146.0ms	339×	body	160	valid