Details

sample185.0ms

Algorithm

intervals

Results

83.0ms	115×	body	1280	valid
56.0ms	50×	body	640	valid
18.0ms	14×	body	2560	valid
10.0ms	28×	body	320	valid
4.0ms	34×	body	80	valid
4.0ms	15×	body	160	valid

simplify7.0ms

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

localize26.0ms

Local error

Found 2 expressions with local error:

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

rewrite65.0ms

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:

8.0ms	(sin (+ x eps))
57.0ms	(- (sin (+ x eps)) (sin x))

series102.0ms

Counts

2 → 6

Calls

2 calls:

30.0ms	(sin (+ x eps))
71.0ms	(- (sin (+ x eps)) (sin x))

simplify1.7s

Counts

32 → 32

Iterations

Iter	Nodes
done	5001
4	2173
3	849
2	313
1	136
0	65

prune152.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.6b

localize47.0ms

Local error

Found 2 expressions with local error:

0.2b	(* (cos (/ (+ eps (+ x x)) 2)) (sin (/ eps 2)))
2.1b	(cos (/ (+ eps (+ x x)) 2))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-sqr-sqrt`
4×	`pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
3×	`associate-r` `associate-l`
2×	`insert-posit16` `add-log-exp`
1×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

2 → 27

Calls

2 calls:

11.0ms	(* (cos (/ (+ eps (+ x x)) 2)) (sin (/ eps 2)))
33.0ms	(cos (/ (+ eps (+ x x)) 2))

series116.0ms

Counts

2 → 6

Calls

2 calls:

77.0ms	(* (cos (/ (+ eps (+ x x)) 2)) (sin (/ eps 2)))
39.0ms	(cos (/ (+ eps (+ x x)) 2))

simplify2.0s

Counts

33 → 33

Iterations

Iter	Nodes
done	5003
4	2841
3	1099
2	363
1	138
0	65

prune188.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.6b

localize62.0ms

Local error

Found 4 expressions with local error:

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

rewrite131.0ms

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 (/ (+ eps (+ x x)) 2)) (sin (/ eps 2))))
39.0ms	(cos (/ (+ eps (+ x x)) 2))
37.0ms	(cos (/ (+ eps (+ x x)) 2))
45.0ms	(cos (/ (+ eps (+ x x)) 2))

series221.0ms

Counts

4 → 12

Calls

4 calls:

118.0ms	(cbrt (* (cos (/ (+ eps (+ x x)) 2)) (sin (/ eps 2))))
35.0ms	(cos (/ (+ eps (+ x x)) 2))
25.0ms	(cos (/ (+ eps (+ x x)) 2))
43.0ms	(cos (/ (+ eps (+ x x)) 2))

simplify2.3s

Counts

46 → 46

Iterations

Iter	Nodes
done	5001
4	3165
3	781
2	246
1	120
0	60

prune414.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.6b

localize56.0ms

Local error

Found 4 expressions with local error:

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

rewrite131.0ms

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:

8.0ms	(cbrt (* (cos (/ (+ eps (+ x x)) 2)) (sin (/ eps 2))))
43.0ms	(cos (/ (+ eps (+ x x)) 2))
39.0ms	(cos (/ (+ eps (+ x x)) 2))
40.0ms	(cos (/ (+ eps (+ x x)) 2))

series261.0ms

Counts

4 → 12

Calls

4 calls:

146.0ms	(cbrt (* (cos (/ (+ eps (+ x x)) 2)) (sin (/ eps 2))))
38.0ms	(cos (/ (+ eps (+ x x)) 2))
37.0ms	(cos (/ (+ eps (+ x x)) 2))
40.0ms	(cos (/ (+ eps (+ x x)) 2))

simplify2.2s

Counts

46 → 46

Iterations

Iter	Nodes
done	5001
4	3165
3	781
2	246
1	120
0	60

prune324.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 0.6b

regimes159.0ms

Accuracy

98.3% (0.3b remaining)

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

bsearch261.0ms

Steps

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

simplify10.0ms

Iterations

Iter	Nodes
done	34
1	34
0	25

end0.0ms

sample8.2s

Algorithm

intervals

Results

4.1s	3310×	body	1280	valid
1.6s	1858×	body	640	valid
1.2s	618×	body	2560	valid
508.0ms	1111×	body	80	valid
394.0ms	764×	body	320	valid
123.0ms	339×	body	160	valid