Details

sample153.0ms

Algorithm

intervals

Results

70.0ms	112×	body	1280	valid
34.0ms	25×	body	2560	valid
23.0ms	55×	body	640	valid
5.0ms	21×	body	320	valid
3.0ms	36×	body	80	valid
1.0ms	7×	body	160	valid

simplify7.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	10
2	10
1	9
0	6

prune46.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.9b

localize29.0ms

Local error

Found 2 expressions with local error:

1.5b	(- (sin (+ x eps)) (sin x))
3.3b	(sin (+ x eps))

rewrite41.0ms

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`
1×	`sub-neg` `flip3--` `diff-log` `diff-sin` `associate--l+` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 24

Calls

2 calls:

33.0ms	(- (sin (+ x eps)) (sin x))
8.0ms	(sin (+ x eps))

series85.0ms

Counts

2 → 6

Calls

2 calls:

44.0ms	(- (sin (+ x eps)) (sin x))
41.0ms	(sin (+ x eps))

simplify1.1s

Counts

30 → 30

Iterations

Iter	Nodes
done	5001
3	1449
2	381
1	135
0	63

prune181.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.4b

localize43.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ x (+ x eps))
0.2b	(* (cos (/ (+ x (+ x eps)) 2)) (sin (/ eps 2)))
3.2b	(cos (/ (+ x (+ x eps)) 2))

rewrite72.0ms

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` `distribute-lft-out`
1×	`+-commutative` `associate-+r+` `flip3-+` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `unswap-sqr`

Counts

3 → 40

Calls

3 calls:

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

series170.0ms

Counts

3 → 9

Calls

3 calls:

42.0ms	(+ x (+ x eps))
83.0ms	(* (cos (/ (+ x (+ x eps)) 2)) (sin (/ eps 2)))
45.0ms	(cos (/ (+ x (+ x eps)) 2))

simplify797.0ms

Counts

49 → 49

Iterations

Iter	Nodes
done	5000
2	993
1	211
0	86

prune312.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.3b

localize42.0ms

Local error

Found 4 expressions with local error:

0.4b	(cbrt (cos (/ (+ x (+ x eps)) 2)))
3.2b	(cos (/ (+ x (+ x eps)) 2))
3.2b	(cos (/ (+ x (+ x eps)) 2))
3.2b	(cos (/ (+ x (+ x eps)) 2))

rewrite102.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 32

Calls

4 calls:

1.0ms	(cbrt (cos (/ (+ x (+ x eps)) 2)))
40.0ms	(cos (/ (+ x (+ x eps)) 2))
28.0ms	(cos (/ (+ x (+ x eps)) 2))
31.0ms	(cos (/ (+ x (+ x eps)) 2))

series218.0ms

Counts

4 → 12

Calls

4 calls:

116.0ms	(cbrt (cos (/ (+ x (+ x eps)) 2)))
34.0ms	(cos (/ (+ x (+ x eps)) 2))
34.0ms	(cos (/ (+ x (+ x eps)) 2))
34.0ms	(cos (/ (+ x (+ x eps)) 2))

simplify2.3s

Counts

44 → 44

Iterations

Iter	Nodes
done	5000
4	3743
3	771
2	212
1	89
0	42

prune333.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.3b

localize72.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (sin (/ eps 2)))
0.6b	(cbrt (sin (/ eps 2)))
0.6b	(cbrt (sin (/ eps 2)))
3.2b	(cos (/ (+ x (+ x eps)) 2))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`pow1` `add-cbrt-cube` `add-exp-log` `add-log-exp`
3×	`pow1/3`

Counts

4 → 40

Calls

4 calls:

2.0ms	(cbrt (sin (/ eps 2)))
2.0ms	(cbrt (sin (/ eps 2)))
2.0ms	(cbrt (sin (/ eps 2)))
25.0ms	(cos (/ (+ x (+ x eps)) 2))

series532.0ms

Counts

4 → 12

Calls

4 calls:

177.0ms	(cbrt (sin (/ eps 2)))
186.0ms	(cbrt (sin (/ eps 2)))
131.0ms	(cbrt (sin (/ eps 2)))
38.0ms	(cos (/ (+ x (+ x eps)) 2))

simplify1.1s

Counts

52 → 52

Iterations

Iter	Nodes
done	5001
3	1408
2	329
1	126
0	60

prune358.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 0.3b

regimes270.0ms

Accuracy

99.6% (0.1b remaining)

Error of 0.5b against oracle of 0.4b and baseline of 15.1b

bsearch233.0ms

Steps

Iters	Range		Point
11	5.267526695779846e-25	1126.7541422477805	8.790268235921677e-09
10	-3.2052418334402957e-07	-8.353467643873847e-20	-7.57640278482506e-09

simplify11.0ms

Iterations

Iter	Nodes
done	35
1	35
0	27

end0.0ms

sample6.6s

Algorithm

intervals

Results

3.7s	3217×	body	1280	valid
1.1s	1872×	body	640	valid
980.0ms	651×	body	2560	valid
407.0ms	784×	body	320	valid
108.0ms	1121×	body	80	valid
79.0ms	355×	body	160	valid