Details

sample154.0ms

Algorithm

intervals

Results

72.0ms	125×	body	1280	valid
29.0ms	23×	body	2560	valid
29.0ms	59×	body	640	valid
9.0ms	37×	body	320	valid
2.0ms	10×	body	160	valid
0.0ms	2×	body	80	valid

simplify4.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	10
2	10
1	9
0	6

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.8b

localize11.0ms

Local error

Found 2 expressions with local error:

1.4b	(- (cos (+ x eps)) (cos x))
3.6b	(cos (+ x eps))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt` `*-un-lft-identity` `add-log-exp`
2×	`pow1` `cos-sum` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
1×	`associate--l-` `sub-neg` `flip3--` `diff-log` `diff-cos` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 24

Calls

2 calls:

38.0ms	(- (cos (+ x eps)) (cos x))
14.0ms	(cos (+ x eps))

series113.0ms

Counts

2 → 6

Calls

2 calls:

74.0ms	(- (cos (+ x eps)) (cos x))
40.0ms	(cos (+ x eps))

simplify2.9s

Counts

30 → 30

Iterations

Iter	Nodes
done	5015
5	4022
4	1465
3	652
2	280
1	135
0	65

prune193.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.6b

localize29.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ x (+ x eps))
0.3b	(* (sin (/ (+ x (+ x eps)) 2)) (sin (/ eps 2)))
3.6b	(sin (/ (+ x (+ x eps)) 2))

rewrite110.0ms

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-+` `sin-mult` `unswap-sqr`

Counts

3 → 41

Calls

3 calls:

16.0ms	(+ x (+ x eps))
56.0ms	(* (sin (/ (+ x (+ x eps)) 2)) (sin (/ eps 2)))
36.0ms	(sin (/ (+ x (+ x eps)) 2))

series183.0ms

Counts

3 → 9

Calls

3 calls:

26.0ms	(+ x (+ x eps))
116.0ms	(* (sin (/ (+ x (+ x eps)) 2)) (sin (/ eps 2)))
41.0ms	(sin (/ (+ x (+ x eps)) 2))

simplify2.1s

Counts

50 → 50

Iterations

Iter	Nodes
done	5012
3	2436
2	628
1	212
0	91

prune413.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.5b

localize64.0ms

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)))
3.6b	(sin (/ (+ x (+ x eps)) 2))

rewrite48.0ms

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)))
42.0ms	(sin (/ (+ x (+ x eps)) 2))

series507.0ms

Counts

4 → 12

Calls

4 calls:

136.0ms	(cbrt (sin (/ eps 2)))
166.0ms	(cbrt (sin (/ eps 2)))
165.0ms	(cbrt (sin (/ eps 2)))
40.0ms	(sin (/ (+ x (+ x eps)) 2))

simplify2.0s

Counts

52 → 52

Iterations

Iter	Nodes
done	5001
4	2268
3	640
2	234
1	123
0	60

prune410.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 0.5b

localize63.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (sin (/ (+ x (+ x eps)) 2)))
3.6b	(sin (/ (+ x (+ x eps)) 2))
3.6b	(sin (/ (+ x (+ x eps)) 2))
3.6b	(sin (/ (+ x (+ x eps)) 2))

rewrite137.0ms

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:

21.0ms	(cbrt (sin (/ (+ x (+ x eps)) 2)))
47.0ms	(sin (/ (+ x (+ x eps)) 2))
40.0ms	(sin (/ (+ x (+ x eps)) 2))
28.0ms	(sin (/ (+ x (+ x eps)) 2))

series254.0ms

Counts

4 → 12

Calls

4 calls:

123.0ms	(cbrt (sin (/ (+ x (+ x eps)) 2)))
37.0ms	(sin (/ (+ x (+ x eps)) 2))
54.0ms	(sin (/ (+ x (+ x eps)) 2))
39.0ms	(sin (/ (+ x (+ x eps)) 2))

simplify2.0s

Counts

44 → 44

Iterations

Iter	Nodes
done	5001
4	2566
3	736
2	258
1	121
0	57

prune302.0ms

Pruning

13 alts after pruning (10 fresh and 3 done)

Merged error: 0.5b

regimes264.0ms

Accuracy

97.7% (0.3b remaining)

Error of 0.8b against oracle of 0.4b and baseline of 15.3b

bsearch213.0ms

Steps

Iters	Range		Point
9	1.7501962730858363e-09	0.00351971213897904	1.2896790119530399e-05
10	-733100.9210806559	-4.034181863829644e-08	-0.00010824109259697614

simplify11.0ms

Iterations

Iter	Nodes
done	35
1	35
0	26

end0.0ms

sample6.5s

Algorithm

intervals

Results

4.1s	4442×	body	1280	valid
1.0s	645×	body	2560	valid
888.0ms	1831×	body	640	valid
187.0ms	731×	body	320	valid
45.0ms	259×	body	160	valid
8.0ms	92×	body	80	valid