Details

sample238.0ms

Algorithm

intervals

Results

141.0ms	130×	body	1280	valid
34.0ms	72×	body	640	valid
28.0ms	17×	body	2560	valid
10.0ms	29×	body	320	valid
1.0ms	6×	body	160	valid
0.0ms	2×	body	80	valid

simplify9.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	9	7
2	10	7
done	10	7

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.7b

localize24.0ms

Local error

Found 2 expressions with local error:

0.9b	(- (cos (+ x eps)) (cos x))
3.1b	(cos (+ x eps))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 24

Calls

2 calls:

30.0ms	(- (cos (+ x eps)) (cos x))
22.0ms	(cos (+ x eps))

series171.0ms

Counts

2 → 6

Calls

2 calls:

100.0ms	(- (cos (+ x eps)) (cos x))
71.0ms	(cos (+ x eps))

simplify1.2s

Counts

30 → 30

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	65	311
1	135	299
2	339	283
3	1210	275
done	5000	273

prune209.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.6b

localize41.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (+ x eps) x)
0.3b	(* (sin (/ eps 2)) (sin (/ (+ (+ x eps) x) 2)))
3.1b	(sin (/ (+ (+ x eps) x) 2))

rewrite351.0ms

Algorithm

rewrite-expression-head

Rules

10×	`*-un-lft-identity`
8×	`add-log-exp`
7×	`add-sqr-sqrt`
5×	`pow1` `add-exp-log` `add-cube-cbrt` `add-cbrt-cube`
3×	`associate-r` `associate-l` `sum-log` `distribute-lft-out`
1×	`+-commutative` `associate-+l+` `flip3-+` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `sin-mult` `unswap-sqr`

Counts

3 → 41

Calls

3 calls:

61.0ms	(+ (+ x eps) x)
189.0ms	(* (sin (/ eps 2)) (sin (/ (+ (+ x eps) x) 2)))
97.0ms	(sin (/ (+ (+ x eps) x) 2))

series214.0ms

Counts

3 → 9

Calls

3 calls:

42.0ms	(+ (+ x eps) x)
112.0ms	(* (sin (/ eps 2)) (sin (/ (+ (+ x eps) x) 2)))
59.0ms	(sin (/ (+ (+ x eps) x) 2))

simplify800.0ms

Counts

50 → 50

Iterations

Useful iterations: done (796.0ms)

Iter	Nodes	Cost
0	91	654
1	212	646
2	852	570
done	5000	550

prune409.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.5b

localize62.0ms

Local error

Found 4 expressions with local error:

0.7b	(cbrt (sin (/ (+ (+ x eps) x) 2)))
3.1b	(sin (/ (+ (+ x eps) x) 2))
3.1b	(sin (/ (+ (+ x eps) x) 2))
3.1b	(sin (/ (+ (+ x eps) x) 2))

rewrite305.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 32

Calls

4 calls:

34.0ms	(cbrt (sin (/ (+ (+ x eps) x) 2)))
86.0ms	(sin (/ (+ (+ x eps) x) 2))
89.0ms	(sin (/ (+ (+ x eps) x) 2))
94.0ms	(sin (/ (+ (+ x eps) x) 2))

series325.0ms

Counts

4 → 12

Calls

4 calls:

169.0ms	(cbrt (sin (/ (+ (+ x eps) x) 2)))
52.0ms	(sin (/ (+ (+ x eps) x) 2))
51.0ms	(sin (/ (+ (+ x eps) x) 2))
52.0ms	(sin (/ (+ (+ x eps) x) 2))

simplify6.0s

Counts

44 → 44

Iterations

Useful iterations: 4 (1.6s)

Iter	Nodes	Cost
0	57	570
1	120	567
2	304	501
3	1056	477
4	4975	467
done	5001	467

prune486.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0.5b

localize63.0ms

Local error

Found 4 expressions with local error:

3.1b	(sin (/ (+ (+ x eps) x) 2))
4.3b	(cbrt (* (sin (/ eps 2)) (sin (/ (+ (+ x eps) x) 2))))
4.3b	(cbrt (* (sin (/ eps 2)) (sin (/ (+ (+ x eps) x) 2))))
4.3b	(cbrt (* (sin (/ eps 2)) (sin (/ (+ (+ x eps) x) 2))))

rewrite226.0ms

Algorithm

rewrite-expression-head

Rules

4×	`pow1` `add-exp-log` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `add-log-exp`
3×	`cbrt-prod` `cbrt-div` `pow1/3` `sin-mult`

Counts

4 → 37

Calls

4 calls:

75.0ms	(sin (/ (+ (+ x eps) x) 2))
43.0ms	(cbrt (* (sin (/ eps 2)) (sin (/ (+ (+ x eps) x) 2))))
47.0ms	(cbrt (* (sin (/ eps 2)) (sin (/ (+ (+ x eps) x) 2))))
59.0ms	(cbrt (* (sin (/ eps 2)) (sin (/ (+ (+ x eps) x) 2))))

series810.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(sin (/ (+ (+ x eps) x) 2))
287.0ms	(cbrt (* (sin (/ eps 2)) (sin (/ (+ (+ x eps) x) 2))))
230.0ms	(cbrt (* (sin (/ eps 2)) (sin (/ (+ (+ x eps) x) 2))))
239.0ms	(cbrt (* (sin (/ eps 2)) (sin (/ (+ (+ x eps) x) 2))))

simplify1.1s

Counts

49 → 49

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	66	924
1	136	918
2	315	818
3	1108	751
done	5000	721

prune470.0ms

Pruning

12 alts after pruning (9 fresh and 3 done)

Merged error: 0.5b

regimes453.0ms

Accuracy

97.8% (0.3b remaining)

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

bsearch303.0ms

Steps

Iters	Range		Point
10	5.024206171497321e-19	2.8868360106527892e-08	2.860803493028998e-08
10	-4.26929226401081	-4.5846337071089676e-10	-3.597466725231278e-05

simplify9.0ms

Iterations

Useful iterations: 1 (5.0ms)

Iter	Nodes	Cost
0	26	51
1	36	38
done	36	38

end0.0ms

sample8.7s

Algorithm

intervals

Results

4.3s	4495×	body	1280	valid
1.8s	633×	body	2560	valid
1.7s	1850×	body	640	valid
372.0ms	672×	body	320	valid
61.0ms	281×	body	160	valid
8.0ms	69×	body	80	valid