Details

sample171.0ms

Algorithm

intervals

Results

86.0ms	111×	body	1280	valid
29.0ms	20×	body	2560	valid
24.0ms	56×	body	640	valid
7.0ms	23×	body	320	valid
4.0ms	36×	body	80	valid
2.0ms	10×	body	160	valid

simplify3.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	10
2	10
1	9
0	6

prune34.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.5b

localize15.0ms

Local error

Found 2 expressions with local error:

0.9b	(- (sin (+ x eps)) (sin x))
2.3b	(sin (+ x eps))

rewrite40.0ms

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:

32.0ms	(- (sin (+ x eps)) (sin x))
7.0ms	(sin (+ x eps))

series105.0ms

Counts

2 → 6

Calls

2 calls:

67.0ms	(- (sin (+ x eps)) (sin x))
38.0ms	(sin (+ x eps))

simplify978.0ms

Counts

30 → 30

Iterations

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

prune135.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.3b

localize37.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ x (+ x eps))
0.2b	(/ (+ x (+ x eps)) 2)
0.3b	(* (cos (/ (+ x (+ x eps)) 2)) (sin (/ eps 2)))
2.5b	(cos (/ (+ x (+ x eps)) 2))

rewrite122.0ms

Algorithm

rewrite-expression-head

Rules

41×	`*-un-lft-identity`
18×	`add-sqr-sqrt`
16×	`add-cube-cbrt`
15×	`times-frac` `distribute-lft-out`
9×	`add-log-exp`
8×	`add-cbrt-cube` `add-exp-log`
6×	`pow1`
5×	`associate-/l*`
3×	`associate-/r` `sum-log` `associate-r` `associate-l*`
2×	`flip3-+` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `associate-+r+` `clear-num` `frac-2neg` `div-exp` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `div-inv` `unswap-sqr`

Counts

4 → 77

Calls

4 calls:

12.0ms	(+ x (+ x eps))
52.0ms	(/ (+ x (+ x eps)) 2)
19.0ms	(* (cos (/ (+ x (+ x eps)) 2)) (sin (/ eps 2)))
36.0ms	(cos (/ (+ x (+ x eps)) 2))

series211.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(+ x (+ x eps))
54.0ms	(/ (+ x (+ x eps)) 2)
95.0ms	(* (cos (/ (+ x (+ x eps)) 2)) (sin (/ eps 2)))
30.0ms	(cos (/ (+ x (+ x eps)) 2))

simplify1.0s

Counts

89 → 89

Iterations

Iter	Nodes
done	5000
2	1387
1	303
0	128

prune505.0ms

Pruning

9 alts after pruning (8 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)) (cos (/ (+ x (+ x eps)) 2))) (cos (/ (+ x (+ x eps)) 2))))
2.5b	(cos (/ (+ x (+ x eps)) 2))
2.5b	(cos (/ (+ x (+ x eps)) 2))
2.5b	(cos (/ (+ x (+ x eps)) 2))

rewrite509.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `add-log-exp`
1×	`cbrt-prod` `cbrt-div` `pow1/3` `pow3` `associate-*l/` `cos-mult` `rem-cbrt-cube`

Counts

4 → 32

Calls

4 calls:

11.0ms	(cbrt (* (* (cos (/ (+ x (+ x eps)) 2)) (cos (/ (+ x (+ x eps)) 2))) (cos (/ (+ x (+ x eps)) 2))))
40.0ms	(cos (/ (+ x (+ x eps)) 2))
429.0ms	(cos (/ (+ x (+ x eps)) 2))
27.0ms	(cos (/ (+ x (+ x eps)) 2))

series122.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(cbrt (* (* (cos (/ (+ x (+ x eps)) 2)) (cos (/ (+ x (+ x eps)) 2))) (cos (/ (+ x (+ x eps)) 2))))
31.0ms	(cos (/ (+ x (+ x eps)) 2))
26.0ms	(cos (/ (+ x (+ x eps)) 2))
31.0ms	(cos (/ (+ x (+ x eps)) 2))

simplify1.6s

Counts

44 → 44

Iterations

Iter	Nodes
done	5001
4	2950
3	656
2	181
1	81
0	43

prune351.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.3b

localize120.0ms

Local error

Found 4 expressions with local error:

2.5b	(cos (/ (+ x (+ x eps)) 2))
2.5b	(cos (/ (+ x (+ x eps)) 2))
2.5b	(cos (/ (+ x (+ x eps)) 2))
2.5b	(cos (/ (+ x (+ x eps)) 2))

rewrite120.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `add-log-exp`

Counts

4 → 28

Calls

4 calls:

29.0ms	(cos (/ (+ x (+ x eps)) 2))
23.0ms	(cos (/ (+ x (+ x eps)) 2))
41.0ms	(cos (/ (+ x (+ x eps)) 2))
25.0ms	(cos (/ (+ x (+ x eps)) 2))

series128.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(cos (/ (+ x (+ x eps)) 2))
35.0ms	(cos (/ (+ x (+ x eps)) 2))
31.0ms	(cos (/ (+ x (+ x eps)) 2))
33.0ms	(cos (/ (+ x (+ x eps)) 2))

simplify1.5s

Counts

40 → 40

Iterations

Iter	Nodes
done	5000
4	1809
3	458
2	137
1	58
0	26

prune322.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.3b

regimes281.0ms

Accuracy

98.6% (0.2b remaining)

Error of 0.6b against oracle of 0.4b and baseline of 15.1b

bsearch180.0ms

Steps

Iters	Range		Point
8	2.673612976528507e-11	7.42116589675916e-09	5.463141894552383e-09
9	-3322970397.4786234	-6367.3348759504115	-6443.306290177518

simplify11.0ms

Iterations

Iter	Nodes
done	35
1	35
0	25

end0.0ms

sample6.0s

Algorithm

intervals

Results

3.3s	3320×	body	1280	valid
1.1s	637×	body	2560	valid
854.0ms	1868×	body	640	valid
290.0ms	725×	body	320	valid
92.0ms	1106×	body	80	valid
61.0ms	344×	body	160	valid