Details

sample147.0ms

Algorithm

intervals

Results

73.0ms	110×	body	1280	valid
32.0ms	25×	body	2560	valid
17.0ms	46×	body	640	valid
8.0ms	26×	body	320	valid
3.0ms	38×	body	80	valid
2.0ms	11×	body	160	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: 39.6b

localize12.0ms

Local error

Found 2 expressions with local error:

1.4b	(- (sin (+ x eps)) (sin x))
3.7b	(sin (+ x eps))

rewrite64.0ms

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:

56.0ms	(- (sin (+ x eps)) (sin x))
8.0ms	(sin (+ x eps))

series85.0ms

Counts

2 → 6

Calls

2 calls:

64.0ms	(- (sin (+ x eps)) (sin x))
20.0ms	(sin (+ x eps))

simplify3.4s

Counts

30 → 30

Iterations

Iter	Nodes
done	5000
5	4797
4	1781
3	755
2	305
1	135
0	63

prune157.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.4b

localize21.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ x (+ x eps))
0.3b	(* (cos (/ (+ x (+ x eps)) 2)) (sin (* 1/2 eps)))
3.7b	(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:

24.0ms	(+ x (+ x eps))
19.0ms	(* (cos (/ (+ x (+ x eps)) 2)) (sin (* 1/2 eps)))
28.0ms	(cos (/ (+ x (+ x eps)) 2))

series204.0ms

Counts

3 → 9

Calls

3 calls:

40.0ms	(+ x (+ x eps))
127.0ms	(* (cos (/ (+ x (+ x eps)) 2)) (sin (* 1/2 eps)))
37.0ms	(cos (/ (+ x (+ x eps)) 2))

simplify2.4s

Counts

49 → 49

Iterations

Iter	Nodes
done	5011
3	2895
2	636
1	209
0	84

prune391.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.4b

localize80.0ms

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))))
3.7b	(cos (/ (+ x (+ x eps)) 2))
3.7b	(cos (/ (+ x (+ x eps)) 2))
3.7b	(cos (/ (+ x (+ x eps)) 2))

rewrite124.0ms

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:

22.0ms	(cbrt (* (* (cos (/ (+ x (+ x eps)) 2)) (cos (/ (+ x (+ x eps)) 2))) (cos (/ (+ x (+ x eps)) 2))))
33.0ms	(cos (/ (+ x (+ x eps)) 2))
26.0ms	(cos (/ (+ x (+ x eps)) 2))
42.0ms	(cos (/ (+ x (+ x eps)) 2))

series154.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(cbrt (* (* (cos (/ (+ x (+ x eps)) 2)) (cos (/ (+ x (+ x eps)) 2))) (cos (/ (+ x (+ x eps)) 2))))
31.0ms	(cos (/ (+ x (+ x eps)) 2))
38.0ms	(cos (/ (+ x (+ x eps)) 2))
42.0ms	(cos (/ (+ x (+ x eps)) 2))

simplify2.7s

Counts

44 → 44

Iterations

Iter	Nodes
done	5005
5	3259
4	1040
3	384
2	137
1	81
0	43

prune397.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.3b

localize91.0ms

Local error

Found 4 expressions with local error:

0.4b	(cbrt (* (cos (/ (+ x (+ x eps)) 2)) (cos (/ (+ x (+ x eps)) 2))))
3.7b	(cos (/ (+ x (+ x eps)) 2))
3.7b	(cos (/ (+ x (+ x eps)) 2))
3.7b	(cos (/ (+ x (+ x eps)) 2))

rewrite412.0ms

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` `cos-mult`

Counts

4 → 31

Calls

4 calls:

3.0ms	(cbrt (* (cos (/ (+ x (+ x eps)) 2)) (cos (/ (+ x (+ x eps)) 2))))
30.0ms	(cos (/ (+ x (+ x eps)) 2))
328.0ms	(cos (/ (+ x (+ x eps)) 2))
49.0ms	(cos (/ (+ x (+ x eps)) 2))

series229.0ms

Counts

4 → 12

Calls

4 calls:

125.0ms	(cbrt (* (cos (/ (+ x (+ x eps)) 2)) (cos (/ (+ x (+ x eps)) 2))))
36.0ms	(cos (/ (+ x (+ x eps)) 2))
41.0ms	(cos (/ (+ x (+ x eps)) 2))
26.0ms	(cos (/ (+ x (+ x eps)) 2))

simplify1.3s

Counts

43 → 43

Iterations

Iter	Nodes
done	5003
4	1678
3	585
2	188
1	103
0	48

prune280.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.3b

regimes247.0ms

Accuracy

98.4% (0.2b remaining)

Error of 0.6b against oracle of 0.4b and baseline of 15.0b

bsearch195.0ms

Steps

Iters	Range		Point
8	3.528148116602709e-22	3.721454938748264e-18	3.630608855951668e-18
10	-2.725519985046895e-08	-4.357977289634356e-25	-9.918151501731852e-09

simplify13.0ms

Iterations

Iter	Nodes
done	37
1	37
0	28

end0.0ms

sample5.7s

Algorithm

intervals

Results

3.3s	3309×	body	1280	valid
881.0ms	671×	body	2560	valid
878.0ms	1805×	body	640	valid
237.0ms	794×	body	320	valid
85.0ms	1079×	body	80	valid
55.0ms	342×	body	160	valid