Details

sample194.0ms

Algorithm

intervals

Results

88.0ms	105×	body	1280	valid
45.0ms	28×	body	2560	valid
31.0ms	59×	body	640	valid
8.0ms	23×	body	320	valid
4.0ms	32×	body	80	valid
2.0ms	9×	body	160	valid

simplify4.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

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

prune42.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 40.7b

localize15.0ms

Local error

Found 2 expressions with local error:

1.9b	(- (sin (+ x eps)) (sin x))
4.4b	(sin (+ x eps))

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 24

Calls

2 calls:

61.0ms	(- (sin (+ x eps)) (sin x))
10.0ms	(sin (+ x eps))

series66.0ms

Counts

2 → 6

Calls

2 calls:

45.0ms	(- (sin (+ x eps)) (sin x))
21.0ms	(sin (+ x eps))

simplify3.0s

Counts

30 → 30

Iterations

Useful iterations: 4 (416.0ms)

Iter	Nodes	Cost
0	64	309
1	135	295
2	284	281
3	572	275
4	1162	271
5	2763	271
done	5000	271

prune77.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

localize18.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (+ x eps) x)
0.3b	(* (sin (/ eps 2)) (cos (/ (+ (+ x eps) x) 2)))
4.4b	(cos (/ (+ (+ x eps) x) 2))

rewrite112.0ms

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` `sin-cos-mult` `cbrt-unprod` `flip-+` `unswap-sqr`

Counts

3 → 41

Calls

3 calls:

44.0ms	(+ (+ x eps) x)
22.0ms	(* (sin (/ eps 2)) (cos (/ (+ (+ x eps) x) 2)))
43.0ms	(cos (/ (+ (+ x eps) x) 2))

series144.0ms

Counts

3 → 9

Calls

3 calls:

34.0ms	(+ (+ x eps) x)
65.0ms	(* (sin (/ eps 2)) (cos (/ (+ (+ x eps) x) 2)))
45.0ms	(cos (/ (+ (+ x eps) x) 2))

simplify4.2s

Counts

50 → 50

Iterations

Useful iterations: 4 (2.6s)

Iter	Nodes	Cost
0	91	656
1	213	646
2	546	566
3	1366	548
4	4627	540
done	5000	540

prune177.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.2b

localize36.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sin (/ eps 2)) (cbrt (pow (cos (/ (+ (+ x eps) x) 2)) 3)))
0.5b	(cbrt (pow (cos (/ (+ (+ x eps) x) 2)) 3))
0.5b	(pow (cos (/ (+ (+ x eps) x) 2)) 3)
4.4b	(cos (/ (+ (+ x eps) x) 2))

rewrite153.0ms

Algorithm

rewrite-expression-head

Rules

28×	`cbrt-prod`
24×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `-un-lft-identity` `associate-r*`
10×	`unpow-prod-down` `cube-prod`
7×	`pow1` `add-exp-log`
6×	`add-cbrt-cube`
5×	`unswap-sqr`
4×	`add-log-exp` `sqr-pow`
3×	`cube-mult` `pow-unpow` `unpow3` `associate-l`
1×	`pow-to-exp` `pow-pow` `pow1/3` `pow-prod-down` `pow-exp` `prod-exp` `*-commutative` `rem-cbrt-cube` `cbrt-unprod` `rem-cube-cbrt`

Counts

4 → 85

Calls

4 calls:

47.0ms	(* (sin (/ eps 2)) (cbrt (pow (cos (/ (+ (+ x eps) x) 2)) 3)))
5.0ms	(cbrt (pow (cos (/ (+ (+ x eps) x) 2)) 3))
6.0ms	(pow (cos (/ (+ (+ x eps) x) 2)) 3)
91.0ms	(cos (/ (+ (+ x eps) x) 2))

series195.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(* (sin (/ eps 2)) (cbrt (pow (cos (/ (+ (+ x eps) x) 2)) 3)))
33.0ms	(cbrt (pow (cos (/ (+ (+ x eps) x) 2)) 3))
62.0ms	(pow (cos (/ (+ (+ x eps) x) 2)) 3)
42.0ms	(cos (/ (+ (+ x eps) x) 2))

simplify3.9s

Counts

97 → 97

Iterations

Useful iterations: 3 (1.4s)

Iter	Nodes	Cost
0	117	1733
1	247	1447
2	705	1279
3	3806	1245
done	5000	1245

prune289.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.2b

localize25.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (cos (/ (+ (+ x eps) x) 2)))
4.4b	(cos (/ (+ (+ x eps) x) 2))
4.4b	(cos (/ (+ (+ x eps) x) 2))
4.4b	(cos (/ (+ (+ x eps) x) 2))

rewrite180.0ms

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:

2.0ms	(cbrt (cos (/ (+ (+ x eps) x) 2)))
60.0ms	(cos (/ (+ (+ x eps) x) 2))
68.0ms	(cos (/ (+ (+ x eps) x) 2))
49.0ms	(cos (/ (+ (+ x eps) x) 2))

series247.0ms

Counts

4 → 12

Calls

4 calls:

131.0ms	(cbrt (cos (/ (+ (+ x eps) x) 2)))
26.0ms	(cos (/ (+ (+ x eps) x) 2))
45.0ms	(cos (/ (+ (+ x eps) x) 2))
44.0ms	(cos (/ (+ (+ x eps) x) 2))

simplify2.1s

Counts

44 → 44

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	42	551
1	88	540
2	162	466
3	289	447
4	509	447
5	831	447
6	1833	447
done	5000	415

prune183.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 0.2b

regimes111.0ms

Accuracy

97.1% (0.4b remaining)

Error of 0.8b against oracle of 0.3b and baseline of 14.8b

bsearch229.0ms

Steps

Iters	Range		Point
10	9.030143500550019e-40	8.658023511829189e-30	8.55589437692315e-30
10	-7.35943201301068	-4.7981562703001505e-12	-8.505892634593632e-09

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	27	51
1	35	51
done	35	51

end0.0ms

sample5.1s

Algorithm

intervals

Results

2.5s	3322×	body	1280	valid
1.1s	1823×	body	640	valid
795.0ms	625×	body	2560	valid
208.0ms	815×	body	320	valid
95.0ms	353×	body	160	valid
73.0ms	1062×	body	80	valid