Details

sample178.0ms

Algorithm

intervals

Results

86.0ms	113×	body	1280	valid
28.0ms	20×	body	2560	valid
24.0ms	54×	body	640	valid
14.0ms	15×	body	160	valid
9.0ms	26×	body	320	valid
3.0ms	28×	body	80	valid

simplify5.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.1b

localize20.0ms

Local error

Found 2 expressions with local error:

1.2b	(- (sin (+ x eps)) (sin x))
4.0b	(sin (+ x eps))

rewrite111.0ms

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:

99.0ms	(- (sin (+ x eps)) (sin x))
11.0ms	(sin (+ x eps))

series103.0ms

Counts

2 → 6

Calls

2 calls:

70.0ms	(- (sin (+ x eps)) (sin x))
33.0ms	(sin (+ x eps))

simplify976.0ms

Counts

30 → 30

Iterations

Useful iterations: done (975.0ms)

Iter	Nodes	Cost
0	64	309
1	135	295
2	381	281
3	1453	275
done	5000	271

prune156.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.5b

localize35.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (+ x eps) x)
0.3b	(* (sin (/ eps 2)) (cos (/ (+ (+ x eps) x) 2)))
4.1b	(cos (/ (+ (+ x eps) x) 2))

rewrite135.0ms

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:

33.0ms	(+ (+ x eps) x)
22.0ms	(* (sin (/ eps 2)) (cos (/ (+ (+ x eps) x) 2)))
78.0ms	(cos (/ (+ (+ x eps) x) 2))

series127.0ms

Counts

3 → 9

Calls

3 calls:

36.0ms	(+ (+ x eps) x)
55.0ms	(* (sin (/ eps 2)) (cos (/ (+ (+ x eps) x) 2)))
36.0ms	(cos (/ (+ (+ x eps) x) 2))

simplify644.0ms

Counts

50 → 50

Iterations

Useful iterations: done (643.0ms)

Iter	Nodes	Cost
0	91	656
1	219	646
2	982	568
done	5000	552

prune212.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.4b

localize35.0ms

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)
4.1b	(cos (/ (+ (+ x eps) x) 2))

rewrite103.0ms

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:

25.0ms	(* (sin (/ eps 2)) (cbrt (pow (cos (/ (+ (+ x eps) x) 2)) 3)))
3.0ms	(cbrt (pow (cos (/ (+ (+ x eps) x) 2)) 3))
4.0ms	(pow (cos (/ (+ (+ x eps) x) 2)) 3)
70.0ms	(cos (/ (+ (+ x eps) x) 2))

series181.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(* (sin (/ eps 2)) (cbrt (pow (cos (/ (+ (+ x eps) x) 2)) 3)))
25.0ms	(cbrt (pow (cos (/ (+ (+ x eps) x) 2)) 3))
58.0ms	(pow (cos (/ (+ (+ x eps) x) 2)) 3)
42.0ms	(cos (/ (+ (+ x eps) x) 2))

simplify1.8s

Counts

97 → 97

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	117	1733
1	299	1463
2	1825	1279
done	5001	1263

prune421.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0.4b

localize28.0ms

Local error

Found 4 expressions with local error:

0.4b	(cbrt (cos (/ (+ (+ x eps) x) 2)))
0.5b	(cbrt (pow (cos (/ (+ (+ x eps) x) 2)) 2))
4.1b	(cos (/ (+ (+ x eps) x) 2))
4.1b	(cos (/ (+ (+ x eps) x) 2))

rewrite168.0ms

Algorithm

rewrite-expression-head

Rules

11×	`cbrt-prod`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`unpow-prod-down`
2×	`pow1/3`
1×	`unpow2` `sqr-pow`

Counts

4 → 41

Calls

4 calls:

2.0ms	(cbrt (cos (/ (+ (+ x eps) x) 2)))
5.0ms	(cbrt (pow (cos (/ (+ (+ x eps) x) 2)) 2))
88.0ms	(cos (/ (+ (+ x eps) x) 2))
71.0ms	(cos (/ (+ (+ x eps) x) 2))

series339.0ms

Counts

4 → 12

Calls

4 calls:

115.0ms	(cbrt (cos (/ (+ (+ x eps) x) 2)))
133.0ms	(cbrt (pow (cos (/ (+ (+ x eps) x) 2)) 2))
40.0ms	(cos (/ (+ (+ x eps) x) 2))
50.0ms	(cos (/ (+ (+ x eps) x) 2))

simplify1.1s

Counts

53 → 53

Iterations

Useful iterations: 3 (473.0ms)

Iter	Nodes	Cost
0	71	779
1	154	704
2	462	630
3	1857	608
done	5004	608

prune274.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.4b

regimes181.0ms

Accuracy

99.5% (0.1b remaining)

Error of 0.5b against oracle of 0.4b and baseline of 15.5b

bsearch220.0ms

Steps

Iters	Range		Point
9	5.841499356922819e-12	0.0004268116563047139	1.7444808358242096e-08
9	-8.253445947576724e-07	-1.3572074081350282e-15	-1.1066748065615766e-08

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

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

end0.0ms

sample5.8s

Algorithm

intervals

Results

2.8s	3296×	body	1280	valid
1.2s	1883×	body	640	valid
1.1s	609×	body	2560	valid
250.0ms	762×	body	320	valid
90.0ms	1092×	body	80	valid
64.0ms	358×	body	160	valid