Details

sample98.0ms

Algorithm

intervals

Results

39.0ms	51×	body	2560	valid
16.0ms	40×	body	1280	valid
16.0ms	57×	body	640	valid
6.0ms	63×	body	80	valid
6.0ms	27×	body	320	valid
3.0ms	18×	body	160	valid

simplify26.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	13	8
2	21	8
3	26	8
4	28	8
done	28	8

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.0b

localize12.0ms

Local error

Found 2 expressions with local error:

1.5b	(- 1.0 (cos x))
15.7b	(/ (- 1.0 (cos x)) (* x x))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt` `*-un-lft-identity`
7×	`add-exp-log` `add-cbrt-cube`
5×	`times-frac` `associate-/l*`
4×	`add-cube-cbrt` `add-log-exp`
3×	`distribute-lft-out--` `difference-of-squares`
2×	`pow1` `cbrt-undiv` `flip3--` `div-exp` `flip--` `associate-/l/`
1×	`sub-neg` `frac-2neg` `diff-log` `div-sub` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

2 → 42

Calls

2 calls:

11.0ms	(- 1.0 (cos x))
47.0ms	(/ (- 1.0 (cos x)) (* x x))

series144.0ms

Counts

2 → 6

Calls

2 calls:

37.0ms	(- 1.0 (cos x))
106.0ms	(/ (- 1.0 (cos x)) (* x x))

simplify2.1s

Counts

48 → 48

Iterations

Useful iterations: 2 (148.0ms)

Iter	Nodes	Cost
0	88	507
1	212	489
2	548	441
3	1500	441
done	5000	441

prune178.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.2b

localize7.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (/ (- 1.0 (cos x)) x) x)
0.1b	(/ (- 1.0 (cos x)) x)
1.5b	(- 1.0 (cos x))

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

132×	`times-frac`
103×	`add-sqr-sqrt` `*-un-lft-identity`
69×	`add-cube-cbrt`
24×	`associate-/l*`
17×	`distribute-lft-out--` `difference-of-squares`
10×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/r*` `div-inv`
5×	`add-log-exp`
4×	`cbrt-undiv` `div-exp`
3×	`pow1` `div-sub` `associate-/l/`
2×	`flip3--` `frac-2neg` `clear-num` `flip--`
1×	`sub-neg` `diff-log`

Counts

3 → 147

Calls

3 calls:

27.0ms	(/ (/ (- 1.0 (cos x)) x) x)
17.0ms	(/ (- 1.0 (cos x)) x)
7.0ms	(- 1.0 (cos x))

series149.0ms

Counts

3 → 9

Calls

3 calls:

54.0ms	(/ (/ (- 1.0 (cos x)) x) x)
66.0ms	(/ (- 1.0 (cos x)) x)
30.0ms	(- 1.0 (cos x))

simplify2.7s

Counts

156 → 156

Iterations

Useful iterations: done (2.7s)

Iter	Nodes	Cost
0	229	2262
1	522	2156
2	1258	2046
3	3200	2024
done	5000	2009

prune444.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize19.0ms

Local error

Found 3 expressions with local error:

0.1b	(* (/ (- 1.0 (cos x)) x) (/ 1 x))
0.1b	(/ (- 1.0 (cos x)) x)
1.5b	(- 1.0 (cos x))

rewrite117.0ms

Algorithm

rewrite-expression-head

Rules

62×	`add-sqr-sqrt`
47×	`*-un-lft-identity`
46×	`times-frac`
29×	`add-cube-cbrt`
27×	`add-exp-log`
19×	`associate-l`
17×	`add-cbrt-cube`
13×	`associate-r`
9×	`div-exp`
8×	`prod-exp` `distribute-lft-out--` `difference-of-squares`
6×	`unswap-sqr`
5×	`pow1` `cbrt-undiv` `associate-/l*` `add-log-exp`
4×	`cbrt-unprod`
3×	`associate-/r*` `div-inv`
2×	`rec-exp` `flip3--` `1-exp` `flip--` `associate-/l/`
1×	`frac-times` `sub-neg` `frac-2neg` `diff-log` `div-sub` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `un-div-inv` `*-commutative`

Counts

3 → 115

Calls

3 calls:

68.0ms	(* (/ (- 1.0 (cos x)) x) (/ 1 x))
32.0ms	(/ (- 1.0 (cos x)) x)
12.0ms	(- 1.0 (cos x))

series164.0ms

Counts

3 → 9

Calls

3 calls:

68.0ms	(* (/ (- 1.0 (cos x)) x) (/ 1 x))
65.0ms	(/ (- 1.0 (cos x)) x)
30.0ms	(- 1.0 (cos x))

simplify4.1s

Counts

124 → 124

Iterations

Useful iterations: 3 (2.8s)

Iter	Nodes	Cost
0	189	1536
1	510	1380
2	1417	1222
3	4862	1205
done	5000	1205

prune311.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.1b

localize15.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (- (/ 1.0 x) (/ (cos x) x)) x)
0.1b	(/ (cos x) x)
1.6b	(- (/ 1.0 x) (/ (cos x) x))

rewrite193.0ms

Algorithm

rewrite-expression-head

Rules

98×	`add-sqr-sqrt`
95×	`times-frac`
78×	`*-un-lft-identity`
38×	`add-cube-cbrt`
20×	`distribute-lft-out--` `difference-of-squares`
15×	`associate-/l*`
12×	`div-inv`
7×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/r*`
5×	`distribute-rgt-out--` `add-log-exp`
4×	`associate-/l/`
3×	`pow1`
2×	`cbrt-undiv` `flip3--` `frac-2neg` `div-exp` `clear-num` `frac-sub` `flip--` `sub-div`
1×	`sub-neg` `diff-log` `div-sub`

Counts

3 → 118

Calls

3 calls:

116.0ms	(/ (- (/ 1.0 x) (/ (cos x) x)) x)
21.0ms	(/ (cos x) x)
46.0ms	(- (/ 1.0 x) (/ (cos x) x))

series251.0ms

Counts

3 → 9

Calls

3 calls:

123.0ms	(/ (- (/ 1.0 x) (/ (cos x) x)) x)
36.0ms	(/ (cos x) x)
91.0ms	(- (/ 1.0 x) (/ (cos x) x))

simplify1.7s

Counts

127 → 127

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	203	1857
1	461	1635
2	1036	1570
3	2708	1565
done	5000	1545

prune287.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0.1b

regimes53.0ms

Accuracy

99.5% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 30.4b

bsearch77.0ms

Steps

Iters	Range		Point
9	5.155942382976535e-09	0.21963308938311268	0.029805544534800093
11	-2445851338.3862987	-4.2674702477225e-16	-0.03339438899281232

simplify4.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	25	41
1	34	32
done	34	32

end0.0ms

sample3.0s

Algorithm

intervals

Results

1.1s	1593×	body	2560	valid
546.0ms	1236×	body	1280	valid
528.0ms	2264×	body	80	valid
368.0ms	1486×	body	640	valid
222.0ms	946×	body	320	valid
50.0ms	475×	body	160	valid