Details

sample52.0ms

Algorithm

intervals

Results

21.0ms	47×	body	2560	valid
10.0ms	45×	body	1280	valid
6.0ms	44×	body	640	valid
4.0ms	38×	body	320	valid
2.0ms	71×	body	80	valid
1.0ms	11×	body	160	valid

simplify15.0ms

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

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.4b

localize6.0ms

Local error

Found 2 expressions with local error:

2.4b	(- 1.0 (cos x))
13.4b	(/ (- 1.0 (cos x)) (* x x))

rewrite29.0ms

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:

6.0ms	(- 1.0 (cos x))
22.0ms	(/ (- 1.0 (cos x)) (* x x))

series63.0ms

Counts

2 → 6

Calls

2 calls:

19.0ms	(- 1.0 (cos x))
44.0ms	(/ (- 1.0 (cos x)) (* x x))

simplify1.4s

Counts

48 → 48

Iterations

Useful iterations: 2 (99.0ms)

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

prune102.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize12.0ms

Local error

Found 3 expressions with local error:

0.3b	(* 1/720 (pow x 4))
0.4b	(* 1/24 (pow x 2))
12.6b	(- (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (pow x 2)))

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
15×	`associate-r`
13×	`add-exp-log`
9×	`add-cube-cbrt` `*-un-lft-identity`
8×	`unpow-prod-down` `add-log-exp`
7×	`add-cbrt-cube` `unswap-sqr`
6×	`associate-l` `prod-exp`
4×	`sqr-pow`
3×	`pow1`
2×	`pow-to-exp` `diff-log` `pow-exp` `*-commutative` `cbrt-unprod` `unpow2`
1×	`sub-neg` `flip3--` `associate--l+` `sum-log` `flip--`

Counts

3 → 66

Calls

3 calls:

11.0ms	(* 1/720 (pow x 4))
13.0ms	(* 1/24 (pow x 2))
50.0ms	(- (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (pow x 2)))

series110.0ms

Counts

3 → 9

Calls

3 calls:

37.0ms	(* 1/720 (pow x 4))
28.0ms	(* 1/24 (pow x 2))
44.0ms	(- (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (pow x 2)))

simplify1.9s

Counts

75 → 75

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	121	780
1	272	701
2	685	643
3	2993	629
done	5002	626

prune151.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.1b

localize6.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (/ (- 1.0 (cos x)) x) x)
0.1b	(/ (- 1.0 (cos x)) x)
2.4b	(- 1.0 (cos x))

rewrite50.0ms

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:

22.0ms	(/ (/ (- 1.0 (cos x)) x) x)
16.0ms	(/ (- 1.0 (cos x)) x)
6.0ms	(- 1.0 (cos x))

series110.0ms

Counts

3 → 9

Calls

3 calls:

47.0ms	(/ (/ (- 1.0 (cos x)) x) x)
44.0ms	(/ (- 1.0 (cos x)) x)
19.0ms	(- 1.0 (cos x))

simplify1.7s

Counts

156 → 156

Iterations

Useful iterations: done (1.7s)

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

prune272.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.1b

localize7.0ms

Local error

Found 3 expressions with local error:

0.1b	(* (/ (- 1.0 (cos x)) x) (/ 1 x))
0.1b	(/ (- 1.0 (cos x)) x)
2.4b	(- 1.0 (cos x))

rewrite63.0ms

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:

38.0ms	(* (/ (- 1.0 (cos x)) x) (/ 1 x))
15.0ms	(/ (- 1.0 (cos x)) x)
6.0ms	(- 1.0 (cos x))

series110.0ms

Counts

3 → 9

Calls

3 calls:

47.0ms	(* (/ (- 1.0 (cos x)) x) (/ 1 x))
43.0ms	(/ (- 1.0 (cos x)) x)
19.0ms	(- 1.0 (cos x))

simplify3.1s

Counts

124 → 124

Iterations

Useful iterations: 3 (1.9s)

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

prune206.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.1b

regimes45.0ms

Accuracy

99.6% (0.1b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 31.4b

bsearch73.0ms

Steps

Iters	Range		Point
11	6.1632953816490534e-12	2923699147.8271213	0.03227596253233406
10	-21283307590.397102	-3.152803306627408e-07	-0.03309682507506567

simplify4.0ms

Iterations

Useful iterations: 1 (2.0ms)

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

end0.0ms

sample1.6s

Algorithm

intervals

Results

737.0ms	1602×	body	2560	valid
294.0ms	1266×	body	1280	valid
213.0ms	1456×	body	640	valid
104.0ms	949×	body	320	valid
81.0ms	2234×	body	80	valid
35.0ms	493×	body	160	valid