Details

sample99.0ms

Algorithm

intervals

Results

53.0ms	59×	body	2560	valid
13.0ms	33×	body	1280	valid
11.0ms	47×	body	640	valid
6.0ms	84×	body	80	valid
4.0ms	22×	body	320	valid
1.0ms	11×	body	160	valid

simplify23.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	182
1	13	182
2	21	182
3	26	182
4	28	182
done	28	182

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.7b

localize10.0ms

Local error

Found 2 expressions with local error:

1.9b	(- 1.0 (cos x))
16.6b	(/ (- 1.0 (cos x)) (* x x))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt` `*-un-lft-identity`
7×	`add-cbrt-cube` `add-exp-log`
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×	`clear-num` `associate-/r*` `sub-neg` `frac-2neg` `diff-log` `div-sub` `prod-exp` `cbrt-unprod` `div-inv`

Counts

2 → 42

Calls

2 calls:

9.0ms	(- 1.0 (cos x))
21.0ms	(/ (- 1.0 (cos x)) (* x x))

series114.0ms

Counts

2 → 6

Calls

2 calls:

28.0ms	(- 1.0 (cos x))
86.0ms	(/ (- 1.0 (cos x)) (* x x))

simplify2.4s

Counts

48 → 48

Iterations

Useful iterations: 3 (958.0ms)

Iter	Nodes	Cost
0	88	12774
1	217	11197
2	651	10906
3	2415	10826
done	5074	10826

prune230.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize40.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sqrt (- 1.0 (cos x))) x)
0.1b	(* (/ (sqrt (- 1.0 (cos x))) x) (/ (sqrt (- 1.0 (cos x))) x))
1.9b	(- 1.0 (cos x))
1.9b	(- 1.0 (cos x))

rewrite104.0ms

Algorithm

rewrite-expression-head

Rules

167×	`add-sqr-sqrt`
156×	`times-frac`
143×	`*-un-lft-identity`
104×	`sqrt-prod`
89×	`add-cube-cbrt`
40×	`swap-sqr`
28×	`associate-r` `associate-l`
24×	`distribute-lft-out--`
18×	`add-cbrt-cube` `add-exp-log` `difference-of-squares`
11×	`pow1`
9×	`unswap-sqr`
8×	`associate-/l*` `add-log-exp`
5×	`cbrt-undiv` `div-exp` `div-inv`
4×	`prod-exp` `cbrt-unprod`
3×	`associate-/r*` `flip3--` `flip--`
2×	`sub-neg` `sqrt-div` `diff-log` `associate-/l/`
1×	`pow2` `frac-times` `clear-num` `frac-2neg` `pow-plus` `pow-prod-down` `associate-l/` `associate-r/` `pow-sqr` `*-commutative` `pow-prod-up`

Counts

4 → 206

Calls

4 calls:

14.0ms	(/ (sqrt (- 1.0 (cos x))) x)
65.0ms	(* (/ (sqrt (- 1.0 (cos x))) x) (/ (sqrt (- 1.0 (cos x))) x))
6.0ms	(- 1.0 (cos x))
9.0ms	(- 1.0 (cos x))

series214.0ms

Counts

4 → 12

Calls

4 calls:

94.0ms	(/ (sqrt (- 1.0 (cos x))) x)
62.0ms	(* (/ (sqrt (- 1.0 (cos x))) x) (/ (sqrt (- 1.0 (cos x))) x))
37.0ms	(- 1.0 (cos x))
20.0ms	(- 1.0 (cos x))

simplify3.7s

Counts

218 → 218

Iterations

Useful iterations: done (3.7s)

Iter	Nodes	Cost
0	231	83592
1	724	76565
2	2361	73375
done	5000	71335

prune828.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

localize13.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (/ (- 1.0 (cos x)) x) x)
0.1b	(/ (- 1.0 (cos x)) x)
1.9b	(- 1.0 (cos x))

rewrite48.0ms

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-cbrt-cube` `add-exp-log`
6×	`associate-/r*` `div-inv`
5×	`add-log-exp`
4×	`cbrt-undiv` `div-exp`
3×	`pow1` `div-sub` `associate-/l/`
2×	`clear-num` `frac-2neg` `flip3--` `flip--`
1×	`sub-neg` `diff-log`

Counts

3 → 147

Calls

3 calls:

18.0ms	(/ (/ (- 1.0 (cos x)) x) x)
15.0ms	(/ (- 1.0 (cos x)) x)
5.0ms	(- 1.0 (cos x))

series153.0ms

Counts

3 → 9

Calls

3 calls:

77.0ms	(/ (/ (- 1.0 (cos x)) x) x)
54.0ms	(/ (- 1.0 (cos x)) x)
22.0ms	(- 1.0 (cos x))

simplify1.8s

Counts

156 → 156

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	229	57628
1	530	53855
2	1389	52814
done	5001	52654

prune769.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.1b	(exp (- 1.0 (cos x)))
0.1b	(/ (log (exp (- 1.0 (cos x)))) x)
1.9b	(- 1.0 (cos x))
2.0b	(log (exp (- 1.0 (cos x))))

rewrite107.0ms

Algorithm

rewrite-expression-head

Rules

39×	`add-sqr-sqrt` `*-un-lft-identity`
30×	`exp-prod` `log-pow`
27×	`times-frac`
25×	`add-cube-cbrt`
9×	`pow1` `associate-/l*` `add-log-exp`
7×	`distribute-lft-out--` `difference-of-squares`
6×	`add-cbrt-cube` `add-exp-log`
5×	`log-prod`
4×	`exp-sum`
3×	`associate-/r*` `sub-neg` `exp-diff`
2×	`log-div` `diff-log` `rem-exp-log`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `flip3--` `div-sub` `div-exp` `rem-log-exp` `div-inv` `flip--`

Counts

4 → 103

Calls

4 calls:

22.0ms	(exp (- 1.0 (cos x)))
62.0ms	(/ (log (exp (- 1.0 (cos x)))) x)
5.0ms	(- 1.0 (cos x))
12.0ms	(log (exp (- 1.0 (cos x))))

series201.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(exp (- 1.0 (cos x)))
70.0ms	(/ (log (exp (- 1.0 (cos x)))) x)
23.0ms	(- 1.0 (cos x))
36.0ms	(log (exp (- 1.0 (cos x))))

simplify2.2s

Counts

115 → 115

Iterations

Useful iterations: 3 (903.0ms)

Iter	Nodes	Cost
0	162	40681
1	322	27802
2	806	27022
3	2714	26900
done	5015	26900

prune416.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

regimes130.0ms

Accuracy

98.8% (0.4b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 30.6b

bsearch88.0ms

Steps

Iters	Range		Point
9	5.312512837176874e-08	0.1909160003853501	0.036569739872455896
7	-0.18371106458419734	-0.0075399940621682995	-0.034728198898871646

simplify5.0ms

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	24	807
1	27	807
done	27	807

end0.0ms

sample3.3s

Algorithm

intervals

Results

1.3s	1561×	body	2560	valid
980.0ms	1275×	body	1280	valid
437.0ms	1482×	body	640	valid
218.0ms	933×	body	320	valid
129.0ms	2280×	body	80	valid
118.0ms	469×	body	160	valid