Details

sample102.0ms

Algorithm

intervals

Results

44.0ms	40×	body	2560	valid
21.0ms	52×	body	1280	valid
11.0ms	40×	body	640	valid
8.0ms	37×	body	320	valid
4.0ms	67×	body	80	valid
3.0ms	20×	body	160	valid

simplify13.0ms

Counts

1 → 1

Iterations

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

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.3b

localize14.0ms

Local error

Found 2 expressions with local error:

1.7b	(- 1.0 (cos x))
14.3b	(/ (- 1.0 (cos x)) (* x x))

rewrite22.0ms

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:

5.0ms	(- 1.0 (cos x))
16.0ms	(/ (- 1.0 (cos x)) (* x x))

series104.0ms

Counts

2 → 6

Calls

2 calls:

20.0ms	(- 1.0 (cos x))
84.0ms	(/ (- 1.0 (cos x)) (* x x))

simplify1.0s

Counts

48 → 48

Iterations

Iter	Nodes
done	5000
2	1129
1	232
0	88

prune185.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.1b

localize11.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (/ (- 1.0 (cos x)) x) x)
0.1b	(/ (- 1.0 (cos x)) x)
1.7b	(- 1.0 (cos x))

rewrite57.0ms

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:

29.0ms	(/ (/ (- 1.0 (cos x)) x) x)
17.0ms	(/ (- 1.0 (cos x)) x)
5.0ms	(- 1.0 (cos x))

series147.0ms

Counts

3 → 9

Calls

3 calls:

57.0ms	(/ (/ (- 1.0 (cos x)) x) x)
63.0ms	(/ (- 1.0 (cos x)) x)
27.0ms	(- 1.0 (cos x))

simplify956.0ms

Counts

156 → 156

Iterations

Iter	Nodes
done	5001
2	2463
1	549
0	229

prune719.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.1b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ 1 (/ x (- 1.0 (cos x)))) x)
0.1b	(/ 1 (/ x (- 1.0 (cos x))))
0.2b	(/ x (- 1.0 (cos x)))
1.7b	(- 1.0 (cos x))

rewrite149.0ms

Algorithm

rewrite-expression-head

Rules

774×	`times-frac`
443×	`add-sqr-sqrt` `*-un-lft-identity`
337×	`add-cube-cbrt`
74×	`associate-/l*`
53×	`distribute-lft-out--` `difference-of-squares`
39×	`associate-/r/`
36×	`add-exp-log`
29×	`associate-/r*`
23×	`div-inv`
22×	`div-exp`
20×	`add-cbrt-cube`
18×	`flip3--` `flip--`
10×	`cbrt-undiv`
6×	`add-log-exp`
5×	`pow1`
4×	`rec-exp` `1-exp`
3×	`clear-num` `frac-2neg`
1×	`sub-neg` `diff-log` `pow-flip` `inv-pow` `associate-/l/`

Counts

4 → 455

Calls

4 calls:

56.0ms	(/ (/ 1 (/ x (- 1.0 (cos x)))) x)
26.0ms	(/ 1 (/ x (- 1.0 (cos x))))
8.0ms	(/ x (- 1.0 (cos x)))
5.0ms	(- 1.0 (cos x))

series244.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(/ (/ 1 (/ x (- 1.0 (cos x)))) x)
74.0ms	(/ 1 (/ x (- 1.0 (cos x))))
77.0ms	(/ x (- 1.0 (cos x)))
31.0ms	(- 1.0 (cos x))

simplify1.3s

Counts

467 → 467

Iterations

Iter	Nodes
done	5001
1	1830
0	643

prune1.2s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.1b

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ 1 (/ x (- 1.0 (cos x)))) x)
0.1b	(/ 1 (/ x (- 1.0 (cos x))))
0.2b	(/ x (- 1.0 (cos x)))
1.7b	(- 1.0 (cos x))

rewrite116.0ms

Algorithm

rewrite-expression-head

Rules

774×	`times-frac`
443×	`add-sqr-sqrt` `*-un-lft-identity`
337×	`add-cube-cbrt`
74×	`associate-/l*`
53×	`distribute-lft-out--` `difference-of-squares`
39×	`associate-/r/`
36×	`add-exp-log`
29×	`associate-/r*`
23×	`div-inv`
22×	`div-exp`
20×	`add-cbrt-cube`
18×	`flip3--` `flip--`
10×	`cbrt-undiv`
6×	`add-log-exp`
5×	`pow1`
4×	`rec-exp` `1-exp`
3×	`clear-num` `frac-2neg`
1×	`sub-neg` `diff-log` `pow-flip` `inv-pow` `associate-/l/`

Counts

4 → 455

Calls

4 calls:

52.0ms	(/ (/ 1 (/ x (- 1.0 (cos x)))) x)
14.0ms	(/ 1 (/ x (- 1.0 (cos x))))
13.0ms	(/ x (- 1.0 (cos x)))
8.0ms	(- 1.0 (cos x))

series236.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(/ (/ 1 (/ x (- 1.0 (cos x)))) x)
63.0ms	(/ 1 (/ x (- 1.0 (cos x))))
52.0ms	(/ x (- 1.0 (cos x)))
39.0ms	(- 1.0 (cos x))

simplify1.3s

Counts

467 → 467

Iterations

Iter	Nodes
done	5001
1	1830
0	643

prune1.2s

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 0.1b

regimes141.0ms

Accuracy

99.2% (0.2b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 30.6b

bsearch142.0ms

Steps

Iters	Range		Point
7	0.00012587414935880383	0.030359728269424062	0.02891102314655495
11	-14746478108.679678	-8.433739504313006e-14	-0.02898551851456167

simplify8.0ms

Iterations

Iter	Nodes
done	34
2	34
1	33
0	26

end0.0ms

sample2.9s

Algorithm

intervals

Results

1.4s	1570×	body	2560	valid
519.0ms	1253×	body	1280	valid
361.0ms	1477×	body	640	valid
183.0ms	967×	body	320	valid
108.0ms	2260×	body	80	valid
54.0ms	473×	body	160	valid