Details

sample114.0ms

Algorithm

intervals

Results

48.0ms	48×	body	2560	valid
26.0ms	52×	body	1280	valid
11.0ms	35×	body	640	valid
8.0ms	32×	body	320	valid
5.0ms	72×	body	80	valid
3.0ms	17×	body	160	valid

simplify19.0ms

Counts

1 → 1

Iterations

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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.5b

localize10.0ms

Local error

Found 2 expressions with local error:

2.1b	(- 1.0 (cos x))
15.8b	(/ (- 1.0 (cos x)) (* x x))

rewrite53.0ms

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:

8.0ms	(- 1.0 (cos x))
22.0ms	(/ (- 1.0 (cos x)) (* x x))

series104.0ms

Counts

2 → 6

Calls

2 calls:

27.0ms	(- 1.0 (cos x))
77.0ms	(/ (- 1.0 (cos x)) (* x x))

simplify1.7s

Counts

48 → 48

Iterations

Iter	Nodes
done	5074
3	2415
2	651
1	217
0	88

prune239.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize35.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (* (* x x) 1/720) 1/24)
0.1b	(* (* x x) (- (* (* x x) 1/720) 1/24))
0.2b	(* (* x x) 1/720)

rewrite150.0ms

Algorithm

rewrite-expression-head

Rules

13×	`pow1` `add-cbrt-cube` `add-exp-log`
7×	`add-sqr-sqrt`
6×	`associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod`
5×	`*-un-lft-identity` `add-cube-cbrt` `add-log-exp`
3×	`sub-neg`
2×	`distribute-rgt-in` `distribute-lft-in` `flip3--` `associate-l` `associate-r/` `-commutative` `flip--` `unswap-sqr`
1×	`diff-log`

Counts

3 → 56

Calls

3 calls:

29.0ms	(- (* (* x x) 1/720) 1/24)
91.0ms	(* (* x x) (- (* (* x x) 1/720) 1/24))
28.0ms	(* (* x x) 1/720)

series255.0ms

Counts

3 → 9

Calls

3 calls:

100.0ms	(- (* (* x x) 1/720) 1/24)
126.0ms	(* (* x x) (- (* (* x x) 1/720) 1/24))
29.0ms	(* (* x x) 1/720)

simplify2.9s

Counts

65 → 65

Iterations

Iter	Nodes
done	5003
3	3314
2	815
1	251
0	87

prune201.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.1b

localize29.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (- 1.0 (cos x)))
2.1b	(- 1.0 (cos x))
2.1b	(- 1.0 (cos x))
2.1b	(- 1.0 (cos x))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt` `*-un-lft-identity`
10×	`add-log-exp`
5×	`cbrt-prod` `add-cube-cbrt`
4×	`pow1` `flip3--` `add-cbrt-cube` `add-exp-log` `flip--` `distribute-lft-out--` `difference-of-squares`
3×	`sub-neg` `diff-log`
2×	`cbrt-div`
1×	`pow1/3`

Counts

4 → 57

Calls

4 calls:

3.0ms	(cbrt (- 1.0 (cos x)))
4.0ms	(- 1.0 (cos x))
4.0ms	(- 1.0 (cos x))
5.0ms	(- 1.0 (cos x))

series223.0ms

Counts

4 → 12

Calls

4 calls:

160.0ms	(cbrt (- 1.0 (cos x)))
20.0ms	(- 1.0 (cos x))
23.0ms	(- 1.0 (cos x))
20.0ms	(- 1.0 (cos x))

simplify2.1s

Counts

69 → 69

Iterations

Iter	Nodes
done	5000
4	3191
3	900
2	345
1	155
0	76

prune330.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.1b

localize38.0ms

Local error

Found 4 expressions with local error:

2.1b	(- 1.0 (cos x))
2.1b	(- 1.0 (cos x))
2.1b	(- 1.0 (cos x))
2.2b	(log (exp (- 1.0 (cos x))))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt` `*-un-lft-identity`
10×	`add-log-exp`
6×	`log-pow` `add-cube-cbrt`
5×	`pow1` `log-prod` `exp-prod`
4×	`sub-neg` `add-cbrt-cube` `add-exp-log` `distribute-lft-out--` `difference-of-squares`
3×	`flip3--` `diff-log` `flip--`
2×	`exp-sum`
1×	`log-div` `exp-diff` `rem-log-exp`

Counts

4 → 62

Calls

4 calls:

4.0ms	(- 1.0 (cos x))
5.0ms	(- 1.0 (cos x))
4.0ms	(- 1.0 (cos x))
12.0ms	(log (exp (- 1.0 (cos x))))

series82.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(- 1.0 (cos x))
20.0ms	(- 1.0 (cos x))
22.0ms	(- 1.0 (cos x))
20.0ms	(log (exp (- 1.0 (cos x))))

simplify2.3s

Counts

74 → 74

Iterations

Iter	Nodes
done	5000
5	4003
4	1410
3	607
2	276
1	140
0	72

prune384.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.1b

regimes200.0ms

Accuracy

98.6% (0.5b remaining)

Error of 0.6b against oracle of 0.1b and baseline of 31.9b

bsearch108.0ms

Steps

Iters	Range		Point
8	0.02586244036059231	44.35744796693956	0.02880979041531034
10	-733100.9210806559	-4.034181863829644e-08	-0.03224345637809938

simplify10.0ms

Iterations

Iter	Nodes
done	37
1	37
0	27

end0.0ms

sample2.8s

Algorithm

intervals

Results

1.1s	1592×	body	2560	valid
831.0ms	1217×	body	1280	valid
349.0ms	1470×	body	640	valid
176.0ms	945×	body	320	valid
168.0ms	2285×	body	80	valid
55.0ms	491×	body	160	valid