Details

sample108.0ms

Algorithm

intervals

Results

57.0ms	67×	body	1280	valid
20.0ms	52×	body	640	valid
6.0ms	29×	body	320	valid
5.0ms	96×	body	80	valid
2.0ms	81×	body	80	nan
1.0ms	12×	body	160	valid

simplify3.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	4
1	5	4
done	5	4

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.9b

localize8.0ms

Local error

Found 1 expressions with local error:

4.8b	(log (+ 1.0 x))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

4×	`log-prod` `*-un-lft-identity`
2×	`pow1` `add-exp-log` `add-sqr-sqrt` `add-cube-cbrt` `log-div`
1×	`flip3-+` `rem-log-exp` `log-pow` `add-cbrt-cube` `flip-+` `distribute-lft-out` `add-log-exp`

Counts

1 → 15

Calls

1 calls:

9.0ms

(log (+ 1.0 x))

series67.0ms

Counts

1 → 3

Calls

1 calls:

67.0ms

(log (+ 1.0 x))

simplify768.0ms

Counts

18 → 18

Iterations

Useful iterations: done (767.0ms)

Iter	Nodes	Cost
0	58	178
1	123	171
2	378	151
3	1338	151
done	5000	146

prune53.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

localize12.0ms

Local error

Found 2 expressions with local error:

0.0b	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
0.0b	(- (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2))))

rewrite133.0ms

Algorithm

rewrite-expression-head

Rules

80×	`times-frac`
70×	`add-sqr-sqrt`
68×	`associate-r`
56×	`unpow-prod-down`
36×	`add-cube-cbrt` `*-un-lft-identity`
25×	`add-exp-log`
24×	`unpow2` `sqr-pow`
17×	`unswap-sqr`
10×	`prod-exp`
9×	`div-exp`
7×	`add-cbrt-cube`
6×	`pow-to-exp` `pow-exp` `add-log-exp`
4×	`pow1`
3×	`associate-r/` `associate-l*`
2×	`diff-log` `frac-sub` `cbrt-unprod`
1×	`cbrt-undiv` `sub-neg` `flip3--` `flip3-+` `pow-prod-down` `associate--l+` `sum-log` `*-commutative` `flip--` `flip-+` `div-inv`

Counts

2 → 126

Calls

2 calls:

47.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
79.0ms	(- (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2))))

series133.0ms

Counts

2 → 6

Calls

2 calls:

88.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
45.0ms	(- (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2))))

simplify2.2s

Counts

132 → 132

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	268	1979
1	761	1743
2	3646	1459
done	5001	1455

prune485.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.1b

localize12.0ms

Local error

Found 3 expressions with local error:

0.3b	(cbrt (pow (log (+ 1.0 x)) 3))
0.3b	(pow (log (+ 1.0 x)) 3)
4.8b	(log (+ 1.0 x))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

14×	`cbrt-prod`
12×	`*-un-lft-identity`
10×	`add-sqr-sqrt` `add-cube-cbrt`
9×	`pow1`
8×	`unpow-prod-down` `cube-prod`
5×	`add-exp-log` `log-pow`
4×	`log-prod` `add-cbrt-cube`
3×	`pow-unpow` `add-log-exp`
2×	`cube-mult` `log-div` `unpow3` `sqr-pow`
1×	`pow-to-exp` `pow-pow` `flip3-+` `pow1/3` `rem-log-exp` `pow-exp` `rem-cbrt-cube` `flip-+` `distribute-lft-out` `rem-cube-cbrt`

Counts

3 → 63

Calls

3 calls:

3.0ms	(cbrt (pow (log (+ 1.0 x)) 3))
3.0ms	(pow (log (+ 1.0 x)) 3)
5.0ms	(log (+ 1.0 x))

series243.0ms

Counts

3 → 9

Calls

3 calls:

73.0ms	(cbrt (pow (log (+ 1.0 x)) 3))
116.0ms	(pow (log (+ 1.0 x)) 3)
54.0ms	(log (+ 1.0 x))

simplify1.7s

Counts

72 → 72

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	158	981
1	448	814
2	2254	736
done	5000	735

prune181.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0.1b

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cbrt (log (+ 1.0 x))) (cbrt (log (+ 1.0 x))))
4.8b	(log (+ 1.0 x))
4.8b	(log (+ 1.0 x))
4.8b	(log (+ 1.0 x))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

24×	`cbrt-prod`
23×	`add-sqr-sqrt` `*-un-lft-identity`
20×	`pow1`
15×	`add-cube-cbrt`
12×	`log-prod`
9×	`add-exp-log` `swap-sqr` `log-pow`
7×	`associate-r` `associate-l`
6×	`log-div` `pow1/3`
4×	`add-cbrt-cube` `add-log-exp` `unswap-sqr`
3×	`flip3-+` `rem-log-exp` `flip-+` `distribute-lft-out`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 90

Calls

4 calls:

22.0ms	(* (cbrt (log (+ 1.0 x))) (cbrt (log (+ 1.0 x))))
5.0ms	(log (+ 1.0 x))
5.0ms	(log (+ 1.0 x))
5.0ms	(log (+ 1.0 x))

series499.0ms

Counts

4 → 12

Calls

4 calls:

272.0ms	(* (cbrt (log (+ 1.0 x))) (cbrt (log (+ 1.0 x))))
59.0ms	(log (+ 1.0 x))
85.0ms	(log (+ 1.0 x))
83.0ms	(log (+ 1.0 x))

simplify1.1s

Counts

102 → 102

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	175	1501
1	474	1370
2	2008	1247
done	5001	1154

prune385.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0.1b

regimes164.0ms

Accuracy

98.9% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 21.5b

bsearch2.0ms

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	26
1	21	26
done	21	26

end0.0ms

sample3.3s

Algorithm

intervals

Results

2.0s	2278×	body	1280	valid
584.0ms	1691×	body	640	valid
136.0ms	807×	body	320	valid
127.0ms	2804×	body	80	valid
66.0ms	2645×	body	80	nan
42.0ms	420×	body	160	valid