Details

sample63.0ms

Algorithm

intervals

Results

19.0ms	55×	body	1280	valid
9.0ms	43×	body	640	valid
8.0ms	248×	body	80	nan
7.0ms	124×	body	80	valid
4.0ms	23×	body	320	valid
1.0ms	11×	body	160	valid

simplify8.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	222
1	9	222
2	10	222
done	10	222

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.6b

localize18.0ms

Local error

Found 2 expressions with local error:

2.4b	(log (+ N 1.0))
2.7b	(- (log (+ N 1.0)) (log N))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

22×	`*-un-lft-identity`
16×	`add-sqr-sqrt` `pow1` `prod-diff`
14×	`log-pow` `add-cube-cbrt`
11×	`log-prod`
4×	`log-div` `fma-neg` `associate--l+` `distribute-lft-out--`
3×	`add-exp-log` `associate--r+`
2×	`associate--l-` `expm1-log1p-u` `flip3-+` `add-cbrt-cube` `flip-+` `log1p-expm1-u` `distribute-lft-out` `add-log-exp`
1×	`sub-neg` `flip3--` `diff-log` `rem-log-exp` `flip--` `difference-of-squares`

Counts

2 → 65

Calls

2 calls:

16.0ms	(log (+ N 1.0))
12.0ms	(- (log (+ N 1.0)) (log N))

series164.0ms

Counts

2 → 6

Calls

2 calls:

42.0ms	(log (+ N 1.0))
122.0ms	(- (log (+ N 1.0)) (log N))

simplify3.0s

Counts

71 → 71

Iterations

Useful iterations: done (2.9s)

Iter	Nodes	Cost
0	127	27370
1	286	23011
2	708	19772
3	2040	19411
done	5001	16861

prune252.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (+ N 1.0) N)
2.6b	(log (/ (+ N 1.0) N))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

33×	`*-un-lft-identity`
24×	`times-frac`
19×	`add-sqr-sqrt` `add-cube-cbrt`
16×	`log-prod`
7×	`add-exp-log` `distribute-lft-out`
4×	`add-cbrt-cube` `associate-/l*`
3×	`pow1` `associate-/r*`
2×	`expm1-log1p-u` `div-exp` `rem-log-exp` `log1p-expm1-u` `div-inv` `add-log-exp` `associate-/l/`
1×	`cbrt-undiv` `log-div` `clear-num` `frac-2neg` `flip3-+` `log-pow` `flip-+`

Counts

2 → 64

Calls

2 calls:

26.0ms	(/ (+ N 1.0) N)
9.0ms	(log (/ (+ N 1.0) N))

series193.0ms

Counts

2 → 6

Calls

2 calls:

70.0ms	(/ (+ N 1.0) N)
123.0ms	(log (/ (+ N 1.0) N))

simplify2.6s

Counts

70 → 70

Iterations

Useful iterations: 2 (232.0ms)

Iter	Nodes	Cost
0	112	18709
1	252	16599
2	629	16217
3	2337	16217
done	5001	16217

prune316.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize50.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (/ (+ N 1.0) N))
0.3b	(cbrt (/ (+ N 1.0) N))
0.3b	(cbrt (/ (+ N 1.0) N))
2.6b	(log (* (* (cbrt (/ (+ N 1.0) N)) (cbrt (/ (+ N 1.0) N))) (cbrt (/ (+ N 1.0) N))))

rewrite126.0ms

Algorithm

rewrite-expression-head

Rules

48×	`cbrt-prod`
46×	`*-un-lft-identity`
36×	`times-frac`
28×	`add-sqr-sqrt` `add-cube-cbrt`
24×	`pow1`
15×	`cbrt-div` `log-pow`
12×	`pow1/3`
10×	`add-exp-log`
9×	`pow-prod-up` `distribute-lft-out`
7×	`log-div`
6×	`pow-plus`
5×	`frac-times` `pow-prod-down` `associate-*l/`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`rem-log-exp` `prod-exp` `associate-*r/` `pow-sqr` `div-inv`
2×	`pow2`
1×	`log-prod` `pow3`

Counts

4 → 116

Calls

4 calls:

4.0ms	(cbrt (/ (+ N 1.0) N))
5.0ms	(cbrt (/ (+ N 1.0) N))
4.0ms	(cbrt (/ (+ N 1.0) N))
107.0ms	(log (* (* (cbrt (/ (+ N 1.0) N)) (cbrt (/ (+ N 1.0) N))) (cbrt (/ (+ N 1.0) N))))

series680.0ms

Counts

4 → 12

Calls

4 calls:

171.0ms	(cbrt (/ (+ N 1.0) N))
155.0ms	(cbrt (/ (+ N 1.0) N))
189.0ms	(cbrt (/ (+ N 1.0) N))
164.0ms	(log (* (* (cbrt (/ (+ N 1.0) N)) (cbrt (/ (+ N 1.0) N))) (cbrt (/ (+ N 1.0) N))))

simplify2.7s

Counts

128 → 128

Iterations

Useful iterations: 3 (1.1s)

Iter	Nodes	Cost
0	149	48937
1	305	43389
2	819	42682
3	3083	39728
done	5002	39728

prune670.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.1b	(* N (* N N))
0.1b	(/ 0.3333333333333333 (* N (* N N)))
0.3b	(/ 0.5 (* N N))
13.2b	(+ (/ 0.3333333333333333 (* N (* N N))) (- (/ 1.0 N) (/ 0.5 (* N N))))

rewrite212.0ms

Algorithm

rewrite-expression-head

Rules

111×	`times-frac`
93×	`associate-+r+`
91×	`*-un-lft-identity` `prod-diff`
87×	`add-sqr-sqrt`
86×	`add-cube-cbrt`
23×	`add-cbrt-cube` `add-exp-log` `div-inv`
18×	`pow1`
9×	`add-log-exp`
7×	`fma-def` `prod-exp` `cbrt-unprod`
6×	`associate-/l*`
5×	`cbrt-undiv` `div-exp` `pow-prod-up`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`associate-l` `pow-prod-down` `frac-add`
2×	`clear-num` `associate-/r*` `sum-log` `frac-2neg` `distribute-lft-out`
1×	`pow2` `+-commutative` `associate-+r-` `sub-neg` `flip3-+` `pow-plus` `flip3--` `diff-log` `cube-unmult` `associate-r` `pow-sqr` `*-commutative` `frac-sub` `flip-+` `flip--` `distribute-lft-out--` `unswap-sqr`

Counts

4 → 194

Calls

4 calls:

17.0ms	(* N (* N N))
13.0ms	(/ 0.3333333333333333 (* N (* N N)))
6.0ms	(/ 0.5 (* N N))
159.0ms	(+ (/ 0.3333333333333333 (* N (* N N))) (- (/ 1.0 N) (/ 0.5 (* N N))))

series206.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(* N (* N N))
57.0ms	(/ 0.3333333333333333 (* N (* N N)))
43.0ms	(/ 0.5 (* N N))
56.0ms	(+ (/ 0.3333333333333333 (* N (* N N))) (- (/ 1.0 N) (/ 0.5 (* N N))))

simplify3.3s

Counts

206 → 206

Iterations

Useful iterations: done (3.3s)

Iter	Nodes	Cost
0	386	75554
1	926	69659
2	2614	60597
done	5004	59092

prune908.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

regimes39.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 29.4b

bsearch60.0ms

Steps

Iters	Range		Point
9	0.1909160003853501	166131308.15705827	4593.354257030818

simplify7.0ms

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	20	725
1	24	725
done	24	725

end0.0ms

sample2.6s

Algorithm

intervals

Results

783.0ms	7971×	body	80	nan
687.0ms	1715×	body	1280	valid
375.0ms	1248×	body	640	valid
291.0ms	4082×	body	80	valid
193.0ms	665×	body	320	valid
28.0ms	290×	body	160	valid