Details

sample71.0ms

Algorithm

intervals

Results

23.0ms	55×	body	1280	valid
11.0ms	43×	body	640	valid
10.0ms	248×	body	80	nan
8.0ms	124×	body	80	valid
4.0ms	23×	body	320	valid
1.0ms	11×	body	160	valid

simplify4.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.6b

localize44.0ms

Local error

Found 2 expressions with local error:

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

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

13×	`*-un-lft-identity`
11×	`log-prod`
7×	`add-sqr-sqrt` `pow1`
5×	`log-pow` `add-cube-cbrt`
4×	`log-div` `associate--l+` `distribute-lft-out--`
3×	`add-exp-log` `associate--r+`
2×	`associate--l-` `flip3-+` `add-cbrt-cube` `flip-+` `distribute-lft-out` `add-log-exp`
1×	`sub-neg` `flip3--` `diff-log` `rem-log-exp` `flip--` `difference-of-squares`

Counts

2 → 41

Calls

2 calls:

6.0ms	(log (+ N 1.0))
18.0ms	(- (log (+ N 1.0)) (log N))

series158.0ms

Counts

2 → 6

Calls

2 calls:

46.0ms	(log (+ N 1.0))
112.0ms	(- (log (+ N 1.0)) (log N))

simplify1.6s

Counts

47 → 47

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	101	15630
1	213	12900
2	530	12195
3	1557	12195
done	5000	12085

prune242.0ms

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))

rewrite36.0ms

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×	`div-exp` `rem-log-exp` `div-inv` `add-log-exp` `associate-/l/`
1×	`cbrt-undiv` `log-div` `clear-num` `frac-2neg` `flip3-+` `log-pow` `flip-+`

Counts

2 → 60

Calls

2 calls:

24.0ms	(/ (+ N 1.0) N)
8.0ms	(log (/ (+ N 1.0) N))

series192.0ms

Counts

2 → 6

Calls

2 calls:

72.0ms	(/ (+ N 1.0) N)
120.0ms	(log (/ (+ N 1.0) N))

simplify2.0s

Counts

66 → 66

Iterations

Useful iterations: 2 (173.0ms)

Iter	Nodes	Cost
0	108	17921
1	243	15986
2	619	15504
3	2289	15504
done	5001	15504

prune276.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize36.0ms

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))))

rewrite95.0ms

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×	`add-cbrt-cube` `add-log-exp`
3×	`rem-log-exp` `prod-exp` `associate-*r/` `pow-sqr` `div-inv`
2×	`pow2`
1×	`log-prod` `pow3`

Counts

4 → 108

Calls

4 calls:

4.0ms	(cbrt (/ (+ N 1.0) N))
8.0ms	(cbrt (/ (+ N 1.0) N))
9.0ms	(cbrt (/ (+ N 1.0) N))
70.0ms	(log (* (* (cbrt (/ (+ N 1.0) N)) (cbrt (/ (+ N 1.0) N))) (cbrt (/ (+ N 1.0) N))))

series648.0ms

Counts

4 → 12

Calls

4 calls:

190.0ms	(cbrt (/ (+ N 1.0) N))
151.0ms	(cbrt (/ (+ N 1.0) N))
178.0ms	(cbrt (/ (+ N 1.0) N))
129.0ms	(log (* (* (cbrt (/ (+ N 1.0) N)) (cbrt (/ (+ N 1.0) N))) (cbrt (/ (+ N 1.0) N))))

simplify2.8s

Counts

120 → 120

Iterations

Useful iterations: 3 (1.1s)

Iter	Nodes	Cost
0	145	46701
1	295	41528
2	783	40646
3	2938	38087
done	5005	38087

prune613.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize39.0ms

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))))

rewrite159.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-cbrt-cube` `add-exp-log`
18×	`pow1`
14×	`*-un-lft-identity`
10×	`add-sqr-sqrt`
9×	`add-cube-cbrt` `add-log-exp`
7×	`prod-exp` `cbrt-unprod`
6×	`times-frac` `associate-/l*`
5×	`cbrt-undiv` `div-exp` `pow-prod-up`
3×	`associate-l` `pow-prod-down` `frac-add`
2×	`associate-+r+` `clear-num` `associate-/r*` `sum-log` `frac-2neg` `div-inv` `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 → 88

Calls

4 calls:

13.0ms	(* N (* N N))
20.0ms	(/ 0.3333333333333333 (* N (* N N)))
11.0ms	(/ 0.5 (* N N))
112.0ms	(+ (/ 0.3333333333333333 (* N (* N N))) (- (/ 1.0 N) (/ 0.5 (* N N))))

series195.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(* N (* N N))
64.0ms	(/ 0.3333333333333333 (* N (* N N)))
40.0ms	(/ 0.5 (* N N))
40.0ms	(+ (/ 0.3333333333333333 (* N (* N N))) (- (/ 1.0 N) (/ 0.5 (* N N))))

simplify2.4s

Counts

100 → 100

Iterations

Useful iterations: done (2.4s)

Iter	Nodes	Cost
0	159	23980
1	440	20061
2	1903	18951
done	5001	18711

prune375.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

regimes47.0ms

Accuracy

100% (0.0b remaining)

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

bsearch67.0ms

Steps

Iters	Range		Point
9	0.1909160003853501	166131308.15705827	4593.354257030818

simplify8.0ms

Iterations

Useful iterations: 0 (3.0ms)

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

end0.0ms

sample2.9s

Algorithm

intervals

Results

756.0ms	1715×	body	1280	valid
516.0ms	7971×	body	80	nan
481.0ms	290×	body	160	valid
396.0ms	1248×	body	640	valid
300.0ms	4082×	body	80	valid
163.0ms	665×	body	320	valid