Details

sample112.0ms

Algorithm

intervals

Results

33.0ms	53×	body	1280	valid
20.0ms	136×	body	80	valid
19.0ms	259×	body	80	nan
19.0ms	43×	body	640	valid
5.0ms	16×	body	320	valid
2.0ms	8×	body	160	valid

simplify8.0ms

Counts

1 → 1

Iterations

Iter	Nodes
3	10
2	10
1	9
0	6

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.4b

localize23.0ms

Local error

Found 2 expressions with local error:

2.1b	(- (log (+ N 1)) (log N))
3.3b	(log (+ N 1))

rewrite26.0ms

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-+` `insert-posit16` `distribute-lft-out` `add-log-exp`
1×	`sub-neg` `flip3--` `diff-log` `rem-log-exp` `flip--` `difference-of-squares`

Counts

2 → 43

Calls

2 calls:

17.0ms	(- (log (+ N 1)) (log N))
7.0ms	(log (+ N 1))

series131.0ms

Counts

2 → 6

Calls

2 calls:

53.0ms	(- (log (+ N 1)) (log N))
78.0ms	(log (+ N 1))

simplify1.9s

Counts

49 → 49

Iterations

Iter	Nodes
4	2935
3	1181
2	416
1	194
0	97

prune175.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (+ 1 N) N)
2.5b	(log (/ (+ 1 N) N))

rewrite33.0ms

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` `insert-posit16` `div-inv` `add-log-exp` `associate-/l/`
1×	`cbrt-undiv` `log-div` `clear-num` `frac-2neg` `flip3-+` `log-pow` `flip-+`

Counts

2 → 62

Calls

2 calls:

26.0ms	(/ (+ 1 N) N)
5.0ms	(log (/ (+ 1 N) N))

series125.0ms

Counts

2 → 6

Calls

2 calls:

55.0ms	(/ (+ 1 N) N)
70.0ms	(log (/ (+ 1 N) N))

simplify2.8s

Counts

68 → 68

Iterations

Iter	Nodes
4	4923
3	1427
2	490
1	222
0	102

prune263.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(* N (* N N))
0.3b	(/ 1/2 (* N N))
0.5b	(/ 1/3 (* N (* N N)))
15.8b	(- (/ 1/2 (* N N)) (/ 1/3 (* N (* N N))))

rewrite99.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-cbrt-cube` `add-exp-log`
18×	`pow1`
14×	`add-sqr-sqrt`
13×	`*-un-lft-identity`
9×	`times-frac` `add-cube-cbrt`
7×	`prod-exp` `cbrt-unprod`
6×	`associate-/l*` `add-log-exp`
5×	`cbrt-undiv` `div-exp` `pow-prod-up`
4×	`insert-posit16`
3×	`associate-l` `pow-prod-down`
2×	`clear-num` `associate-/r*` `frac-2neg` `div-inv` `distribute-lft-out--` `difference-of-squares`
1×	`pow2` `sub-neg` `pow-plus` `flip3--` `diff-log` `cube-unmult` `associate-r` `pow-sqr` `*-commutative` `frac-sub` `flip--` `unswap-sqr`

Counts

4 → 89

Calls

4 calls:

15.0ms	(* N (* N N))
7.0ms	(/ 1/2 (* N N))
14.0ms	(/ 1/3 (* N (* N N)))
63.0ms	(- (/ 1/2 (* N N)) (/ 1/3 (* N (* N N))))

series296.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(* N (* N N))
31.0ms	(/ 1/2 (* N N))
62.0ms	(/ 1/3 (* N (* N N)))
145.0ms	(- (/ 1/2 (* N N)) (/ 1/3 (* N (* N N))))

simplify3.2s

Counts

101 → 101

Iterations

Iter	Nodes
3	5102
2	989
1	327
0	137

prune325.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0.0b

regimes40.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 29.5b

bsearch72.0ms

Steps

Iters	Range		Point
10	1.8230705747381016e-09	318690.85562629136	8386.707428118045

simplify5.0ms

Iterations

Iter	Nodes
2	19
1	19
0	17

end0.0ms

sample3.5s

Algorithm

intervals

Results

1.1s	1773×	body	1280	valid
797.0ms	4056×	body	80	valid
548.0ms	8060×	body	80	nan
548.0ms	1232×	body	640	valid
192.0ms	634×	body	320	valid
86.0ms	305×	body	160	valid