Details

sample78.0ms

Algorithm

intervals

Results

25.0ms	62×	body	1280	valid
14.0ms	272×	body	80	nan
11.0ms	40×	body	640	valid
10.0ms	123×	body	80	valid
4.0ms	19×	body	320	valid
1.0ms	12×	body	160	valid

simplify8.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	12
2	12
1	11
0	6

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.1b

localize16.0ms

Local error

Found 2 expressions with local error:

2.6b	(log (+ N 1))
4.4b	(- (log (+ N 1)) (log N))

rewrite13.0ms

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:

3.0ms	(log (+ N 1))
10.0ms	(- (log (+ N 1)) (log N))

series103.0ms

Counts

2 → 6

Calls

2 calls:

22.0ms	(log (+ N 1))
82.0ms	(- (log (+ N 1)) (log N))

simplify1.2s

Counts

49 → 49

Iterations

Iter	Nodes
done	5000
3	2367
2	571
1	211
0	97

prune215.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize23.0ms

Local error

Found 4 expressions with local error:

0.1b	(* N (* N N))
0.4b	(/ 1/3 (* N (* N N)))
0.7b	(/ 1/2 (* N N))
11.4b	(- (/ 1/3 (* N (* N N))) (/ 1/2 (* N N)))

rewrite112.0ms

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:

13.0ms	(* N (* N N))
14.0ms	(/ 1/3 (* N (* N N)))
6.0ms	(/ 1/2 (* N N))
78.0ms	(- (/ 1/3 (* N (* N N))) (/ 1/2 (* N N)))

series297.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(* N (* N N))
58.0ms	(/ 1/3 (* N (* N N)))
47.0ms	(/ 1/2 (* N N))
137.0ms	(- (/ 1/3 (* N (* N N))) (/ 1/2 (* N N)))

simplify1.4s

Counts

101 → 101

Iterations

Iter	Nodes
done	5000
2	2212
1	385
0	137

prune316.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.1b

localize23.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (+ N 1) N)
4.8b	(log (/ (+ N 1) N))

rewrite35.0ms

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	(/ (+ N 1) N)
7.0ms	(log (/ (+ N 1) N))

series118.0ms

Counts

2 → 6

Calls

2 calls:

67.0ms	(/ (+ N 1) N)
51.0ms	(log (/ (+ N 1) N))

simplify839.0ms

Counts

68 → 68

Iterations

Iter	Nodes
done	5001
2	987
1	234
0	102

prune220.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (/ (+ N 1) N))
0.1b	(sqrt (/ (+ N 1) N))
4.6b	(log (sqrt (/ (+ N 1) N)))
4.6b	(log (sqrt (/ (+ N 1) N)))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

64×	`sqrt-prod`
62×	`*-un-lft-identity`
50×	`times-frac`
44×	`add-sqr-sqrt`
38×	`log-prod` `add-cube-cbrt`
12×	`distribute-lft-out`
10×	`pow1`
6×	`add-exp-log` `log-pow`
4×	`rem-sqrt-square` `sqrt-pow1` `add-cbrt-cube` `pow1/2` `sqrt-div` `insert-posit16` `div-inv` `add-log-exp`
2×	`log-div` `rem-log-exp`

Counts

4 → 122

Calls

4 calls:

11.0ms	(sqrt (/ (+ N 1) N))
11.0ms	(sqrt (/ (+ N 1) N))
8.0ms	(log (sqrt (/ (+ N 1) N)))
8.0ms	(log (sqrt (/ (+ N 1) N)))

series346.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(sqrt (/ (+ N 1) N))
58.0ms	(sqrt (/ (+ N 1) N))
103.0ms	(log (sqrt (/ (+ N 1) N)))
128.0ms	(log (sqrt (/ (+ N 1) N)))

simplify1.0s

Counts

134 → 134

Iterations

Iter	Nodes
done	5001
3	1444
2	449
1	202
0	124

prune595.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.1b

regimes59.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 30.6b

bsearch43.0ms

Steps

Iters	Range		Point
6	3173.18146809654	23716.851585869685	11332.770353358372

simplify5.0ms

Iterations

Iter	Nodes
done	24
1	24
0	19

end0.0ms

sample3.5s

Algorithm

intervals

Results

1.4s	1790×	body	1280	valid
563.0ms	8083×	body	80	nan
510.0ms	1270×	body	640	valid
482.0ms	4031×	body	80	valid
225.0ms	606×	body	320	valid
57.0ms	303×	body	160	valid