Details

sample113.0ms

Algorithm

intervals

Results

33.0ms	297×	body	80	nan
32.0ms	61×	body	1280	valid
12.0ms	133×	body	80	valid
9.0ms	29×	body	640	valid
4.0ms	20×	body	320	valid
2.0ms	13×	body	160	valid

simplify1.0ms

Counts: 1 → 1

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.7b

localize7.0ms

Local error

Found 2 expressions with local error:

2.7b	(log (+ N 1.0))
3.9b	(- (log (+ N 1.0)) (log N))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

13×	`*-un-lft-identity`
11×	`log-prod`
7×	`pow1` `add-sqr-sqrt`
5×	`add-cube-cbrt` `log-pow`
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:

8.0ms	(log (+ N 1.0))
12.0ms	(- (log (+ N 1.0)) (log N))

series231.0ms

Counts

2 → 6

Calls

2 calls:

87.0ms	(log (+ N 1.0))
144.0ms	(- (log (+ N 1.0)) (log N))

simplify129.0ms

Counts: 47 → 47

prune159.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (+ N 1.0) N)
4.1b	(log (/ (+ N 1.0) 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` `div-inv` `associate-/l/` `add-log-exp`
1×	`cbrt-undiv` `log-div` `frac-2neg` `flip3-+` `clear-num` `log-pow` `flip-+`

Counts

2 → 60

Calls

2 calls:

22.0ms	(/ (+ N 1.0) N)
6.0ms	(log (/ (+ N 1.0) N))

series172.0ms

Counts

2 → 6

Calls

2 calls:

63.0ms	(/ (+ N 1.0) N)
109.0ms	(log (/ (+ N 1.0) N))

simplify50.0ms

Counts: 66 → 66

prune202.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sqrt (+ N 1.0)) (sqrt N))
0.1b	(/ (sqrt (+ N 1.0)) (sqrt N))
3.9b	(log (/ (sqrt (+ N 1.0)) (sqrt N)))
3.9b	(log (/ (sqrt (+ N 1.0)) (sqrt N)))

rewrite84.0ms

Algorithm

rewrite-expression-head

Rules

194×	`sqrt-prod`
170×	`*-un-lft-identity`
168×	`times-frac`
118×	`add-sqr-sqrt` `add-cube-cbrt`
92×	`log-prod`
26×	`distribute-lft-out`
14×	`add-exp-log` `associate-/l*`
12×	`associate-/r*`
8×	`add-cbrt-cube`
6×	`pow1`
4×	`sqrt-div` `div-exp` `rem-log-exp` `div-inv` `associate-/l/` `add-log-exp`
2×	`cbrt-undiv` `log-div` `sqrt-undiv` `frac-2neg` `flip3-+` `clear-num` `log-pow` `flip-+`

Counts

4 → 254

Calls

4 calls:

28.0ms	(/ (sqrt (+ N 1.0)) (sqrt N))
16.0ms	(/ (sqrt (+ N 1.0)) (sqrt N))
8.0ms	(log (/ (sqrt (+ N 1.0)) (sqrt N)))
9.0ms	(log (/ (sqrt (+ N 1.0)) (sqrt N)))

series577.0ms

Counts

4 → 12

Calls

4 calls:

98.0ms	(/ (sqrt (+ N 1.0)) (sqrt N))
91.0ms	(/ (sqrt (+ N 1.0)) (sqrt N))
205.0ms	(log (/ (sqrt (+ N 1.0)) (sqrt N)))
184.0ms	(log (/ (sqrt (+ N 1.0)) (sqrt N)))

simplify84.0ms

Counts: 266 → 266

prune863.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt N)
0.6b	(cbrt N)
2.7b	(log (+ N 1.0))
21.4b	(- (- (log (+ N 1.0)) (* 2 (log (cbrt N)))) (log (cbrt N)))

rewrite68.0ms

Algorithm

rewrite-expression-head

Rules

17×	`*-un-lft-identity`
14×	`log-prod`
12×	`add-sqr-sqrt`
10×	`add-cube-cbrt` `associate--l+`
9×	`cbrt-prod`
6×	`pow1` `associate--r+` `add-log-exp`
5×	`add-exp-log`
4×	`add-cbrt-cube`
3×	`diff-log`
2×	`sub-neg` `log-div` `pow1/3` `log-pow` `distribute-lft-out` `distribute-lft-out--`
1×	`associate--l-` `flip3--` `flip3-+` `rem-log-exp` `flip--` `flip-+` `difference-of-squares`

Counts

4 → 66

Calls

4 calls:

1.0ms	(cbrt N)
1.0ms	(cbrt N)
5.0ms	(log (+ N 1.0))
60.0ms	(- (- (log (+ N 1.0)) (* 2 (log (cbrt N)))) (log (cbrt N)))

series902.0ms

Counts

4 → 12

Calls

4 calls:

322.0ms	(cbrt N)
360.0ms	(cbrt N)
86.0ms	(log (+ N 1.0))
134.0ms	(- (- (log (+ N 1.0)) (* 2 (log (cbrt N)))) (log (cbrt N)))

simplify96.0ms

Counts: 78 → 78

prune283.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

regimes28.0ms

Accuracy

100% (0.0b remaining)

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

bsearch65.0ms

Steps

Iters	Range		Point
8	208.71590408624647	421651.551737869	7188.615530504987

simplify79.0ms

end0.0ms

sample2.9s

Algorithm

intervals

Results

932.0ms	1261×	body	640	valid
701.0ms	1764×	body	1280	valid
415.0ms	7805×	body	80	nan
303.0ms	4069×	body	80	valid
120.0ms	590×	body	320	valid
31.0ms	316×	body	160	valid