Details

sample45.0ms

Algorithm

intervals

Results

13.0ms	57×	body	1280	valid
6.0ms	40×	body	640	valid
6.0ms	128×	body	80	valid
5.0ms	239×	body	80	nan
2.0ms	19×	body	320	valid
1.0ms	12×	body	160	valid

simplify5.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	9	4
1	10	4
2	10	4
done	10	4

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.0b

localize7.0ms

Local error

Found 2 expressions with local error:

2.2b	(log (+ N 1.0))
3.3b	(- (log (+ N 1.0)) (log N))

rewrite20.0ms

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:

5.0ms	(log (+ N 1.0))
14.0ms	(- (log (+ N 1.0)) (log N))

series143.0ms

Counts

2 → 6

Calls

2 calls:

47.0ms	(log (+ N 1.0))
96.0ms	(- (log (+ N 1.0)) (log N))

simplify54.0ms

Counts

47 → 47

Iterations

Useful iterations: 3 (50.0ms)

Iter	Nodes	Cost
0	212	281
1	547	264
2	1875	250
3	5001	247
done	5001	247

prune106.0ms

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)
3.5b	(log (/ (+ N 1.0) N))

rewrite28.0ms

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:

19.0ms	(/ (+ N 1.0) N)
6.0ms	(log (/ (+ N 1.0) N))

series138.0ms

Counts

2 → 6

Calls

2 calls:

54.0ms	(/ (+ N 1.0) N)
83.0ms	(log (/ (+ N 1.0) N))

simplify101.0ms

Counts

66 → 66

Iterations

Useful iterations: 2 (19.0ms)

Iter	Nodes	Cost
0	233	373
1	773	351
2	3489	339
3	5002	339
done	5002	339

prune113.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(log (/ (sqrt (+ N 1.0)) N))
0.2b	(/ (sqrt (+ N 1.0)) N)
2.2b	(log (sqrt (+ N 1.0)))
3.2b	(+ (log (sqrt (+ N 1.0))) (log (/ (sqrt (+ N 1.0)) N)))

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

80×	`*-un-lft-identity`
64×	`log-prod`
63×	`times-frac`
52×	`add-sqr-sqrt` `add-cube-cbrt`
48×	`sqrt-prod`
25×	`associate-+r+`
16×	`distribute-lft-out`
11×	`pow1`
10×	`add-exp-log`
8×	`log-pow`
7×	`associate-+l+` `associate-/l*`
6×	`log-div` `sqrt-div` `add-cbrt-cube`
4×	`flip3-+` `flip-+` `add-log-exp`
3×	`rem-log-exp` `associate-/r*` `div-inv`
2×	`associate-+l-` `div-exp` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `associate-+r-` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `sum-log`

Counts

4 → 151

Calls

4 calls:

7.0ms	(log (/ (sqrt (+ N 1.0)) N))
19.0ms	(/ (sqrt (+ N 1.0)) N)
6.0ms	(log (sqrt (+ N 1.0)))
24.0ms	(+ (log (sqrt (+ N 1.0))) (log (/ (sqrt (+ N 1.0)) N)))

series535.0ms

Counts

4 → 12

Calls

4 calls:

146.0ms	(log (/ (sqrt (+ N 1.0)) N))
74.0ms	(/ (sqrt (+ N 1.0)) N)
83.0ms	(log (sqrt (+ N 1.0)))
232.0ms	(+ (log (sqrt (+ N 1.0))) (log (/ (sqrt (+ N 1.0)) N)))

simplify47.0ms

Counts

163 → 163

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	507	1381
1	1521	1277
2	5001	1171
done	5001	1171

prune366.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

2.2b	(log (sqrt (+ N 1.0)))
2.2b	(log (sqrt (+ N 1.0)))
2.2b	(log (sqrt (+ N 1.0)))
3.2b	(+ (pow (log (sqrt (+ N 1.0))) 3) (pow (log (/ (sqrt (+ N 1.0)) N)) 3))

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

34×	`*-un-lft-identity`
26×	`pow1`
25×	`log-pow`
21×	`log-prod`
20×	`distribute-lft-out`
16×	`unpow-prod-down` `cube-prod`
12×	`sqrt-prod`
10×	`add-sqr-sqrt` `add-cube-cbrt`
7×	`add-exp-log`
6×	`log-div` `sqrt-div` `add-log-exp`
4×	`flip3-+` `add-cbrt-cube` `flip-+`
3×	`sqrt-pow1` `pow1/2` `rem-log-exp`
1×	`+-commutative` `sum-log` `sum-cubes`

Counts

4 → 89

Calls

4 calls:

6.0ms	(log (sqrt (+ N 1.0)))
6.0ms	(log (sqrt (+ N 1.0)))
6.0ms	(log (sqrt (+ N 1.0)))
44.0ms	(+ (pow (log (sqrt (+ N 1.0))) 3) (pow (log (/ (sqrt (+ N 1.0)) N)) 3))

series757.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(log (sqrt (+ N 1.0)))
83.0ms	(log (sqrt (+ N 1.0)))
77.0ms	(log (sqrt (+ N 1.0)))
513.0ms	(+ (pow (log (sqrt (+ N 1.0))) 3) (pow (log (/ (sqrt (+ N 1.0)) N)) 3))

simplify64.0ms

Counts

101 → 101

Iterations

Useful iterations: 1 (15.0ms)

Iter	Nodes	Cost
0	706	1109
1	2776	1035
2	5002	1035
done	5002	1035

prune381.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

regimes26.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 29.0b

bsearch29.0ms

Steps

Iters	Range		Point
9	51.26549425761527	15794870057.515802	9256.9590468846

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	10
1	24	10
done	24	10

end0.0ms

sample1.3s

Algorithm

intervals

Results

413.0ms	1730×	body	1280	valid
184.0ms	7837×	body	80	nan
180.0ms	1215×	body	640	valid
170.0ms	4129×	body	80	valid
58.0ms	614×	body	320	valid
19.0ms	312×	body	160	valid