Details

sample99.0ms

Algorithm

intervals

Results

36.0ms	51×	body	1280	valid
15.0ms	39×	body	640	valid
15.0ms	143×	body	80	valid
14.0ms	229×	body	80	nan
4.0ms	12×	body	320	valid
2.0ms	11×	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: 26.7b

localize24.0ms

Local error

Found 2 expressions with local error:

2.5b	(- (log (+ N 1)) (log N))
2.8b	(log (+ N 1))

rewrite21.0ms

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:

14.0ms	(- (log (+ N 1)) (log N))
6.0ms	(log (+ N 1))

series117.0ms

Counts

2 → 6

Calls

2 calls:

94.0ms	(- (log (+ N 1)) (log N))
23.0ms	(log (+ N 1))

simplify2.5s

Counts

49 → 49

Iterations

Iter	Nodes
done	5001
4	3749
3	1329
2	452
1	200
0	97

prune278.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize20.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (+ 1 N) N)
2.6b	(log (/ (+ 1 N) N))

rewrite19.0ms

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:

14.0ms	(/ (+ 1 N) N)
5.0ms	(log (/ (+ 1 N) N))

series129.0ms

Counts

2 → 6

Calls

2 calls:

69.0ms	(/ (+ 1 N) N)
60.0ms	(log (/ (+ 1 N) N))

simplify1.6s

Counts

68 → 68

Iterations

Iter	Nodes
done	5300
3	2187
2	578
1	233
0	102

prune211.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

localize36.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ 1 N))
0.1b	(/ (sqrt (+ 1 N)) N)
2.5b	(+ (log (sqrt (+ 1 N))) (log (/ (sqrt (+ 1 N)) N)))
2.9b	(log (sqrt (+ 1 N)))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

63×	`*-un-lft-identity`
42×	`times-frac`
40×	`add-sqr-sqrt` `sqrt-prod`
39×	`log-prod` `add-cube-cbrt`
25×	`associate-+r+`
14×	`distribute-lft-out`
11×	`pow1`
8×	`sqrt-div`
7×	`associate-+l+` `add-exp-log` `log-pow` `associate-/l*`
6×	`add-cbrt-cube`
5×	`log-div` `flip3-+` `flip-+`
4×	`insert-posit16` `add-log-exp`
3×	`associate-/r*`
2×	`sqrt-pow1` `pow1/2` `associate-+l-` `div-inv` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `clear-num` `associate-+r-` `sum-log` `frac-2neg` `div-exp` `rem-log-exp`

Counts

4 → 135

Calls

4 calls:

10.0ms	(sqrt (+ 1 N))
11.0ms	(/ (sqrt (+ 1 N)) N)
14.0ms	(+ (log (sqrt (+ 1 N))) (log (/ (sqrt (+ 1 N)) N)))
7.0ms	(log (sqrt (+ 1 N)))

series451.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(sqrt (+ 1 N))
107.0ms	(/ (sqrt (+ 1 N)) N)
235.0ms	(+ (log (sqrt (+ 1 N))) (log (/ (sqrt (+ 1 N)) N)))
67.0ms	(log (sqrt (+ 1 N)))

simplify2.7s

Counts

147 → 147

Iterations

Iter	Nodes
done	5004
3	4618
2	1162
1	454
0	215

prune592.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.1b

localize37.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (log (/ (+ 1 N) N)))
2.6b	(log (/ (+ 1 N) N))
2.6b	(log (/ (+ 1 N) N))
2.6b	(log (/ (+ 1 N) N))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

48×	`log-prod`
47×	`*-un-lft-identity`
36×	`times-frac`
29×	`add-sqr-sqrt` `add-cube-cbrt`
13×	`add-exp-log`
9×	`distribute-lft-out`
8×	`pow1`
6×	`rem-log-exp`
4×	`cbrt-prod` `add-cbrt-cube` `log-pow` `insert-posit16` `add-log-exp`
3×	`log-div` `div-exp` `div-inv`
1×	`pow1/3`

Counts

4 → 97

Calls

4 calls:

2.0ms	(cbrt (log (/ (+ 1 N) N)))
7.0ms	(log (/ (+ 1 N) N))
7.0ms	(log (/ (+ 1 N) N))
7.0ms	(log (/ (+ 1 N) N))

series295.0ms

Counts

4 → 12

Calls

4 calls:

130.0ms	(cbrt (log (/ (+ 1 N) N)))
64.0ms	(log (/ (+ 1 N) N))
52.0ms	(log (/ (+ 1 N) N))
49.0ms	(log (/ (+ 1 N) N))

simplify2.0s

Counts

109 → 109

Iterations

Iter	Nodes
done	5000
3	2246
2	723
1	290
0	134

prune469.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.1b

regimes65.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 28.7b

bsearch54.0ms

Steps

Iters	Range		Point
7	315.1021581913647	12461.173664998358	8041.189519456958

simplify4.0ms

Iterations

Iter	Nodes
done	20
1	20
0	16

end0.0ms

sample3.4s

Algorithm

intervals

Results

1.4s	1684×	body	1280	valid
617.0ms	7961×	body	80	nan
523.0ms	1231×	body	640	valid
389.0ms	4163×	body	80	valid
216.0ms	610×	body	320	valid
52.0ms	312×	body	160	valid