Details

sample68.0ms

Algorithm

intervals

Results

22.0ms	55×	body	1280	valid
9.0ms	225×	body	80	nan
9.0ms	133×	body	80	valid
8.0ms	34×	body	640	valid
4.0ms	24×	body	320	valid
1.0ms	10×	body	160	valid

simplify6.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	10
2	10
1	9
0	6

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.6b

localize38.0ms

Local error

Found 2 expressions with local error:

1.8b	(log (+ N 1.0))
2.8b	(- (log (+ N 1.0)) (log N))

rewrite30.0ms

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-+` `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:

7.0ms	(log (+ N 1.0))
21.0ms	(- (log (+ N 1.0)) (log N))

series201.0ms

Counts

2 → 6

Calls

2 calls:

64.0ms	(log (+ N 1.0))
137.0ms	(- (log (+ N 1.0)) (log N))

simplify1.5s

Counts

47 → 47

Iterations

Iter	Nodes
done	5000
3	1557
2	530
1	213
0	101

prune202.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (+ N 1.0) N)
3.4b	(log (/ (+ N 1.0) N))

rewrite41.0ms

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

Counts

2 → 60

Calls

2 calls:

28.0ms	(/ (+ N 1.0) N)
9.0ms	(log (/ (+ N 1.0) N))

series216.0ms

Counts

2 → 6

Calls

2 calls:

89.0ms	(/ (+ N 1.0) N)
127.0ms	(log (/ (+ N 1.0) N))

simplify1.5s

Counts

66 → 66

Iterations

Iter	Nodes
done	5001
3	2289
2	619
1	243
0	108

prune212.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.1b

localize21.0ms

Local error

Found 3 expressions with local error:

0.0b	(log (sqrt N))
0.4b	(/ (+ N 1.0) (sqrt N))
3.0b	(+ (- (log (sqrt N))) (log (/ (+ N 1.0) (sqrt N))))

rewrite68.0ms

Algorithm

rewrite-expression-head

Rules

72×	`*-un-lft-identity`
48×	`times-frac`
40×	`log-prod`
39×	`add-sqr-sqrt` `add-cube-cbrt`
33×	`sqrt-prod`
28×	`associate-+r+`
19×	`distribute-lft-out`
10×	`pow1`
8×	`log-pow`
6×	`associate-+l+` `distribute-neg-in` `associate-/r*` `add-exp-log`
5×	`add-cbrt-cube`
4×	`distribute-rgt-neg-in` `associate-/l*` `add-log-exp`
2×	`sum-log` `flip3-+` `flip-+` `div-inv` `associate-/l/`
1×	`neg-sub0` `cbrt-undiv` `+-commutative` `log-div` `clear-num` `associate-+r-` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `rem-log-exp` `neg-log` `associate-+l-`

Counts

3 → 119

Calls

3 calls:

3.0ms	(log (sqrt N))
29.0ms	(/ (+ N 1.0) (sqrt N))
28.0ms	(+ (- (log (sqrt N))) (log (/ (+ N 1.0) (sqrt N))))

series384.0ms

Counts

3 → 9

Calls

3 calls:

100.0ms	(log (sqrt N))
52.0ms	(/ (+ N 1.0) (sqrt N))
231.0ms	(+ (- (log (sqrt N))) (log (/ (+ N 1.0) (sqrt N))))

simplify1.4s

Counts

128 → 128

Iterations

Iter	Nodes
done	5000
2	1294
1	463
0	199

prune649.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

localize46.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (/ (+ N 1.0) (sqrt N)))
0.5b	(cbrt (/ (+ N 1.0) (sqrt N)))
0.5b	(* (cbrt (/ (+ N 1.0) (sqrt N))) (cbrt (/ (+ N 1.0) (sqrt N))))
3.0b	(+ (- (log (sqrt N))) (log (* (* (cbrt (/ (+ N 1.0) (sqrt N))) (cbrt (/ (+ N 1.0) (sqrt N)))) (cbrt (/ (+ N 1.0) (sqrt N))))))

rewrite454.0ms

Algorithm

rewrite-expression-head

Rules

251×	`*-un-lft-identity`
240×	`cbrt-prod`
208×	`times-frac`
184×	`add-sqr-sqrt`
112×	`add-cube-cbrt`
107×	`sqrt-prod`
68×	`distribute-lft-out`
55×	`swap-sqr`
33×	`pow1`
31×	`associate-r` `associate-l`
18×	`cbrt-div`
16×	`unswap-sqr`
13×	`log-pow`
11×	`pow-prod-down`
8×	`distribute-rgt-neg-in` `pow1/3`
7×	`log-div` `log-prod` `associate-+r-`
6×	`frac-times` `associate-+l+` `distribute-neg-in` `associate-*l/` `add-exp-log` `div-inv`
5×	`add-log-exp`
4×	`add-cbrt-cube` `associate-*r/`
2×	`sum-log` `pow-sqr` `pow-prod-up`
1×	`pow2` `neg-sub0` `+-commutative` `associate-+r+` `flip3-+` `pow-plus` `neg-log` `prod-exp` `*-commutative` `associate-+l-` `cbrt-unprod` `flip-+`

Counts

4 → 267

Calls

4 calls:

5.0ms	(cbrt (/ (+ N 1.0) (sqrt N)))
5.0ms	(cbrt (/ (+ N 1.0) (sqrt N)))
86.0ms	(* (cbrt (/ (+ N 1.0) (sqrt N))) (cbrt (/ (+ N 1.0) (sqrt N))))
339.0ms	(+ (- (log (sqrt N))) (log (* (* (cbrt (/ (+ N 1.0) (sqrt N))) (cbrt (/ (+ N 1.0) (sqrt N)))) (cbrt (/ (+ N 1.0) (sqrt N))))))

series793.0ms

Counts

4 → 12

Calls

4 calls:

169.0ms	(cbrt (/ (+ N 1.0) (sqrt N)))
200.0ms	(cbrt (/ (+ N 1.0) (sqrt N)))
173.0ms	(* (cbrt (/ (+ N 1.0) (sqrt N))) (cbrt (/ (+ N 1.0) (sqrt N))))
251.0ms	(+ (- (log (sqrt N))) (log (* (* (cbrt (/ (+ N 1.0) (sqrt N))) (cbrt (/ (+ N 1.0) (sqrt N)))) (cbrt (/ (+ N 1.0) (sqrt N))))))

simplify2.0s

Counts

279 → 279

Iterations

Iter	Nodes
done	5000
2	1801
1	714
0	331

prune1.5s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.1b

regimes55.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 29.6b

bsearch45.0ms

Steps

Iters	Range		Point
7	44.35744796693956	8445.545519380286	7951.823313362933

simplify5.0ms

Iterations

Iter	Nodes
done	20
1	20
0	17

end0.0ms

sample2.8s

Algorithm

intervals

Results

893.0ms	7962×	body	80	nan
769.0ms	1761×	body	1280	valid
372.0ms	4041×	body	80	valid
322.0ms	1264×	body	640	valid
143.0ms	624×	body	320	valid
33.0ms	310×	body	160	valid