Details

sample81.0ms

Algorithm

intervals

Results

24.0ms	56×	body	1280	valid
11.0ms	35×	body	640	valid
11.0ms	251×	body	80	nan
10.0ms	134×	body	80	valid
4.0ms	24×	body	320	valid
1.0ms	7×	body	160	valid

simplify8.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	9	7
2	10	7
done	10	7

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.4b

localize16.0ms

Local error

Found 2 expressions with local error:

3.4b	(- (log (+ N 1.0)) (log N))
3.5b	(log (+ N 1.0))

rewrite38.0ms

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:

25.0ms	(- (log (+ N 1.0)) (log N))
10.0ms	(log (+ N 1.0))

series233.0ms

Counts

2 → 6

Calls

2 calls:

160.0ms	(- (log (+ N 1.0)) (log N))
74.0ms	(log (+ N 1.0))

simplify3.0s

Counts

47 → 47

Iterations

Useful iterations: done (3.0s)

Iter	Nodes	Cost
0	101	510
1	213	488
2	462	445
3	1063	443
4	2574	438
done	5001	426

prune186.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (+ N 1.0) N)
3.3b	(log (/ (+ N 1.0) N))

rewrite55.0ms

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:

38.0ms	(/ (+ N 1.0) N)
13.0ms	(log (/ (+ N 1.0) N))

series217.0ms

Counts

2 → 6

Calls

2 calls:

59.0ms	(/ (+ N 1.0) N)
157.0ms	(log (/ (+ N 1.0) N))

simplify3.9s

Counts

66 → 66

Iterations

Useful iterations: 4 (1.9s)

Iter	Nodes	Cost
0	108	723
1	232	690
2	583	637
3	1417	624
4	3874	622
done	5001	622

prune182.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (/ (+ N 1.0) N))
0.1b	(sqrt (/ (+ N 1.0) N))
0.2b	(* (sqrt (/ (+ N 1.0) N)) (sqrt (/ (+ N 1.0) N)))
3.3b	(log (* (sqrt (/ (+ N 1.0) N)) (sqrt (/ (+ N 1.0) N))))

rewrite161.0ms

Algorithm

rewrite-expression-head

Rules

122×	`sqrt-prod`
114×	`*-un-lft-identity`
94×	`add-sqr-sqrt`
92×	`times-frac`
60×	`add-cube-cbrt`
37×	`pow1`
27×	`swap-sqr`
24×	`distribute-lft-out`
19×	`associate-r` `associate-l`
18×	`sqrt-pow1` `pow1/2`
14×	`log-pow`
10×	`sqrt-div` `pow-prod-up`
9×	`add-exp-log` `unswap-sqr`
6×	`pow-prod-down` `pow-sqr` `add-cbrt-cube` `div-inv`
4×	`rem-sqrt-square` `add-log-exp`
3×	`log-div`
2×	`pow2` `frac-times` `pow-plus` `associate-r/` `rem-log-exp` `associate-l/` `prod-exp`
1×	`log-prod` `sqrt-unprod` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 185

Calls

4 calls:

11.0ms	(sqrt (/ (+ N 1.0) N))
20.0ms	(sqrt (/ (+ N 1.0) N))
79.0ms	(* (sqrt (/ (+ N 1.0) N)) (sqrt (/ (+ N 1.0) N)))
41.0ms	(log (* (sqrt (/ (+ N 1.0) N)) (sqrt (/ (+ N 1.0) N))))

series516.0ms

Counts

4 → 12

Calls

4 calls:

84.0ms	(sqrt (/ (+ N 1.0) N))
75.0ms	(sqrt (/ (+ N 1.0) N))
191.0ms	(* (sqrt (/ (+ N 1.0) N)) (sqrt (/ (+ N 1.0) N)))
166.0ms	(log (* (sqrt (/ (+ N 1.0) N)) (sqrt (/ (+ N 1.0) N))))

simplify2.0s

Counts

197 → 197

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	183	3094
1	314	2141
2	938	1980
3	2495	1949
done	5002	1925

prune563.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(log (- (log (+ N 1.0)) (log N)))
0.8b	(exp (log (- (log (+ N 1.0)) (log N))))
3.4b	(- (log (+ N 1.0)) (log N))
3.5b	(log (+ N 1.0))

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

27×	`log-prod`
26×	`*-un-lft-identity`
19×	`pow1`
16×	`add-sqr-sqrt`
15×	`log-pow`
12×	`distribute-lft-out--`
10×	`add-cube-cbrt`
8×	`log-div` `exp-sum`
6×	`add-exp-log`
4×	`exp-prod` `associate--l+` `add-cbrt-cube` `add-log-exp`
3×	`flip3--` `flip--` `associate--r+` `difference-of-squares`
2×	`associate--l-` `flip3-+` `exp-diff` `rem-log-exp` `flip-+` `distribute-lft-out`
1×	`sub-neg` `diff-log` `rem-exp-log`

Counts

4 → 82

Calls

4 calls:

7.0ms	(log (- (log (+ N 1.0)) (log N)))
18.0ms	(exp (log (- (log (+ N 1.0)) (log N))))
25.0ms	(- (log (+ N 1.0)) (log N))
6.0ms	(log (+ N 1.0))

series526.0ms

Counts

4 → 12

Calls

4 calls:

224.0ms	(log (- (log (+ N 1.0)) (log N)))
128.0ms	(exp (log (- (log (+ N 1.0)) (log N))))
122.0ms	(- (log (+ N 1.0)) (log N))
52.0ms	(log (+ N 1.0))

simplify1.9s

Counts

94 → 94

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	171	1286
1	347	1186
2	844	1065
3	2418	1051
done	5000	1036

prune270.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

regimes60.0ms

Accuracy

99.8% (0.1b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 29.4b

bsearch2.0ms

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	22	37
1	24	37
done	24	37

end0.0ms

sample2.6s

Algorithm

intervals

Results

795.0ms	1770×	body	1280	valid
479.0ms	8028×	body	80	nan
370.0ms	4092×	body	80	valid
343.0ms	1309×	body	640	valid
97.0ms	563×	body	320	valid
61.0ms	266×	body	160	valid