Details

sample73.0ms

Algorithm

intervals

Results

28.0ms	66×	body	1280	valid
11.0ms	245×	body	80	nan
10.0ms	138×	body	80	valid
5.0ms	21×	body	640	valid
4.0ms	23×	body	320	valid
1.0ms	8×	body	160	valid

simplify10.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	12
2	12
1	11
0	6

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.0b

localize24.0ms

Local error

Found 2 expressions with local error:

1.4b	(log (+ N 1))
3.0b	(- (log (+ N 1)) (log N))

rewrite18.0ms

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:

3.0ms	(log (+ N 1))
14.0ms	(- (log (+ N 1)) (log N))

series123.0ms

Counts

2 → 6

Calls

2 calls:

33.0ms	(log (+ N 1))
90.0ms	(- (log (+ N 1)) (log N))

simplify2.4s

Counts

49 → 49

Iterations

Iter	Nodes
done	5000
4	3864
3	1350
2	463
1	199
0	97

prune206.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize17.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (+ 1 N) N)
2.9b	(log (/ (+ 1 N) N))

rewrite35.0ms

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:

27.0ms	(/ (+ 1 N) N)
7.0ms	(log (/ (+ 1 N) N))

series140.0ms

Counts

2 → 6

Calls

2 calls:

67.0ms	(/ (+ 1 N) N)
72.0ms	(log (/ (+ 1 N) N))

simplify1.3s

Counts

68 → 68

Iterations

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

prune186.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ 1 N))
0.1b	(/ (sqrt (+ 1 N)) N)
1.4b	(log (sqrt (+ 1 N)))
3.2b	(+ (log (sqrt (+ 1 N))) (log (/ (sqrt (+ 1 N)) N)))

rewrite55.0ms

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:

9.0ms	(sqrt (+ 1 N))
24.0ms	(/ (sqrt (+ 1 N)) N)
6.0ms	(log (sqrt (+ 1 N)))
13.0ms	(+ (log (sqrt (+ 1 N))) (log (/ (sqrt (+ 1 N)) N)))

series394.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(sqrt (+ 1 N))
59.0ms	(/ (sqrt (+ 1 N)) N)
71.0ms	(log (sqrt (+ 1 N)))
240.0ms	(+ (log (sqrt (+ 1 N))) (log (/ (sqrt (+ 1 N)) N)))

simplify3.2s

Counts

147 → 147

Iterations

Iter	Nodes
done	5002
3	4823
2	1158
1	455
0	215

prune649.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.1b

localize28.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (sqrt N))
1.4b	(log (sqrt (+ 1 N)))
3.0b	(log (/ (sqrt (+ 1 N)) (sqrt N)))
3.0b	(+ (log (sqrt (+ 1 N))) (log (/ 1 (sqrt N))))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

83×	`*-un-lft-identity`
82×	`log-prod`
78×	`times-frac`
74×	`sqrt-prod`
63×	`add-sqr-sqrt` `add-cube-cbrt`
22×	`associate-+r+`
13×	`pow1`
12×	`add-exp-log` `distribute-lft-out`
8×	`log-pow`
7×	`associate-+l+`
6×	`log-div` `associate-/r*` `add-cbrt-cube`
4×	`sqrt-div` `insert-posit16` `add-log-exp`
3×	`flip3-+` `div-exp` `rem-log-exp` `flip-+` `div-inv` `pow-flip` `associate-/l*`
2×	`sqrt-pow1` `pow1/2` `log-rec` `associate-+l-`
1×	`cbrt-undiv` `+-commutative` `rec-exp` `clear-num` `associate-+r-` `sum-log` `frac-2neg` `1-exp` `unsub-neg` `inv-pow`

Counts

4 → 175

Calls

4 calls:

5.0ms	(/ 1 (sqrt N))
3.0ms	(log (sqrt (+ 1 N)))
8.0ms	(log (/ (sqrt (+ 1 N)) (sqrt N)))
13.0ms	(+ (log (sqrt (+ 1 N))) (log (/ 1 (sqrt N))))

series393.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(/ 1 (sqrt N))
71.0ms	(log (sqrt (+ 1 N)))
143.0ms	(log (/ (sqrt (+ 1 N)) (sqrt N)))
140.0ms	(+ (log (sqrt (+ 1 N))) (log (/ 1 (sqrt N))))

simplify2.6s

Counts

187 → 187

Iterations

Iter	Nodes
done	5000
3	3542
2	1261
1	589
0	292

prune882.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.1b

regimes39.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 29.4b

bsearch25.0ms

Steps

Iters	Range		Point
6	2842.495256040047	21179.114160721674	4842.291926013775

simplify3.0ms

Iterations

Iter	Nodes
done	25
1	25
0	19

end0.0ms

sample2.4s

Algorithm

intervals

Results

912.0ms	1755×	body	1280	valid
473.0ms	7851×	body	80	nan
374.0ms	1228×	body	640	valid
291.0ms	4070×	body	80	valid
122.0ms	642×	body	320	valid
34.0ms	305×	body	160	valid