Details

sample86.0ms

Algorithm

intervals

Results

33.0ms	66×	body	1280	valid
14.0ms	245×	body	80	nan
13.0ms	138×	body	80	valid
6.0ms	21×	body	640	valid
5.0ms	23×	body	320	valid
1.0ms	8×	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: 28.0b

localize42.0ms

Local error

Found 2 expressions with local error:

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

rewrite23.0ms

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:

6.0ms	(log (+ N 1))
16.0ms	(- (log (+ N 1)) (log N))

series117.0ms

Counts

2 → 6

Calls

2 calls:

37.0ms	(log (+ N 1))
79.0ms	(- (log (+ N 1)) (log N))

simplify2.5s

Counts

49 → 49

Iterations

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

prune200.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize16.0ms

Local error

Found 2 expressions with local error:

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

rewrite38.0ms

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:

30.0ms	(/ (+ N 1) N)
7.0ms	(log (/ (+ N 1) N))

series135.0ms

Counts

2 → 6

Calls

2 calls:

84.0ms	(/ (+ N 1) N)
52.0ms	(log (/ (+ N 1) N))

simplify1.6s

Counts

68 → 68

Iterations

Iter	Nodes
done	5021
3	2563
2	620
1	233
0	102

prune296.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

localize27.0ms

Local error

Found 4 expressions with local error:

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

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

95×	`*-un-lft-identity`
84×	`times-frac`
75×	`log-prod`
64×	`add-sqr-sqrt`
63×	`add-cube-cbrt`
56×	`sqrt-prod`
25×	`associate-+l+` `associate-+r+`
18×	`distribute-lft-out`
10×	`pow1` `add-exp-log`
7×	`associate-/l*`
6×	`add-cbrt-cube`
5×	`log-pow`
4×	`sqrt-div` `insert-posit16` `div-inv` `add-log-exp`
3×	`log-div` `associate-/r*` `flip3-+` `div-exp` `rem-log-exp` `flip-+`
2×	`associate-/l/`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `clear-num` `associate-+r-` `sum-log` `frac-2neg` `sqrt-pow1` `pow1/2` `1-exp` `associate-+l-`

Counts

4 → 169

Calls

4 calls:

9.0ms	(sqrt (+ N 1))
21.0ms	(/ (sqrt (+ N 1)) N)
4.0ms	(log (/ (sqrt (+ N 1)) 1))
15.0ms	(+ (log (/ (sqrt (+ N 1)) 1)) (log (/ (sqrt (+ N 1)) N)))

series414.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(sqrt (+ N 1))
75.0ms	(/ (sqrt (+ N 1)) N)
77.0ms	(log (/ (sqrt (+ N 1)) 1))
222.0ms	(+ (log (/ (sqrt (+ N 1)) 1)) (log (/ (sqrt (+ N 1)) N)))

simplify2.2s

Counts

181 → 181

Iterations

Iter	Nodes
done	5007
3	3672
2	1230
1	554
0	261

prune741.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.1b

localize59.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sqrt (+ N 1)) (sqrt N))
1.4b	(log (sqrt (+ 1 N)))
3.0b	(log (/ (sqrt (+ N 1)) (sqrt N)))
3.0b	(- (log (sqrt (+ 1 N))) (log (sqrt N)))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

108×	`sqrt-prod`
101×	`*-un-lft-identity`
84×	`times-frac`
69×	`add-sqr-sqrt`
67×	`add-cube-cbrt`
66×	`log-prod`
15×	`distribute-lft-out`
13×	`pow1`
12×	`log-pow`
10×	`add-exp-log`
7×	`associate--l+` `associate-/l*`
6×	`associate-/r*` `add-cbrt-cube` `sqrt-div` `associate--r+` `distribute-lft-out--`
5×	`log-div`
4×	`insert-posit16` `add-log-exp`
3×	`sqrt-pow1` `flip3-+` `pow1/2` `rem-log-exp` `flip-+`
2×	`associate--l-` `div-exp` `div-inv` `associate-/l/`
1×	`cbrt-undiv` `sqrt-undiv` `clear-num` `sub-neg` `frac-2neg` `flip3--` `diff-log` `flip--` `difference-of-squares`

Counts

4 → 185

Calls

4 calls:

11.0ms	(/ (sqrt (+ N 1)) (sqrt N))
4.0ms	(log (sqrt (+ 1 N)))
8.0ms	(log (/ (sqrt (+ N 1)) (sqrt N)))
23.0ms	(- (log (sqrt (+ 1 N))) (log (sqrt N)))

series633.0ms

Counts

4 → 12

Calls

4 calls:

84.0ms	(/ (sqrt (+ N 1)) (sqrt N))
79.0ms	(log (sqrt (+ 1 N)))
137.0ms	(log (/ (sqrt (+ N 1)) (sqrt N)))
334.0ms	(- (log (sqrt (+ 1 N))) (log (sqrt N)))

simplify2.4s

Counts

197 → 197

Iterations

Iter	Nodes
done	5000
3	3661
2	1283
1	583
0	290

prune926.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.1b

regimes52.0ms

Accuracy

99.9% (0.0b remaining)

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

bsearch45.0ms

Steps

Iters	Range		Point
6	2842.495256040047	21179.114160721674	5400.000739830978

simplify7.0ms

Iterations

Iter	Nodes
done	29
1	29
0	24

end0.0ms

sample3.2s

Algorithm

intervals

Results

1.0s	7851×	body	80	nan
915.0ms	1755×	body	1280	valid
445.0ms	1228×	body	640	valid
391.0ms	4070×	body	80	valid
179.0ms	642×	body	320	valid
44.0ms	305×	body	160	valid