Details

sample126.0ms

Algorithm

intervals

Results

56.0ms	66×	body	1280	valid
19.0ms	245×	body	80	nan
17.0ms	138×	body	80	valid
10.0ms	21×	body	640	valid
7.0ms	23×	body	320	valid
2.0ms	8×	body	160	valid

simplify10.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	13
2	13
1	11
0	6

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.0b

localize20.0ms

Local error

Found 2 expressions with local error:

0.0b	(log1p N)
3.0b	(- (log1p N) (log N))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

14×	`*-un-lft-identity`
13×	`add-sqr-sqrt`
12×	`prod-diff`
11×	`add-cube-cbrt`
6×	`pow1`
4×	`log-pow`
3×	`expm1-log1p-u` `log-prod` `fma-neg` `associate--r+` `add-log-exp`
2×	`log1p-udef` `add-cbrt-cube` `diff-log` `add-exp-log` `insert-posit16` `log1p-expm1-u` `distribute-lft-out--`
1×	`sub-neg` `flip3--` `log1p-expm1` `flip--` `difference-of-squares`

Counts

2 → 49

Calls

2 calls:

0.0ms	(log1p N)
11.0ms	(- (log1p N) (log N))

series92.0ms

Counts

2 → 6

Calls

2 calls:

31.0ms	(log1p N)
62.0ms	(- (log1p N) (log N))

simplify2.2s

Counts

55 → 55

Iterations

Iter	Nodes
done	5001
3	1723
2	580
1	231
0	101

prune153.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (+ 1 N) N)
2.9b	(log (/ (+ 1 N) 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×	`expm1-log1p-u` `div-exp` `rem-log-exp` `insert-posit16` `log1p-expm1-u` `div-inv` `add-log-exp` `associate-/l/`
1×	`cbrt-undiv` `log-div` `clear-num` `frac-2neg` `flip3-+` `log-pow` `flip-+`

Counts

2 → 66

Calls

2 calls:

27.0ms	(/ (+ 1 N) N)
5.0ms	(log (/ (+ 1 N) N))

series165.0ms

Counts

2 → 6

Calls

2 calls:

90.0ms	(/ (+ 1 N) N)
74.0ms	(log (/ (+ 1 N) N))

simplify2.0s

Counts

72 → 72

Iterations

Iter	Nodes
done	5052
3	2586
2	583
1	244
0	106

prune202.0ms

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)))

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

65×	`*-un-lft-identity`
45×	`add-sqr-sqrt`
42×	`times-frac`
40×	`add-cube-cbrt` `sqrt-prod`
39×	`log-prod`
25×	`associate-+r+`
14×	`distribute-lft-out`
13×	`pow1`
10×	`log-pow`
8×	`sqrt-div`
7×	`associate-+l+` `add-exp-log` `associate-/l*`
6×	`fma-def` `add-cbrt-cube`
5×	`log-div` `flip3-+` `flip-+`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r*` `sqrt-pow1` `pow1/2`
2×	`associate-+l-` `hypot-def` `div-inv` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `clear-num` `associate-+r-` `sum-log` `frac-2neg` `div-exp` `rem-log-exp` `hypot-1-def`

Counts

4 → 152

Calls

4 calls:

10.0ms	(sqrt (+ 1 N))
24.0ms	(/ (sqrt (+ 1 N)) N)
7.0ms	(log (sqrt (+ 1 N)))
20.0ms	(+ (log (sqrt (+ 1 N))) (log (/ (sqrt (+ 1 N)) N)))

series409.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(sqrt (+ 1 N))
70.0ms	(/ (sqrt (+ 1 N)) N)
68.0ms	(log (sqrt (+ 1 N)))
230.0ms	(+ (log (sqrt (+ 1 N))) (log (/ (sqrt (+ 1 N)) N)))

simplify3.1s

Counts

164 → 164

Iterations

Iter	Nodes
done	5000
3	4875
2	1234
1	479
0	223

prune658.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.1b

localize48.0ms

Local error

Found 4 expressions with local error:

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

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

114×	`*-un-lft-identity`
108×	`sqrt-prod`
84×	`times-frac`
82×	`add-sqr-sqrt`
80×	`add-cube-cbrt`
66×	`log-prod`
51×	`log-pow`
39×	`pow1`
36×	`prod-diff`
16×	`sqrt-pow1` `pow1/2`
15×	`distribute-lft-out`
10×	`add-exp-log`
7×	`associate--l+` `associate-/l*`
6×	`associate-/r*` `add-cbrt-cube` `fma-neg` `sqrt-div` `associate--r+` `distribute-lft-out--`
5×	`log-div`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`flip3-+` `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 → 235

Calls

4 calls:

20.0ms	(/ (sqrt (+ 1 N)) (sqrt N))
8.0ms	(log (sqrt (+ 1 N)))
8.0ms	(log (/ (sqrt (+ 1 N)) (sqrt N)))
24.0ms	(- (log (sqrt (+ 1 N))) (log (sqrt N)))

series645.0ms

Counts

4 → 12

Calls

4 calls:

97.0ms	(/ (sqrt (+ 1 N)) (sqrt N))
83.0ms	(log (sqrt (+ 1 N)))
160.0ms	(log (/ (sqrt (+ 1 N)) (sqrt N)))
304.0ms	(- (log (sqrt (+ 1 N))) (log (sqrt N)))

simplify3.1s

Counts

247 → 247

Iterations

Iter	Nodes
done	5000
3	4818
2	1519
1	691
0	326

prune1.0s

Pruning

5 alts after pruning (3 fresh and 2 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

bsearch29.0ms

Steps

Iters	Range		Point
6	2842.495256040047	21179.114160721674	4842.291926013775

simplify3.0ms

Iterations

Iter	Nodes
done	22
1	22
0	18

end0.0ms

sample3.4s

Algorithm

intervals

Results

996.0ms	1755×	body	1280	valid
913.0ms	7851×	body	80	nan
481.0ms	4070×	body	80	valid
481.0ms	1228×	body	640	valid
189.0ms	642×	body	320	valid
47.0ms	305×	body	160	valid