Details

sample94.0ms

Algorithm

intervals

Results

32.0ms	61×	body	1280	valid
16.0ms	262×	body	80	nan
13.0ms	42×	body	640	valid
12.0ms	124×	body	80	valid
4.0ms	18×	body	320	valid
2.0ms	11×	body	160	valid

simplify9.0ms

Counts

1 → 1

Iterations

Iter	Nodes
3	11
2	11
1	9
0	6

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.1b

localize12.0ms

Local error

Found 1 expressions with local error:

2.9b	(- (log1p N) (log N))

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

1 → 36

Calls

1 calls:

6.0ms

(- (log1p N) (log N))

series89.0ms

Counts

1 → 3

Calls

1 calls:

89.0ms

(- (log1p N) (log N))

simplify2.7s

Counts

39 → 39

Iterations

Iter	Nodes
4	2902
3	1009
2	369
1	183
0	82

prune342.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize47.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ 1/3 N) (* N N))
0.3b	(/ 1 (* N N))
0.4b	(/ 1/3 N)
11.2b	(fma (/ 1 (* N N)) -1/2 (/ (/ 1/3 N) (* N N)))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

43×	`times-frac`
29×	`add-exp-log`
28×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
23×	`add-cbrt-cube`
19×	`associate-/l*`
12×	`pow1`
11×	`div-exp`
9×	`cbrt-undiv`
6×	`pow-flip`
5×	`associate-/r*` `prod-exp` `div-inv`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`clear-num` `frac-2neg` `cbrt-unprod`
2×	`rec-exp` `1-exp`
1×	`pow2` `pow-plus` `pow-prod-down` `pow-sqr` `pow-prod-up` `fma-udef` `inv-pow` `associate-/l/`

Counts

4 → 121

Calls

4 calls:

18.0ms	(/ (/ 1/3 N) (* N N))
17.0ms	(/ 1 (* N N))
7.0ms	(/ 1/3 N)
0.0ms	(fma (/ 1 (* N N)) -1/2 (/ (/ 1/3 N) (* N N)))

series209.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(/ (/ 1/3 N) (* N N))
18.0ms	(/ 1 (* N N))
22.0ms	(/ 1/3 N)
123.0ms	(fma (/ 1 (* N N)) -1/2 (/ (/ 1/3 N) (* N N)))

simplify3.0s

Counts

133 → 133

Iterations

Iter	Nodes
3	4275
2	941
1	369
0	169

prune1.0s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.1b

localize50.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ 1 (* N N))
0.4b	(/ 1/3 N)
0.8b	(log (exp (/ (/ 1/3 N) (* N N))))
11.2b	(fma (/ 1 (* N N)) -1/2 (log (exp (/ (/ 1/3 N) (* N N)))))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

34×	`times-frac`
23×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
18×	`log-pow`
17×	`exp-prod` `add-exp-log`
13×	`pow1`
11×	`add-cbrt-cube`
6×	`pow-flip` `associate-/l*`
5×	`div-exp`
4×	`expm1-log1p-u` `associate-/r*` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`cbrt-undiv` `log-prod` `prod-exp`
2×	`rec-exp` `clear-num` `frac-2neg` `1-exp`
1×	`pow2` `pow-plus` `rem-log-exp` `pow-prod-down` `pow-sqr` `pow-prod-up` `cbrt-unprod` `fma-udef` `inv-pow`

Counts

4 → 104

Calls

4 calls:

17.0ms	(/ 1 (* N N))
6.0ms	(/ 1/3 N)
21.0ms	(log (exp (/ (/ 1/3 N) (* N N))))
0.0ms	(fma (/ 1 (* N N)) -1/2 (log (exp (/ (/ 1/3 N) (* N N)))))

series210.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(/ 1 (* N N))
24.0ms	(/ 1/3 N)
47.0ms	(log (exp (/ (/ 1/3 N) (* N N))))
119.0ms	(fma (/ 1 (* N N)) -1/2 (log (exp (/ (/ 1/3 N) (* N N)))))

simplify4.5s

Counts

116 → 116

Iterations

Iter	Nodes
4	6482
3	1761
2	651
1	314
0	180

prune1.1s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.1b

localize59.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ 1 (* N N))
0.4b	(/ 1/3 N)
0.8b	(log (exp (/ (/ 1/3 N) (* N N))))
1.8b	(log (exp (/ 1 (* N N))))

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

37×	`times-frac`
26×	`add-sqr-sqrt` `*-un-lft-identity` `log-pow` `add-cube-cbrt`
24×	`exp-prod`
17×	`add-exp-log`
14×	`pow1`
11×	`add-cbrt-cube`
6×	`log-prod` `pow-flip` `associate-/l*`
5×	`div-exp` `div-inv`
4×	`expm1-log1p-u` `associate-/r*` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `prod-exp`
2×	`rec-exp` `clear-num` `frac-2neg` `1-exp` `rem-log-exp`
1×	`pow2` `pow-plus` `pow-prod-down` `pow-sqr` `pow-prod-up` `cbrt-unprod` `inv-pow`

Counts

4 → 115

Calls

4 calls:

24.0ms	(/ 1 (* N N))
7.0ms	(/ 1/3 N)
20.0ms	(log (exp (/ (/ 1/3 N) (* N N))))
15.0ms	(log (exp (/ 1 (* N N))))

series149.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(/ 1 (* N N))
19.0ms	(/ 1/3 N)
69.0ms	(log (exp (/ (/ 1/3 N) (* N N))))
31.0ms	(log (exp (/ 1 (* N N))))

simplify2.0s

Counts

127 → 127

Iterations

Iter	Nodes
4	4314
3	1379
2	562
1	312
0	187

prune1.5s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.1b

regimes25.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 30.9b

bsearch41.0ms

Steps

Iters	Range		Point
8	1.3793691672486585	12139.698930240449	6916.42260176444

simplify5.0ms

Iterations

Iter	Nodes
2	20
1	20
0	19

end0.0ms

sample3.4s

Algorithm

intervals

Results

1.0s	1756×	body	1280	valid
796.0ms	4091×	body	80	valid
612.0ms	8145×	body	80	nan
511.0ms	1262×	body	640	valid
142.0ms	582×	body	320	valid
72.0ms	309×	body	160	valid