Details

sample89.0ms

Algorithm

intervals

Results

27.0ms	53×	body	1280	valid
16.0ms	43×	body	640	valid
15.0ms	259×	body	80	nan
12.0ms	136×	body	80	valid
4.0ms	16×	body	320	valid
1.0ms	8×	body	160	valid

simplify9.0ms

Counts

1 → 1

Iterations

Iter	Nodes
3	11
2	11
1	9
0	6

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.4b

localize9.0ms

Local error

Found 1 expressions with local error:

2.1b	(- (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` `insert-posit16` `log1p-expm1-u` `flip--` `difference-of-squares`

Counts

1 → 37

Calls

1 calls:

6.0ms

(- (log1p N) (log N))

series108.0ms

Counts

1 → 3

Calls

1 calls:

108.0ms

(- (log1p N) (log N))

simplify1.7s

Counts

40 → 40

Iterations

Iter	Nodes
4	2678
3	962
2	372
1	184
0	83

prune95.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (+ 1 N) N)
2.5b	(log (/ (+ 1 N) N))

rewrite41.0ms

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:

29.0ms	(/ (+ 1 N) N)
11.0ms	(log (/ (+ 1 N) N))

series136.0ms

Counts

2 → 6

Calls

2 calls:

87.0ms	(/ (+ 1 N) N)
49.0ms	(log (/ (+ 1 N) N))

simplify4.0s

Counts

72 → 72

Iterations

Iter	Nodes
4	5667
3	1564
2	510
1	231
0	106

prune285.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma (* (/ 1 N) (* (/ 1 N) (/ 1 N))) 1/3 (/ 1 N))
0.1b	(/ (/ 1 N) N)
0.2b	(* (/ 1 N) (/ 1 N))
12.8b	(fma (/ (/ 1 N) N) -1/2 (fma (* (/ 1 N) (* (/ 1 N) (/ 1 N))) 1/3 (/ 1 N)))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

123×	`times-frac`
98×	`add-sqr-sqrt`
82×	`*-un-lft-identity`
74×	`add-cube-cbrt`
53×	`add-exp-log`
22×	`pow1` `div-exp`
21×	`add-cbrt-cube`
16×	`prod-exp`
15×	`swap-sqr`
13×	`associate-r` `associate-l` `associate-/l*`
11×	`div-inv`
9×	`rec-exp` `1-exp` `pow-flip` `inv-pow` `unswap-sqr`
7×	`cbrt-undiv`
5×	`pow-prod-up`
4×	`expm1-log1p-u` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r*` `pow-prod-down` `pow-sqr`
2×	`fma-udef` `pow-div`
1×	`pow2` `frac-times` `clear-num` `frac-2neg` `pow-plus` `associate-l/` `associate-r/` `un-div-inv` `*-commutative` `associate-/l/`

Counts

4 → 197

Calls

4 calls:

0.0ms	(fma (* (/ 1 N) (* (/ 1 N) (/ 1 N))) 1/3 (/ 1 N))
8.0ms	(/ (/ 1 N) N)
22.0ms	(* (/ 1 N) (/ 1 N))
0.0ms	(fma (/ (/ 1 N) N) -1/2 (fma (* (/ 1 N) (* (/ 1 N) (/ 1 N))) 1/3 (/ 1 N)))

series181.0ms

Counts

4 → 12

Calls

4 calls:

91.0ms	(fma (* (/ 1 N) (* (/ 1 N) (/ 1 N))) 1/3 (/ 1 N))
19.0ms	(/ (/ 1 N) N)
27.0ms	(* (/ 1 N) (/ 1 N))
44.0ms	(fma (/ (/ 1 N) N) -1/2 (fma (* (/ 1 N) (* (/ 1 N) (/ 1 N))) 1/3 (/ 1 N)))

simplify7.9s

Counts

209 → 209

Iterations

Iter	Nodes
3	4005
2	1341
1	665
0	263

prune731.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ 1 N) N)
0.1b	(/ (/ 1 N) N)
1.2b	(log (exp (/ (/ 1 N) N)))
12.8b	(fma (/ (/ 1 N) N) -1/2 (fma (* (/ 1 N) (log (exp (/ (/ 1 N) N)))) 1/3 (/ 1 N)))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

216×	`times-frac`
124×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
44×	`log-pow`
43×	`exp-prod`
26×	`associate-/l*`
22×	`add-exp-log`
14×	`add-cbrt-cube` `div-inv`
12×	`div-exp`
11×	`pow1`
6×	`cbrt-undiv` `associate-/r*`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp` `pow-div`
3×	`log-prod`
2×	`rec-exp` `clear-num` `frac-2neg` `1-exp` `pow-flip` `inv-pow` `associate-/l/`
1×	`rem-log-exp` `fma-udef`

Counts

4 → 223

Calls

4 calls:

8.0ms	(/ (/ 1 N) N)
8.0ms	(/ (/ 1 N) N)
8.0ms	(log (exp (/ (/ 1 N) N)))
0.0ms	(fma (/ (/ 1 N) N) -1/2 (fma (* (/ 1 N) (log (exp (/ (/ 1 N) N)))) 1/3 (/ 1 N)))

series92.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(/ (/ 1 N) N)
25.0ms	(/ (/ 1 N) N)
18.0ms	(log (exp (/ (/ 1 N) N)))
28.0ms	(fma (/ (/ 1 N) N) -1/2 (fma (* (/ 1 N) (log (exp (/ (/ 1 N) N)))) 1/3 (/ 1 N)))

simplify2.8s

Counts

235 → 235

Iterations

Iter	Nodes
3	2203
2	823
1	418
0	265

prune996.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes50.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 29.5b

bsearch40.0ms

Steps

Iters	Range		Point
10	1.8230705747381016e-09	318690.85562629136	8386.707428118045

simplify4.0ms

Iterations

Iter	Nodes
2	18
1	18
0	16

end0.0ms

sample3.5s

Algorithm

intervals

Results

1.5s	1773×	body	1280	valid
559.0ms	8060×	body	80	nan
488.0ms	1232×	body	640	valid
459.0ms	4056×	body	80	valid
157.0ms	634×	body	320	valid
83.0ms	305×	body	160	valid