Details

analyze2.0ms

Algorithm

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
50%	50%	0%	2
50%	25%	25%	3
50%	0%	50%	4

sample39.0ms

Algorithm

intervals

Results

15.0ms	55×	body	1280	valid
8.0ms	47×	body	640	valid
6.0ms	121×	body	80	valid
3.0ms	24×	body	320	valid
1.0ms	9×	body	160	valid

simplify2.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	7	7
1	7	7

prune2.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 32.0b

Counts

2 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

2.8b	(- (log (+ N 1.0)) (log N))
2.9b	(log (+ N 1.0))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

13×	`*-un-lft-identity`
11×	`log-prod`
7×	`pow1` `add-sqr-sqrt`
5×	`add-cube-cbrt` `log-pow`
4×	`log-div` `associate--l+` `distribute-lft-out--`
3×	`add-exp-log` `associate--r+`
2×	`associate--l-` `flip3-+` `add-cbrt-cube` `flip-+` `distribute-lft-out` `add-log-exp`
1×	`sub-neg` `flip3--` `diff-log` `rem-log-exp` `flip--` `difference-of-squares`

Counts

2 → 40

Calls

2 calls:

7.0ms	(- (log (+ N 1.0)) (log N))
3.0ms	(log (+ N 1.0))

series8.0ms

Counts

2 → 6

Calls

2 calls:

5.0ms	(- (log (+ N 1.0)) (log N))
3.0ms	(log (+ N 1.0))

simplify52.0ms

Algorithm

egg-herbie

Counts

46 → 46

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4952	422
1	4952	422

prune83.0ms

Filtered

35 candidates to 46 candidates (-31.4%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	42	4	46
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	43	4	47

Merged error: 0.0b

Counts

47 → 4

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (/ 1.0 N) (/ (- (/ 0.3333333333333333 N) 0.5) (* N N)))
0.4b	(/ (- (/ 0.3333333333333333 N) 0.5) (* N N))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
10×	`*-un-lft-identity`
8×	`times-frac`
7×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/l*`
4×	`add-cube-cbrt` `add-log-exp` `difference-of-squares`
2×	`pow1` `cbrt-undiv` `div-sub` `div-exp` `associate-/l/` `distribute-lft-out--`
1×	`+-commutative` `associate-+r-` `flip3--` `frac-2neg` `flip3-+` `frac-add` `prod-exp` `clear-num` `associate-/r*` `sum-log` `flip--` `cbrt-unprod` `flip-+` `div-inv` `distribute-lft-out`

Counts

2 → 44

Calls

2 calls:

15.0ms	(+ (/ 1.0 N) (/ (- (/ 0.3333333333333333 N) 0.5) (* N N)))
10.0ms	(/ (- (/ 0.3333333333333333 N) 0.5) (* N N))

series12.0ms

Counts

2 → 6

Calls

2 calls:

4.0ms	(+ (/ 1.0 N) (/ (- (/ 0.3333333333333333 N) 0.5) (* N N)))
8.0ms	(/ (- (/ 0.3333333333333333 N) 0.5) (* N N))

simplify38.0ms

Algorithm

egg-herbie

Counts

50 → 50

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5393	663

prune68.0ms

Filtered

36 candidates to 50 candidates (-38.9%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	48	2	50
Fresh	1	2	3
Picked	0	1	1
Done	0	0	0
Total	49	5	54

Merged error: 0.0b

Counts

54 → 5

localize12.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (cbrt (+ (/ (- (/ 0.3333333333333333 N) 0.5) (* N N)) (/ 1.0 N))) (cbrt (+ (/ (- (/ 0.3333333333333333 N) 0.5) (* N N)) (/ 1.0 N))))
19.9b	(cbrt (+ (/ (- (/ 0.3333333333333333 N) 0.5) (* N N)) (/ 1.0 N)))
19.9b	(cbrt (+ (/ (- (/ 0.3333333333333333 N) 0.5) (* N N)) (/ 1.0 N)))
19.9b	(cbrt (+ (/ (- (/ 0.3333333333333333 N) 0.5) (* N N)) (/ 1.0 N)))

rewrite91.0ms

Algorithm

rewrite-expression-head

Rules

36×	`cbrt-prod`
35×	`*-un-lft-identity`
33×	`cbrt-div`
23×	`add-sqr-sqrt`
15×	`add-cube-cbrt`
11×	`pow1` `flip3-+` `frac-add` `flip-+`
9×	`frac-times` `pow1/3` `swap-sqr` `distribute-lft-out`
7×	`associate-r` `associate-l`
6×	`add-exp-log`
4×	`add-cbrt-cube` `add-log-exp` `unswap-sqr`
3×	`associate-r/` `associate-l/`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 105

Calls

4 calls:

37.0ms	(* (cbrt (+ (/ (- (/ 0.3333333333333333 N) 0.5) (* N N)) (/ 1.0 N))) (cbrt (+ (/ (- (/ 0.3333333333333333 N) 0.5) (* N N)) (/ 1.0 N))))
18.0ms	(cbrt (+ (/ (- (/ 0.3333333333333333 N) 0.5) (* N N)) (/ 1.0 N)))
17.0ms	(cbrt (+ (/ (- (/ 0.3333333333333333 N) 0.5) (* N N)) (/ 1.0 N)))
16.0ms	(cbrt (+ (/ (- (/ 0.3333333333333333 N) 0.5) (* N N)) (/ 1.0 N)))

series51.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(* (cbrt (+ (/ (- (/ 0.3333333333333333 N) 0.5) (* N N)) (/ 1.0 N))) (cbrt (+ (/ (- (/ 0.3333333333333333 N) 0.5) (* N N)) (/ 1.0 N))))
12.0ms	(cbrt (+ (/ (- (/ 0.3333333333333333 N) 0.5) (* N N)) (/ 1.0 N)))
14.0ms	(cbrt (+ (/ (- (/ 0.3333333333333333 N) 0.5) (* N N)) (/ 1.0 N)))
12.0ms	(cbrt (+ (/ (- (/ 0.3333333333333333 N) 0.5) (* N N)) (/ 1.0 N)))

simplify53.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	5032	3253

prune322.0ms

Filtered

87 candidates to 117 candidates (-34.5%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	117	0	117
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	117	5	122

Merged error: 0.0b

Counts

122 → 5

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (+ N 1.0) N)
2.6b	(log (/ (+ N 1.0) N))

rewrite11.0ms

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` `div-inv` `associate-/l/` `add-log-exp`
1×	`cbrt-undiv` `log-div` `frac-2neg` `flip3-+` `clear-num` `log-pow` `flip-+`

Counts

2 → 60

Calls

2 calls:

5.0ms	(/ (+ N 1.0) N)
4.0ms	(log (/ (+ N 1.0) N))

series8.0ms

Counts

2 → 6

Calls

2 calls:

4.0ms	(/ (+ N 1.0) N)
4.0ms	(log (/ (+ N 1.0) N))

simplify40.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	5054	615

prune71.0ms

Filtered

46 candidates to 66 candidates (-43.5%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	65	1	66
Fresh	0	2	2
Picked	1	0	1
Done	0	2	2
Total	66	5	71

Merged error: 0.0b

Counts

71 → 5

regimes40.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 31.5b

bsearch19.0ms

Steps

Iters	Range		Point
8	27.389928840129397	258888.6766231188	8415.917960713386

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	32
1	20	32

end0.0ms

analyze1.0ms

Algorithm

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
50%	50%	0%	2
50%	25%	25%	3
50%	0%	50%	4

sample1.1s

Algorithm

intervals

Results

509.0ms	1756×	body	1280	valid
226.0ms	1231×	body	640	valid
200.0ms	4065×	body	80	valid
77.0ms	634×	body	320	valid
24.0ms	314×	body	160	valid

Details

analyze2.0ms

sample39.0ms

simplify2.0ms

prune2.0ms

localize6.0ms

rewrite10.0ms

series8.0ms

simplify52.0ms

prune83.0ms

localize7.0ms

rewrite26.0ms

series12.0ms

simplify38.0ms

prune68.0ms

localize12.0ms

rewrite91.0ms

series51.0ms

simplify53.0ms

prune322.0ms

localize6.0ms

rewrite11.0ms

series8.0ms

simplify40.0ms

prune71.0ms

regimes40.0ms

bsearch19.0ms

simplify1.0ms

end0.0ms

analyze1.0ms

sample1.1s

Profiling