Details

analyze1.0ms (0.1%)

Algorithm

1×

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

sample48.0ms (2%)

Algorithm

1×

intervals

Results

16.0ms	54×	body	1280	valid
12.0ms	118×	body	80	valid
10.0ms	47×	body	640	valid
3.0ms	23×	body	320	valid
1.0ms	14×	body	160	valid

simplify5.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	71	7
1	71	7

prune5.0ms (0.2%)

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: 32.4b

Counts

2 → 1

localize7.0ms (0.3%)

Local error

Found 2 expressions with local error:

3.5b	(- (log (+ N 1.0)) (log N))
4.2b	(log (+ N 1.0))

rewrite11.0ms (0.4%)

Algorithm

1×	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))

series10.0ms (0.4%)

Counts

2 → 6

Calls

2 calls:

6.0ms	(- (log (+ N 1.0)) (log N))
4.0ms	(log (+ N 1.0))

simplify41.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

46 → 46

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5481	434

prune93.0ms (3.8%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	44	2	46
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	45	2	47

Merged error: 0.0b

Counts

47 → 2

localize10.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(+ (/ 1.0 N) (/ 0.3333333333333333 (pow N 3)))
0.1b	(/ 0.3333333333333333 (pow N 3))
0.4b	(/ 0.5 (* N N))
10.8b	(- (+ (/ 1.0 N) (/ 0.3333333333333333 (pow N 3))) (/ 0.5 (* N N)))

rewrite72.0ms (3%)

Algorithm

1×	rewrite-expression-head

Rules

42×	`*-un-lft-identity` `times-frac`
35×	`add-sqr-sqrt`
31×	`add-cube-cbrt`
14×	`add-exp-log`
13×	`associate-/r*`
12×	`unpow-prod-down` `cube-prod`
11×	`add-cbrt-cube` `add-log-exp`
6×	`associate-/l*`
5×	`div-exp`
4×	`pow1` `cube-mult` `unpow3` `sqr-pow`
3×	`cbrt-undiv` `frac-sub` `distribute-lft-out`
2×	`frac-2neg` `flip3-+` `diff-log` `frac-add` `clear-num` `sum-log` `flip-+` `div-inv` `distribute-lft-out--` `difference-of-squares`
1×	`+-commutative` `pow-to-exp` `sub-neg` `flip3--` `pow-exp` `prod-exp` `associate--l+` `flip--` `cbrt-unprod`

Counts

4 → 120

Calls

4 calls:

31.0ms	(- (+ (/ 1.0 N) (/ 0.3333333333333333 (pow N 3))) (/ 0.5 (* N N)))
26.0ms	(+ (/ 1.0 N) (/ 0.3333333333333333 (pow N 3)))
7.0ms	(/ 0.3333333333333333 (pow N 3))
5.0ms	(/ 0.5 (* N N))

series19.0ms (0.8%)

Counts

4 → 12

Calls

4 calls:

8.0ms	(+ (/ 1.0 N) (/ 0.3333333333333333 (pow N 3)))
5.0ms	(- (+ (/ 1.0 N) (/ 0.3333333333333333 (pow N 3))) (/ 0.5 (* N N)))
4.0ms	(/ 0.3333333333333333 (pow N 3))
3.0ms	(/ 0.5 (* N N))

simplify48.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5000	1465

prune228.0ms (9.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	131	1	132
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	131	3	134

Merged error: 0.0b

Counts

134 → 3

localize7.0ms (0.3%)

Local error

Found 2 expressions with local error:

0.0b	(/ (+ N 1.0) N)
3.7b	(log (/ (+ N 1.0) N))

rewrite12.0ms (0.5%)

Algorithm

1×	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))

series9.0ms (0.4%)

Counts

2 → 6

Calls

2 calls:

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

simplify43.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	4970	619
1	4970	619

prune100.0ms (4.1%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	65	1	66
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	65	4	69

Merged error: 0.0b

Counts

69 → 4

localize9.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.3b	(cbrt (log (/ (+ N 1.0) N)))
3.7b	(log (/ (+ N 1.0) N))
3.7b	(log (/ (+ N 1.0) N))
3.7b	(log (/ (+ N 1.0) N))

rewrite18.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

48×	`log-prod`
47×	`*-un-lft-identity`
36×	`times-frac`
29×	`add-sqr-sqrt` `add-cube-cbrt`
13×	`add-exp-log`
9×	`distribute-lft-out`
8×	`pow1`
6×	`rem-log-exp`
4×	`cbrt-prod` `log-pow` `add-cbrt-cube` `add-log-exp`
3×	`log-div` `div-exp` `div-inv`
1×	`pow1/3`

Counts

4 → 93

Calls

4 calls:

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

series25.0ms (1%)

Counts

4 → 12

Calls

4 calls:

13.0ms	(cbrt (log (/ (+ N 1.0) N)))
4.0ms	(log (/ (+ N 1.0) N))
4.0ms	(log (/ (+ N 1.0) N))
4.0ms	(log (/ (+ N 1.0) N))

simplify75.0ms (3.1%)

Algorithm

1×	egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	4962	1183
1	4962	1183

prune301.0ms (12.3%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	104	1	105
Fresh	0	1	1
Picked	1	0	1
Done	0	2	2
Total	105	4	109

Merged error: 0b

Counts

109 → 4

regimes36.0ms (1.5%)

Accuracy

Total 0.0b remaining (5%)

Threshold costs 0.0b (5%)

bsearch14.0ms (0.6%)

Steps

Iters	Range		Point
8	46.411787995442566	414138.19612384395	7834.05326038219

simplify1.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	37	25
1	37	25

end0.0ms (0%)

sample1.2s (48.9%)

Algorithm

1×

intervals

Results

522.0ms	1739×	body	1280	valid
246.0ms	1272×	body	640	valid
212.0ms	4081×	body	80	valid
83.0ms	602×	body	320	valid
25.0ms	306×	body	160	valid

Details

analyze1.0ms (0.1%)

sample48.0ms (2%)

simplify5.0ms (0.2%)

prune5.0ms (0.2%)

localize7.0ms (0.3%)

rewrite11.0ms (0.4%)

series10.0ms (0.4%)

simplify41.0ms (1.7%)

prune93.0ms (3.8%)

localize10.0ms (0.4%)

rewrite72.0ms (3%)

series19.0ms (0.8%)

simplify48.0ms (1.9%)

prune228.0ms (9.3%)

localize7.0ms (0.3%)

rewrite12.0ms (0.5%)

series9.0ms (0.4%)

simplify43.0ms (1.8%)

prune100.0ms (4.1%)

localize9.0ms (0.4%)

rewrite18.0ms (0.8%)

series25.0ms (1%)

simplify75.0ms (3.1%)

prune301.0ms (12.3%)

regimes36.0ms (1.5%)

bsearch14.0ms (0.6%)

simplify1.0ms (0.1%)

end0.0ms (0%)

sample1.2s (48.9%)

Profiling