Details

analyze1.0ms

Algorithm

sampling

Space saved by range analysis: 0.048828%

Space saved by search: 50.024414%

Guaranteed chance to sample good point: 100%

sample36.0ms

Algorithm

intervals

Results

14.0ms	48×	body	1280	valid
7.0ms	136×	body	80	valid
6.0ms	34×	body	640	valid
3.0ms	24×	body	320	valid
1.0ms	14×	body	160	valid

simplify4.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	9	4
1	10	4
2	10	4

prune3.0ms

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: 28.7b

Counts

2 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

3.5b	(log (+ N 1.0))
4.7b	(- (log (+ N 1.0)) (log N))

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 → 41

Calls

2 calls:

3.0ms	(log (+ N 1.0))
6.0ms	(- (log (+ N 1.0)) (log N))

series10.0ms

Counts

2 → 6

Calls

2 calls:

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

simplify56.0ms

Algorithm

egg-herbie

Counts

47 → 47

Iterations

Useful iterations: 2 (14.0ms)

Iter	Nodes	Cost
0	232	285
1	628	264
2	2171	244
3	5001	244

prune88.0ms

Filtered

34 candidates to 47 candidates (-38.2%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	44	3	47
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	45	3	48

Merged error: 0.1b

Counts

48 → 3

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (+ N 1.0) N)
4.6b	(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))

simplify92.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 2 (18.0ms)

Iter	Nodes	Cost
0	221	370
1	736	343
2	3220	333
3	5002	333

prune85.0ms

Filtered

46 candidates to 66 candidates (-43.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	65	1	66
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	65	4	69

Merged error: 0.1b

Counts

69 → 4

localize9.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (/ (+ N 1.0) N))
0.3b	(cbrt (/ (+ N 1.0) N))
4.7b	(log (cbrt (/ (+ N 1.0) N)))
4.7b	(log (cbrt (/ (+ N 1.0) N)))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

64×	`cbrt-prod`
62×	`*-un-lft-identity`
48×	`times-frac`
38×	`add-sqr-sqrt` `add-cube-cbrt` `log-prod`
12×	`distribute-lft-out`
6×	`pow1` `add-exp-log`
4×	`cbrt-div` `pow1/3` `log-pow` `add-cbrt-cube` `div-inv` `add-log-exp`
2×	`log-div` `rem-log-exp`

Counts

4 → 110

Calls

4 calls:

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

series37.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(cbrt (/ (+ N 1.0) N))
8.0ms	(cbrt (/ (+ N 1.0) N))
9.0ms	(log (cbrt (/ (+ N 1.0) N)))
11.0ms	(log (cbrt (/ (+ N 1.0) N)))

simplify110.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 2 (21.0ms)

Iter	Nodes	Cost
0	261	1042
1	782	972
2	3437	942
3	5002	942

prune273.0ms

Filtered

94 candidates to 122 candidates (-29.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	120	2	122
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	121	5	126

Merged error: 0.1b

Counts

126 → 5

localize16.0ms

Local error

Found 4 expressions with local error:

3.5b	(log (+ N 1.0))
3.5b	(log (+ N 1.0))
3.5b	(log (+ N 1.0))
4.7b	(- (pow (log (+ N 1.0)) 3) (pow (log N) 3))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-sqr-sqrt` `*-un-lft-identity`
24×	`unpow-prod-down` `cube-prod`
23×	`pow1`
19×	`log-pow`
17×	`distribute-lft-out--`
16×	`difference-of-squares`
12×	`log-prod`
8×	`sqr-pow`
7×	`add-exp-log` `add-cube-cbrt`
6×	`log-div` `add-log-exp`
4×	`add-cbrt-cube`
3×	`flip3-+` `rem-log-exp` `flip-+` `distribute-lft-out`
1×	`difference-cubes` `sub-neg` `flip3--` `diff-log` `flip--`

Counts

4 → 91

Calls

4 calls:

3.0ms	(log (+ N 1.0))
3.0ms	(log (+ N 1.0))
3.0ms	(log (+ N 1.0))
16.0ms	(- (pow (log (+ N 1.0)) 3) (pow (log N) 3))

series32.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(log (+ N 1.0))
3.0ms	(log (+ N 1.0))
3.0ms	(log (+ N 1.0))
23.0ms	(- (pow (log (+ N 1.0)) 3) (pow (log N) 3))

simplify61.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	614	957
1	2326	913
2	5001	895

prune230.0ms

Filtered

66 candidates to 103 candidates (-56.1%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	102	1	103
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	102	6	108

Merged error: 0.1b

Counts

108 → 6

Details

analyze1.0ms

sample36.0ms

simplify4.0ms

prune3.0ms

localize6.0ms

rewrite10.0ms

series10.0ms

simplify56.0ms

prune88.0ms

localize5.0ms

rewrite11.0ms

series8.0ms

simplify92.0ms

prune85.0ms

localize9.0ms

rewrite22.0ms

series37.0ms

simplify110.0ms

prune273.0ms

localize16.0ms

rewrite28.0ms

series32.0ms

simplify61.0ms

prune230.0ms

regimes63.0ms

bsearch1.0ms

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