Details

sample40.0ms

Algorithm

intervals

Results

10.0ms	41×	body	1280	valid
7.0ms	45×	body	640	valid
6.0ms	149×	body	80	valid
6.0ms	248×	body	80	nan
2.0ms	19×	body	320	valid
0.0ms	2×	body	160	valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

prune2.0ms

Filtered

1 candidates to 0 candidates (0.0%)

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: 25.4b

Counts

2 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

1.2b	(- (log (+ N 1.0)) (log N))
2.0b	(log (+ N 1.0))

rewrite11.0ms

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:

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

series134.0ms

Counts

2 → 6

Calls

2 calls:

90.0ms	(- (log (+ N 1.0)) (log N))
44.0ms	(log (+ N 1.0))

simplify55.0ms

Algorithm

egg-herbie

Counts

47 → 47

Iterations

Useful iterations: 3 (51.0ms)

Iter	Nodes	Cost
0	212	281
1	547	264
2	1874	250
3	5001	247

prune95.0ms

Filtered

47 candidates to 33 candidates (70.2%)

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: 0.0b

Counts

48 → 3

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (+ N 1.0) N)
1.4b	(log (/ (+ N 1.0) N))

rewrite15.0ms

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:

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

series126.0ms

Counts

2 → 6

Calls

2 calls:

44.0ms	(/ (+ N 1.0) N)
82.0ms	(log (/ (+ N 1.0) N))

simplify103.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 2 (21.0ms)

Iter	Nodes	Cost
0	233	373
1	773	351
2	3489	339
3	5002	339

prune96.0ms

Filtered

66 candidates to 45 candidates (68.2%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	64	2	66
Fresh	0	2	2
Picked	1	0	1
Done	0	0	0
Total	65	4	69

Merged error: 0.0b

Counts

69 → 4

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(log (log (+ N 1.0)))
0.6b	(exp (log (log (+ N 1.0))))
2.0b	(log (+ N 1.0))
21.8b	(- (exp (log (log (+ N 1.0)))) (log N))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 63

Calls

4 calls:

1.0ms	(log (log (+ N 1.0)))
2.0ms	(exp (log (log (+ N 1.0))))
3.0ms	(log (+ N 1.0))
7.0ms	(- (exp (log (log (+ N 1.0)))) (log N))

series261.0ms

Counts

4 → 12

Calls

4 calls:

86.0ms	(log (log (+ N 1.0)))
40.0ms	(exp (log (log (+ N 1.0))))
44.0ms	(log (+ N 1.0))
92.0ms	(- (exp (log (log (+ N 1.0)))) (log N))

simplify118.0ms

Algorithm

egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 3 (111.0ms)

Iter	Nodes	Cost
0	355	529
1	1074	481
2	4439	443
3	5002	427

prune143.0ms

Filtered

75 candidates to 52 candidates (69.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	75	0	75
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	75	4	79

Merged error: 0.0b

Counts

79 → 4

localize8.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (/ (+ N 1.0) N))
0.5b	(cbrt (/ (+ N 1.0) N))
1.1b	(log (cbrt (/ (+ N 1.0) N)))
1.1b	(log (cbrt (/ (+ N 1.0) N)))

rewrite27.0ms

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:

7.0ms	(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)))

series670.0ms

Counts

4 → 12

Calls

4 calls:

130.0ms	(cbrt (/ (+ N 1.0) N))
123.0ms	(cbrt (/ (+ N 1.0) N))
212.0ms	(log (cbrt (/ (+ N 1.0) N)))
205.0ms	(log (cbrt (/ (+ N 1.0) N)))

simplify109.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 3 (97.0ms)

Iter	Nodes	Cost
0	267	1056
1	755	996
2	3236	966
3	5001	948

prune304.0ms

Filtered

122 candidates to 94 candidates (77.0%)

Pruning

5 alts after pruning (3 fresh and 2 done)

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

Merged error: 0.0b

Counts

126 → 5

regimes30.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 29.7b

bsearch32.0ms

Steps

Iters	Range		Point
9	164.2181510969774	3048118974.682059	4180.675942041932

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	13
1	27	13

end0.0ms

sample1.2s

Algorithm

intervals

Results

416.0ms	1714×	body	1280	valid
187.0ms	1248×	body	640	valid
183.0ms	7900×	body	80	nan
171.0ms	4108×	body	80	valid
60.0ms	630×	body	320	valid
18.0ms	300×	body	160	valid