Details

sample42.0ms

Algorithm

intervals

Results

13.0ms	54×	body	1280	valid
6.0ms	255×	body	80	nan
6.0ms	39×	body	640	valid
5.0ms	133×	body	80	valid
2.0ms	24×	body	320	valid
0.0ms	6×	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: 29.0b

Counts

2 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

1.9b	(log (+ N 1.0))
2.9b	(- (log (+ N 1.0)) (log N))

rewrite14.0ms

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

series134.0ms

Counts

2 → 6

Calls

2 calls:

41.0ms	(log (+ N 1.0))
93.0ms	(- (log (+ N 1.0)) (log N))

simplify54.0ms

Algorithm

egg-herbie

Counts

47 → 47

Iterations

Useful iterations: 3 (50.0ms)

Iter	Nodes	Cost
0	212	281
1	547	264
2	1875	250
3	5001	247

prune89.0ms

Filtered

47 candidates to 33 candidates (70.2%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	45	2	47
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	46	2	48

Merged error: 0.0b

Counts

48 → 2

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (+ N 1.0) N)
2.9b	(log (/ (+ N 1.0) N))

rewrite12.0ms

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))

series128.0ms

Counts

2 → 6

Calls

2 calls:

45.0ms	(/ (+ N 1.0) N)
82.0ms	(log (/ (+ N 1.0) N))

simplify104.0ms

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

prune86.0ms

Filtered

66 candidates to 45 candidates (68.2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	65	1	66
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	65	3	68

Merged error: 0.0b

Counts

68 → 3

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (+ N 1.0) N)
0.0b	(log (log (/ (+ N 1.0) N)))
0.8b	(exp (log (log (/ (+ N 1.0) N))))
2.9b	(log (/ (+ N 1.0) N))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

38×	`*-un-lft-identity`
24×	`add-sqr-sqrt` `add-cube-cbrt` `log-prod` `times-frac`
10×	`add-exp-log`
9×	`pow1`
7×	`distribute-lft-out`
6×	`add-cbrt-cube`
5×	`log-pow`
4×	`exp-prod` `exp-sum` `associate-/l*` `add-log-exp`
3×	`rem-log-exp` `associate-/r*`
2×	`div-exp` `div-inv` `associate-/l/`
1×	`cbrt-undiv` `log-div` `frac-2neg` `flip3-+` `clear-num` `flip-+` `rem-exp-log`

Counts

4 → 89

Calls

4 calls:

5.0ms	(/ (+ N 1.0) N)
1.0ms	(log (log (/ (+ N 1.0) N)))
2.0ms	(exp (log (log (/ (+ N 1.0) N))))
5.0ms	(log (/ (+ N 1.0) N))

series360.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(/ (+ N 1.0) N)
147.0ms	(log (log (/ (+ N 1.0) N)))
82.0ms	(exp (log (log (/ (+ N 1.0) N))))
82.0ms	(log (/ (+ N 1.0) N))

simplify39.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	361	634
1	1261	587
2	5002	561

prune173.0ms

Filtered

101 candidates to 69 candidates (68.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	100	1	101
Fresh	0	1	1
Picked	1	0	1
Done	0	1	1
Total	101	3	104

Merged error: 0.0b

Counts

104 → 3

localize14.0ms

Local error

Found 4 expressions with local error:

0.7b	(pow (exp (* (cbrt (log (log (/ (+ N 1.0) N)))) (cbrt (log (log (/ (+ N 1.0) N)))))) (cbrt (log (log (/ (+ N 1.0) N)))))
2.9b	(log (/ (+ N 1.0) N))
2.9b	(log (/ (+ N 1.0) N))
2.9b	(log (/ (+ N 1.0) N))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

49×	`*-un-lft-identity`
48×	`log-prod`
36×	`times-frac`
31×	`add-sqr-sqrt` `add-cube-cbrt`
13×	`add-exp-log`
9×	`pow1` `distribute-lft-out`
7×	`pow-unpow`
6×	`rem-log-exp`
5×	`add-log-exp`
4×	`cbrt-prod` `log-pow` `add-cbrt-cube`
3×	`unpow-prod-down` `log-div` `pow-pow` `div-exp` `div-inv`
1×	`pow-to-exp` `exp-prod` `exp-to-pow` `pow-exp` `sqr-pow`

Counts

4 → 104

Calls

4 calls:

6.0ms	(pow (exp (* (cbrt (log (log (/ (+ N 1.0) N)))) (cbrt (log (log (/ (+ N 1.0) N)))))) (cbrt (log (log (/ (+ N 1.0) N)))))
5.0ms	(log (/ (+ N 1.0) N))
4.0ms	(log (/ (+ N 1.0) N))
4.0ms	(log (/ (+ N 1.0) N))

series890.0ms

Counts

4 → 12

Calls

4 calls:

643.0ms	(pow (exp (* (cbrt (log (log (/ (+ N 1.0) N)))) (cbrt (log (log (/ (+ N 1.0) N)))))) (cbrt (log (log (/ (+ N 1.0) N)))))
82.0ms	(log (/ (+ N 1.0) N))
83.0ms	(log (/ (+ N 1.0) N))
83.0ms	(log (/ (+ N 1.0) N))

simplify99.0ms

Algorithm

egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 2 (83.0ms)

Iter	Nodes	Cost
0	851	1715
1	4278	1615
2	5001	1609

prune371.0ms

Filtered

116 candidates to 82 candidates (70.7%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	115	1	116
Fresh	0	1	1
Picked	1	0	1
Done	0	1	1
Total	116	3	119

Merged error: 0.0b

Counts

119 → 3

regimes25.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 28.9b

bsearch26.0ms

Steps

Iters	Range		Point
8	573.0632436401448	2027774.326345067	7702.708028507434

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	10
1	24	10

end0.0ms

sample1.3s

Algorithm

intervals

Results

417.0ms	1701×	body	1280	valid
194.0ms	7950×	body	80	nan
193.0ms	1241×	body	640	valid
173.0ms	4150×	body	80	valid
63.0ms	614×	body	320	valid
18.0ms	294×	body	160	valid