Details

sample43.0ms

Algorithm

intervals

Results

16.0ms	67×	body	1280	valid
5.0ms	240×	body	80	nan
5.0ms	128×	body	80	valid
5.0ms	32×	body	640	valid
2.0ms	23×	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

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.4b

localize7.0ms

Local error

Found 2 expressions with local error:

2.0b	(log (+ N 1.0))
2.4b	(- (log (+ N 1.0)) (log N))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

22×	`*-un-lft-identity`
16×	`pow1` `add-sqr-sqrt` `prod-diff`
14×	`add-cube-cbrt` `log-pow`
11×	`log-prod`
4×	`log-div` `fma-neg` `associate--l+` `distribute-lft-out--`
3×	`add-exp-log` `associate--r+`
2×	`associate--l-` `expm1-log1p-u` `flip3-+` `add-cbrt-cube` `flip-+` `log1p-expm1-u` `distribute-lft-out` `add-log-exp`
1×	`sub-neg` `flip3--` `diff-log` `rem-log-exp` `flip--` `difference-of-squares`

Counts

2 → 65

Calls

2 calls:

3.0ms	(log (+ N 1.0))
11.0ms	(- (log (+ N 1.0)) (log N))

series131.0ms

Counts

2 → 6

Calls

2 calls:

39.0ms	(log (+ N 1.0))
92.0ms	(- (log (+ N 1.0)) (log N))

simplify123.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 3 (117.0ms)

Iter	Nodes	Cost
0	277	598
1	837	444
2	3748	347
3	5001	343

prune130.0ms

Filtered

71 candidates to 43 candidates (60.6%)

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (+ N 1.0) N)
2.3b	(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×	`expm1-log1p-u` `div-exp` `rem-log-exp` `log1p-expm1-u` `div-inv` `associate-/l/` `add-log-exp`
1×	`cbrt-undiv` `log-div` `frac-2neg` `flip3-+` `clear-num` `log-pow` `flip-+`

Counts

2 → 64

Calls

2 calls:

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

series132.0ms

Counts

2 → 6

Calls

2 calls:

50.0ms	(/ (+ N 1.0) N)
82.0ms	(log (/ (+ N 1.0) N))

simplify107.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 3 (101.0ms)

Iter	Nodes	Cost
0	243	383
1	808	358
2	3663	347
3	5001	344

prune123.0ms

Filtered

70 candidates to 50 candidates (71.4%)

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize7.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (/ (+ N 1.0) N))
0.1b	(sqrt (/ (+ N 1.0) N))
2.3b	(log (sqrt (/ (+ N 1.0) N)))
2.3b	(log (sqrt (/ (+ N 1.0) N)))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

64×	`sqrt-prod`
62×	`*-un-lft-identity`
50×	`times-frac`
44×	`add-sqr-sqrt`
38×	`add-cube-cbrt` `log-prod`
12×	`distribute-lft-out`
10×	`pow1`
6×	`add-exp-log` `log-pow`
4×	`expm1-log1p-u` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `sqrt-div` `add-cbrt-cube` `log1p-expm1-u` `div-inv` `add-log-exp`
2×	`log-div` `rem-log-exp`

Counts

4 → 126

Calls

4 calls:

5.0ms	(sqrt (/ (+ N 1.0) N))
5.0ms	(sqrt (/ (+ N 1.0) N))
5.0ms	(log (sqrt (/ (+ N 1.0) N)))
6.0ms	(log (sqrt (/ (+ N 1.0) N)))

series335.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(sqrt (/ (+ N 1.0) N))
42.0ms	(sqrt (/ (+ N 1.0) N))
124.0ms	(log (sqrt (/ (+ N 1.0) N)))
120.0ms	(log (sqrt (/ (+ N 1.0) N)))

simplify66.0ms

Algorithm

egg-herbie

Counts

138 → 138

Iterations

Useful iterations: 3 (55.0ms)

Iter	Nodes	Cost
0	205	1000
1	482	936
2	1903	904
3	5001	886

prune336.0ms

Filtered

138 candidates to 102 candidates (73.9%)

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sqrt (+ N 1.0)) (sqrt N))
2.3b	(log (sqrt (/ (+ N 1.0) N)))
2.4b	(log (sqrt (/ (sqrt (+ N 1.0)) (sqrt N))))
2.4b	(log (sqrt (/ (sqrt (+ N 1.0)) (sqrt N))))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

250×	`sqrt-prod`
143×	`*-un-lft-identity`
138×	`times-frac`
117×	`log-prod`
99×	`add-sqr-sqrt` `add-cube-cbrt`
22×	`distribute-lft-out`
10×	`pow1`
9×	`add-exp-log` `log-pow`
7×	`associate-/l*`
6×	`associate-/r*` `add-cbrt-cube`
5×	`sqrt-div`
4×	`expm1-log1p-u` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`log-div` `sqrt-pow1` `pow1/2` `rem-log-exp`
2×	`associate-/l/`
1×	`cbrt-undiv` `sqrt-undiv` `frac-2neg` `flip3-+` `div-exp` `clear-num` `flip-+`

Counts

4 → 231

Calls

4 calls:

7.0ms	(/ (sqrt (+ N 1.0)) (sqrt N))
6.0ms	(log (sqrt (/ (+ N 1.0) N)))
9.0ms	(log (sqrt (/ (sqrt (+ N 1.0)) (sqrt N))))
9.0ms	(log (sqrt (/ (sqrt (+ N 1.0)) (sqrt N))))

series600.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(/ (sqrt (+ N 1.0)) (sqrt N))
127.0ms	(log (sqrt (/ (+ N 1.0) N)))
203.0ms	(log (sqrt (/ (sqrt (+ N 1.0)) (sqrt N))))
207.0ms	(log (sqrt (/ (sqrt (+ N 1.0)) (sqrt N))))

simplify64.0ms

Algorithm

egg-herbie

Counts

243 → 243

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	585	2754
1	1691	2641
2	5001	2517

prune663.0ms

Filtered

243 candidates to 134 candidates (55.1%)

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

regimes27.0ms

Accuracy

99.9% (0.0b remaining)

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

bsearch35.0ms

Steps

Iters	Range		Point
8	136.14768989527596	514944.2915634037	6821.280985723192

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	28
1	36	28

end0.0ms

sample1.2s

Algorithm

intervals

Results

434.0ms	1764×	body	1280	valid
193.0ms	1305×	body	640	valid
184.0ms	7943×	body	80	nan
162.0ms	4051×	body	80	valid
59.0ms	610×	body	320	valid
16.0ms	270×	body	160	valid