Details

sample44.0ms

Algorithm

intervals

Results

13.0ms	52×	body	1280	valid
6.0ms	237×	body	80	nan
5.0ms	130×	body	80	valid
5.0ms	34×	body	640	valid
3.0ms	26×	body	320	valid
1.0ms	14×	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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.5b

localize7.0ms

Local error

Found 2 expressions with local error:

2.6b	(log (+ N 1.0))
3.9b	(- (log (+ N 1.0)) (log N))

rewrite21.0ms

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:

4.0ms	(log (+ N 1.0))
14.0ms	(- (log (+ N 1.0)) (log N))

series143.0ms

Counts

2 → 6

Calls

2 calls:

45.0ms	(log (+ N 1.0))
98.0ms	(- (log (+ N 1.0)) (log N))

simplify123.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 3 (118.0ms)

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

prune129.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (+ N 1.0) N)
3.8b	(log (/ (+ N 1.0) N))

rewrite28.0ms

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:

20.0ms	(/ (+ N 1.0) N)
6.0ms	(log (/ (+ N 1.0) N))

series135.0ms

Counts

2 → 6

Calls

2 calls:

50.0ms	(/ (+ N 1.0) N)
85.0ms	(log (/ (+ N 1.0) N))

simplify104.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 3 (99.0ms)

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

prune123.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize8.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sqrt (+ N 1.0)) (sqrt N))
0.1b	(/ (sqrt (+ N 1.0)) (sqrt N))
3.8b	(log (/ (sqrt (+ N 1.0)) (sqrt N)))
3.8b	(log (/ (sqrt (+ N 1.0)) (sqrt N)))

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

194×	`sqrt-prod`
170×	`*-un-lft-identity`
168×	`times-frac`
118×	`add-sqr-sqrt` `add-cube-cbrt`
92×	`log-prod`
26×	`distribute-lft-out`
14×	`add-exp-log` `associate-/l*`
12×	`associate-/r*`
8×	`add-cbrt-cube`
6×	`pow1`
4×	`expm1-log1p-u` `sqrt-div` `div-exp` `rem-log-exp` `log1p-expm1-u` `div-inv` `associate-/l/` `add-log-exp`
2×	`cbrt-undiv` `log-div` `sqrt-undiv` `frac-2neg` `flip3-+` `clear-num` `log-pow` `flip-+`

Counts

4 → 262

Calls

4 calls:

19.0ms	(/ (sqrt (+ N 1.0)) (sqrt N))
17.0ms	(/ (sqrt (+ N 1.0)) (sqrt N))
9.0ms	(log (/ (sqrt (+ N 1.0)) (sqrt N)))
9.0ms	(log (/ (sqrt (+ N 1.0)) (sqrt N)))

series380.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(/ (sqrt (+ N 1.0)) (sqrt N))
59.0ms	(/ (sqrt (+ N 1.0)) (sqrt N))
132.0ms	(log (/ (sqrt (+ N 1.0)) (sqrt N)))
125.0ms	(log (/ (sqrt (+ N 1.0)) (sqrt N)))

simplify51.0ms

Algorithm

egg-herbie

Counts

274 → 274

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	389	2712
1	1182	2592
2	5001	2440

prune521.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sqrt (sqrt (+ N 1.0))) (sqrt (sqrt N)))
3.8b	(log (/ (sqrt (+ N 1.0)) (sqrt N)))
3.9b	(log (/ (sqrt (sqrt (+ N 1.0))) (sqrt (sqrt N))))
3.9b	(log (/ (sqrt (sqrt (+ N 1.0))) (sqrt (sqrt N))))

rewrite88.0ms

Algorithm

rewrite-expression-head

Rules

632×	`sqrt-prod`
312×	`times-frac`
278×	`*-un-lft-identity`
234×	`log-prod`
210×	`add-sqr-sqrt` `add-cube-cbrt`
34×	`distribute-lft-out`
15×	`add-exp-log`
10×	`associate-/l*`
9×	`associate-/r*`
7×	`pow1`
6×	`rem-log-exp` `add-cbrt-cube`
4×	`expm1-log1p-u` `sqrt-div` `div-exp` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`log-div` `log-pow`
2×	`associate-/l/`
1×	`cbrt-undiv` `sqrt-undiv` `frac-2neg` `flip3-+` `clear-num` `flip-+`

Counts

4 → 399

Calls

4 calls:

21.0ms	(/ (sqrt (sqrt (+ N 1.0))) (sqrt (sqrt N)))
9.0ms	(log (/ (sqrt (+ N 1.0)) (sqrt N)))
13.0ms	(log (/ (sqrt (sqrt (+ N 1.0))) (sqrt (sqrt N))))
17.0ms	(log (/ (sqrt (sqrt (+ N 1.0))) (sqrt (sqrt N))))

series696.0ms

Counts

4 → 12

Calls

4 calls:

139.0ms	(/ (sqrt (sqrt (+ N 1.0))) (sqrt (sqrt N)))
133.0ms	(log (/ (sqrt (+ N 1.0)) (sqrt N)))
210.0ms	(log (/ (sqrt (sqrt (+ N 1.0))) (sqrt (sqrt N))))
214.0ms	(log (/ (sqrt (sqrt (+ N 1.0))) (sqrt (sqrt N))))

simplify111.0ms

Algorithm

egg-herbie

Counts

411 → 411

Iterations

Useful iterations: 2 (69.0ms)

Iter	Nodes	Cost
0	896	6046
1	2885	5869
2	5001	5531

prune866.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

regimes24.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 29.8b

bsearch27.0ms

Steps

Iters	Range		Point
8	26.826342714152005	112870.16560235518	8116.362270388288

simplify5.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	17
1	24	17

end0.0ms

sample1.4s

Algorithm

intervals

Results

442.0ms	1763×	body	1280	valid
198.0ms	1275×	body	640	valid
193.0ms	8191×	body	80	nan
171.0ms	4026×	body	80	valid
67.0ms	641×	body	320	valid
19.0ms	295×	body	160	valid