Details

sample44.0ms

Algorithm

intervals

Results

12.0ms	50×	body	1280	valid
8.0ms	233×	body	80	nan
6.0ms	39×	body	640	valid
5.0ms	130×	body	80	valid
2.0ms	21×	body	320	valid
1.0ms	16×	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: 29.2b

localize7.0ms

Local error

Found 2 expressions with local error:

1.2b	(log (+ N 1.0))
3.8b	(- (log (+ N 1.0)) (log N))

rewrite13.0ms

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))
8.0ms	(- (log (+ N 1.0)) (log N))

series137.0ms

Counts

2 → 6

Calls

2 calls:

45.0ms	(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

prune127.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize16.0ms

Local error

Found 4 expressions with local error:

1.2b	(log (+ N 1.0))
1.2b	(log (+ N 1.0))
1.2b	(log (+ N 1.0))
3.8b	(- (pow (log (+ N 1.0)) 3) (pow (log N) 3))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

196×	`prod-diff`
140×	`unpow-prod-down` `cube-prod`
118×	`add-sqr-sqrt` `*-un-lft-identity`
94×	`add-cube-cbrt`
81×	`pow1`
77×	`log-pow`
37×	`sqr-pow`
29×	`cube-mult` `unpow3`
17×	`distribute-lft-out--`
16×	`difference-of-squares`
14×	`fma-neg`
12×	`log-prod`
7×	`add-exp-log`
6×	`log-div` `add-log-exp`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`flip3-+` `rem-log-exp` `flip-+` `distribute-lft-out`
1×	`difference-cubes` `sub-neg` `flip3--` `diff-log` `flip--`

Counts

4 → 309

Calls

4 calls:

3.0ms	(log (+ N 1.0))
6.0ms	(log (+ N 1.0))
3.0ms	(log (+ N 1.0))
18.0ms	(- (pow (log (+ N 1.0)) 3) (pow (log N) 3))

series322.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(log (+ N 1.0))
41.0ms	(log (+ N 1.0))
45.0ms	(log (+ N 1.0))
190.0ms	(- (pow (log (+ N 1.0)) 3) (pow (log N) 3))

simplify120.0ms

Algorithm

egg-herbie

Counts

321 → 321

Iterations

Useful iterations: 2 (81.0ms)

Iter	Nodes	Cost
0	789	4321
1	2843	3063
2	5002	3061

prune371.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (+ N 1.0) N)
3.9b	(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×	`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:

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

series135.0ms

Counts

2 → 6

Calls

2 calls:

52.0ms	(/ (+ N 1.0) N)
83.0ms	(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

prune138.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.1b

localize14.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt N)
0.6b	(cbrt N)
0.6b	(cbrt N)
5.1b	(+ (log (/ (sqrt (+ N 1.0)) (* (cbrt N) (cbrt N)))) (log (/ (sqrt (+ N 1.0)) (cbrt N))))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

57×	`log-prod`
56×	`*-un-lft-identity`
49×	`times-frac`
46×	`associate-+r+`
38×	`add-sqr-sqrt` `add-cube-cbrt`
30×	`cbrt-prod`
28×	`sqrt-prod`
11×	`associate-+l+` `distribute-lft-out`
9×	`pow1`
5×	`log-pow`
4×	`add-exp-log` `expm1-log1p-u` `fma-def` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`
2×	`log-div` `div-inv`
1×	`+-commutative` `associate-+l-` `associate-+r-` `flip3-+` `sum-log` `flip-+`

Counts

4 → 119

Calls

4 calls:

1.0ms	(cbrt N)
1.0ms	(cbrt N)
1.0ms	(cbrt N)
19.0ms	(+ (log (/ (sqrt (+ N 1.0)) (* (cbrt N) (cbrt N)))) (log (/ (sqrt (+ N 1.0)) (cbrt N))))

series800.0ms

Counts

4 → 12

Calls

4 calls:

188.0ms	(cbrt N)
183.0ms	(cbrt N)
182.0ms	(cbrt N)
246.0ms	(+ (log (/ (sqrt (+ N 1.0)) (* (cbrt N) (cbrt N)))) (log (/ (sqrt (+ N 1.0)) (cbrt N))))

simplify50.0ms

Algorithm

egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	515	1353
1	1641	1284
2	5001	1181

prune368.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

regimes36.0ms

Accuracy

99.5% (0.1b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 29.1b

bsearch32.0ms

Steps

Iters	Range		Point
8	6793.132116615613	39135938.24223837	7693.698204215917

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	30	19
1	30	19

end0.0ms

sample1.2s

Algorithm

intervals

Results

416.0ms	1731×	body	1280	valid
192.0ms	8115×	body	80	nan
181.0ms	1199×	body	640	valid
169.0ms	4132×	body	80	valid
58.0ms	600×	body	320	valid
21.0ms	338×	body	160	valid