Details

sample57.0ms

Algorithm

intervals

Results

20.0ms	64×	body	1280	valid
9.0ms	268×	body	80	nan
7.0ms	33×	body	640	valid
7.0ms	118×	body	80	valid
4.0ms	31×	body	320	valid
1.0ms	10×	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: 32.3b

localize7.0ms

Local error

Found 2 expressions with local error:

2.0b	(log (+ N 1.0))
3.4b	(- (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:

2.0ms	(log (+ N 1.0))
11.0ms	(- (log (+ N 1.0)) (log N))

series135.0ms

Counts

2 → 6

Calls

2 calls:

40.0ms	(log (+ N 1.0))
94.0ms	(- (log (+ N 1.0)) (log N))

simplify121.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 3 (115.0ms)

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

prune131.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 2 expressions with local error:

0.1b	(fma (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5) (/ 1.0 N))
0.2b	(/ 1 (pow N 2))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

24×	`times-frac`
19×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
12×	`unpow-prod-down`
11×	`add-exp-log`
8×	`associate-/r*`
6×	`div-exp`
4×	`add-cbrt-cube` `unpow2` `sqr-pow`
3×	`pow-to-exp` `rec-exp` `1-exp` `pow-exp` `associate-/l*`
2×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
1×	`cbrt-undiv` `pow-flip` `frac-2neg` `clear-num` `fma-udef` `div-inv` `inv-pow`

Counts

2 → 69

Calls

2 calls:

0.0ms	(fma (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5) (/ 1.0 N))
4.0ms	(/ 1 (pow N 2))

series54.0ms

Counts

2 → 6

Calls

2 calls:

37.0ms	(fma (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5) (/ 1.0 N))
16.0ms	(/ 1 (pow N 2))

simplify32.0ms

Algorithm

egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 2 (26.0ms)

Iter	Nodes	Cost
0	208	384
1	789	315
2	5001	269

prune95.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (+ N 1.0) N)
3.6b	(log (/ (+ N 1.0) N))

rewrite13.0ms

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:

8.0ms	(/ (+ N 1.0) N)
3.0ms	(log (/ (+ N 1.0) N))

series129.0ms

Counts

2 → 6

Calls

2 calls:

46.0ms	(/ (+ N 1.0) N)
84.0ms	(log (/ (+ N 1.0) N))

simplify102.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 3 (97.0ms)

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

prune126.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt N)
0.6b	(cbrt N)
0.6b	(cbrt N)
22.3b	(log (/ (/ (+ N 1.0) (* (cbrt N) (cbrt N))) (cbrt N)))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

72×	`times-frac`
52×	`log-prod`
48×	`*-un-lft-identity`
36×	`add-sqr-sqrt` `add-cube-cbrt`
33×	`cbrt-prod`
14×	`add-exp-log`
7×	`div-inv`
6×	`distribute-lft-out`
5×	`pow1` `div-exp`
4×	`expm1-log1p-u` `rem-log-exp` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`
1×	`log-div` `prod-exp` `log-pow`

Counts

4 → 106

Calls

4 calls:

0.0ms	(cbrt N)
0.0ms	(cbrt N)
0.0ms	(cbrt N)
9.0ms	(log (/ (/ (+ N 1.0) (* (cbrt N) (cbrt N))) (cbrt N)))

series636.0ms

Counts

4 → 12

Calls

4 calls:

180.0ms	(cbrt N)
174.0ms	(cbrt N)
185.0ms	(cbrt N)
96.0ms	(log (/ (/ (+ N 1.0) (* (cbrt N) (cbrt N))) (cbrt N)))

simplify42.0ms

Algorithm

egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	437	1139
1	1390	1097
2	5001	1044

prune314.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

regimes19.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 32.1b

bsearch37.0ms

Steps

Iters	Range		Point
8	21.02059315853866	376494.23081693525	5490.275945865693

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	16
1	27	16

end0.0ms

sample1.6s

Algorithm

intervals

Results

542.0ms	1727×	body	1280	valid
266.0ms	7862×	body	80	nan
254.0ms	1196×	body	640	valid
232.0ms	4138×	body	80	valid
88.0ms	646×	body	320	valid
25.0ms	293×	body	160	valid