Details

sample46.0ms

Algorithm

intervals

Results

18.0ms	60×	body	1280	valid
6.0ms	254×	body	80	nan
6.0ms	40×	body	640	valid
5.0ms	122×	body	80	valid
2.0ms	20×	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: 31.6b

localize7.0ms

Local error

Found 2 expressions with local error:

2.6b	(log (+ N 1.0))
4.1b	(- (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))

series136.0ms

Counts

2 → 6

Calls

2 calls:

45.0ms	(log (+ N 1.0))
91.0ms	(- (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

prune126.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize10.0ms

Local error

Found 2 expressions with local error:

0.1b	(fma (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5) (/ 1.0 N))
0.4b	(/ 1 (pow N 2))

rewrite8.0ms

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:

1.0ms	(fma (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5) (/ 1.0 N))
5.0ms	(/ 1 (pow N 2))

series51.0ms

Counts

2 → 6

Calls

2 calls:

36.0ms	(fma (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5) (/ 1.0 N))
15.0ms	(/ 1 (pow N 2))

simplify31.0ms

Algorithm

egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 2 (26.0ms)

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

prune100.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

localize12.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ 1 (pow N 2))
0.4b	(/ 1 (pow N 2))
10.1b	(sqrt (fma (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5) (/ 1.0 N)))
10.1b	(sqrt (fma (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5) (/ 1.0 N)))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

48×	`times-frac`
42×	`add-sqr-sqrt`
40×	`add-cube-cbrt` `*-un-lft-identity`
24×	`unpow-prod-down`
22×	`add-exp-log`
16×	`associate-/r*`
12×	`div-exp`
8×	`add-cbrt-cube` `unpow2` `sqr-pow`
6×	`pow1` `pow-to-exp` `rec-exp` `1-exp` `pow-exp` `sqrt-prod` `associate-/l*`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`cbrt-undiv` `rem-sqrt-square` `pow-flip` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `div-inv` `inv-pow`

Counts

4 → 148

Calls

4 calls:

5.0ms	(/ 1 (pow N 2))
5.0ms	(/ 1 (pow N 2))
1.0ms	(sqrt (fma (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5) (/ 1.0 N)))
2.0ms	(sqrt (fma (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5) (/ 1.0 N)))

series150.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(/ 1 (pow N 2))
15.0ms	(/ 1 (pow N 2))
60.0ms	(sqrt (fma (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5) (/ 1.0 N)))
59.0ms	(sqrt (fma (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5) (/ 1.0 N)))

simplify37.0ms

Algorithm

egg-herbie

Counts

160 → 160

Iterations

Useful iterations: 2 (27.0ms)

Iter	Nodes	Cost
0	237	852
1	849	730
2	5002	634

prune292.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (+ N 1.0) N)
4.2b	(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)
5.0ms	(log (/ (+ N 1.0) N))

series131.0ms

Counts

2 → 6

Calls

2 calls:

50.0ms	(/ (+ N 1.0) N)
81.0ms	(log (/ (+ N 1.0) N))

simplify105.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 3 (100.0ms)

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

prune117.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.1b

regimes25.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 31.7b

bsearch16.0ms

Steps

Iters	Range		Point
5	4050.4462513149238	12331.842748450485	9398.860464890142

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	9
1	21	9

end0.0ms

sample1.2s

Algorithm

intervals

Results

421.0ms	1732×	body	1280	valid
187.0ms	7827×	body	80	nan
186.0ms	1242×	body	640	valid
165.0ms	4096×	body	80	valid
59.0ms	609×	body	320	valid
19.0ms	321×	body	160	valid