Details

sample58.0ms

Algorithm

intervals

Results

17.0ms	62×	body	1280	valid
11.0ms	263×	body	80	nan
10.0ms	127×	body	80	valid
8.0ms	41×	body	640	valid
2.0ms	19×	body	320	valid
1.0ms	7×	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: 30.4b

localize7.0ms

Local error

Found 2 expressions with local error:

1.6b	(log (+ N 1.0))
2.5b	(- (log (+ N 1.0)) (log N))

rewrite12.0ms

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))
7.0ms	(- (log (+ N 1.0)) (log N))

series141.0ms

Counts

2 → 6

Calls

2 calls:

41.0ms	(log (+ N 1.0))
100.0ms	(- (log (+ N 1.0)) (log N))

simplify122.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 3 (116.0ms)

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: 0b

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (+ N 1.0) N)
2.7b	(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:

7.0ms	(/ (+ N 1.0) N)
3.0ms	(log (/ (+ N 1.0) N))

series134.0ms

Counts

2 → 6

Calls

2 calls:

50.0ms	(/ (+ N 1.0) N)
84.0ms	(log (/ (+ N 1.0) N))

simplify105.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 3 (98.0ms)

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

prune118.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(- 1.0 (/ 0.5 N))
0.0b	(fma (/ 1 N) (- 1.0 (/ 0.5 N)) (/ 0.3333333333333333 (pow N 3)))
0.2b	(/ 0.3333333333333333 (pow N 3))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

68×	`add-sqr-sqrt`
65×	`*-un-lft-identity`
64×	`times-frac`
63×	`add-cube-cbrt`
39×	`prod-diff`
12×	`unpow-prod-down` `cube-prod` `associate-/r*`
8×	`add-exp-log`
5×	`add-cbrt-cube` `add-log-exp`
4×	`cube-mult` `unpow3` `div-inv` `sqr-pow`
3×	`pow1` `expm1-log1p-u` `fma-neg` `div-exp` `log1p-expm1-u` `associate-/l*`
2×	`difference-of-squares`
1×	`cbrt-undiv` `pow-to-exp` `sub-neg` `flip3--` `frac-2neg` `diff-log` `pow-exp` `clear-num` `flip--` `fma-udef` `distribute-lft-out--`

Counts

3 → 136

Calls

3 calls:

8.0ms	(- 1.0 (/ 0.5 N))
0.0ms	(fma (/ 1 N) (- 1.0 (/ 0.5 N)) (/ 0.3333333333333333 (pow N 3)))
4.0ms	(/ 0.3333333333333333 (pow N 3))

series113.0ms

Counts

3 → 9

Calls

3 calls:

36.0ms	(- 1.0 (/ 0.5 N))
37.0ms	(fma (/ 1 N) (- 1.0 (/ 0.5 N)) (/ 0.3333333333333333 (pow N 3)))
40.0ms	(/ 0.3333333333333333 (pow N 3))

simplify73.0ms

Algorithm

egg-herbie

Counts

145 → 145

Iterations

Useful iterations: 2 (59.0ms)

Iter	Nodes	Cost
0	575	1382
1	2489	916
2	5002	841

prune209.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(log (log (+ N 1.0)))
0.7b	(exp (log (log (+ N 1.0))))
1.6b	(log (+ N 1.0))
26.0b	(- (exp (log (log (+ N 1.0)))) (log N))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

36×	`log-prod`
31×	`*-un-lft-identity`
30×	`add-sqr-sqrt`
28×	`prod-diff`
26×	`add-cube-cbrt`
25×	`exp-sum`
22×	`pow1`
18×	`log-pow`
7×	`fma-neg`
6×	`add-exp-log`
5×	`add-log-exp`
4×	`expm1-log1p-u` `exp-prod` `add-cbrt-cube` `log1p-expm1-u`
3×	`associate--r+`
2×	`log-div` `rem-log-exp` `distribute-lft-out--` `difference-of-squares`
1×	`sub-neg` `flip3--` `flip3-+` `diff-log` `flip--` `flip-+` `rem-exp-log` `distribute-lft-out`

Counts

4 → 106

Calls

4 calls:

2.0ms	(log (log (+ N 1.0)))
2.0ms	(exp (log (log (+ N 1.0))))
2.0ms	(log (+ N 1.0))
13.0ms	(- (exp (log (log (+ N 1.0)))) (log N))

series269.0ms

Counts

4 → 12

Calls

4 calls:

89.0ms	(log (log (+ N 1.0)))
41.0ms	(exp (log (log (+ N 1.0))))
46.0ms	(log (+ N 1.0))
93.0ms	(- (exp (log (log (+ N 1.0)))) (log N))

simplify53.0ms

Algorithm

egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	448	1188
1	1481	809
2	5001	615

prune207.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes21.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 29.2b

bsearch35.0ms

Steps

Iters	Range		Point
9	0.817620533678417	257763.20554958374	7930.678370699702

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	9
1	21	9

end0.0ms

sample1.7s

Algorithm

intervals

Results

507.0ms	1800×	body	1280	valid
338.0ms	7979×	body	80	nan
308.0ms	4103×	body	80	valid
228.0ms	1241×	body	640	valid
77.0ms	578×	body	320	valid
25.0ms	278×	body	160	valid