Details

sample43.0ms

Algorithm

intervals

Results

12.0ms	49×	body	1280	valid
6.0ms	247×	body	80	nan
6.0ms	38×	body	640	valid
6.0ms	134×	body	80	valid
2.0ms	20×	body	320	valid
1.0ms	15×	body	160	valid

simplify6.0ms

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

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 28.7b

Counts

2 → 1

localize10.0ms

Local error

Found 2 expressions with local error:

2.5b	(log (+ N 1.0))
4.6b	(- (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))

series135.0ms

Counts

2 → 6

Calls

2 calls:

41.0ms	(log (+ N 1.0))
93.0ms	(- (log (+ N 1.0)) (log N))

simplify131.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 3 (121.0ms)

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

prune121.0ms

Filtered

71 candidates to 43 candidates (60.6%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	67	4	71
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	68	4	72

Merged error: 0.1b

Counts

72 → 4

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (+ N 1.0) N)
4.7b	(log (/ (+ N 1.0) N))

rewrite15.0ms

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)
5.0ms	(log (/ (+ N 1.0) N))

series129.0ms

Counts

2 → 6

Calls

2 calls:

45.0ms	(/ (+ N 1.0) N)
83.0ms	(log (/ (+ N 1.0) N))

simplify109.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 3 (102.0ms)

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

prune109.0ms

Filtered

70 candidates to 50 candidates (71.4%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	68	2	70
Fresh	1	2	3
Picked	1	0	1
Done	0	0	0
Total	70	4	74

Merged error: 0.1b

Counts

74 → 4

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(log (/ (sqrt (+ N 1.0)) N))
0.1b	(/ (sqrt (+ N 1.0)) N)
2.5b	(log (sqrt (+ N 1.0)))
5.0b	(+ (log (sqrt (+ N 1.0))) (log (/ (sqrt (+ N 1.0)) N)))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

81×	`*-un-lft-identity`
64×	`log-prod`
63×	`times-frac`
53×	`add-sqr-sqrt` `add-cube-cbrt`
48×	`sqrt-prod`
25×	`associate-+r+`
16×	`distribute-lft-out`
13×	`pow1`
11×	`log-pow`
10×	`add-exp-log`
7×	`associate-+l+` `associate-/l*`
6×	`log-div` `fma-def` `sqrt-div` `add-cbrt-cube`
4×	`expm1-log1p-u` `flip3-+` `flip-+` `log1p-expm1-u` `add-log-exp`
3×	`rem-log-exp` `associate-/r*` `div-inv`
2×	`associate-+l-` `sqrt-pow1` `pow1/2` `div-exp` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `associate-+r-` `frac-2neg` `clear-num` `sum-log`

Counts

4 → 165

Calls

4 calls:

6.0ms	(log (/ (sqrt (+ N 1.0)) N))
6.0ms	(/ (sqrt (+ N 1.0)) N)
4.0ms	(log (sqrt (+ N 1.0)))
14.0ms	(+ (log (sqrt (+ N 1.0))) (log (/ (sqrt (+ N 1.0)) N)))

series547.0ms

Counts

4 → 12

Calls

4 calls:

151.0ms	(log (/ (sqrt (+ N 1.0)) N))
74.0ms	(/ (sqrt (+ N 1.0)) N)
84.0ms	(log (sqrt (+ N 1.0)))
238.0ms	(+ (log (sqrt (+ N 1.0))) (log (/ (sqrt (+ N 1.0)) N)))

simplify56.0ms

Algorithm

egg-herbie

Counts

177 → 177

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	528	1419
1	1596	1318
2	5002	1212

prune348.0ms

Filtered

177 candidates to 121 candidates (68.4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	175	2	177
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	175	6	181

Merged error: 0.1b

Counts

181 → 6

localize20.0ms

Local error

Found 4 expressions with local error:

2.5b	(log (sqrt (+ N 1.0)))
2.5b	(log (sqrt (+ N 1.0)))
2.5b	(log (sqrt (+ N 1.0)))
4.9b	(+ (pow (log (sqrt (+ N 1.0))) 3) (pow (log (/ (sqrt (+ N 1.0)) N)) 3))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

37×	`*-un-lft-identity`
31×	`log-pow`
30×	`pow1`
22×	`unpow-prod-down` `cube-prod`
21×	`log-prod`
20×	`distribute-lft-out`
18×	`fma-def`
13×	`add-sqr-sqrt` `add-cube-cbrt`
12×	`sqrt-prod`
7×	`add-exp-log`
6×	`log-div` `sqrt-div` `add-log-exp`
5×	`sqrt-pow1` `pow1/2`
4×	`expm1-log1p-u` `flip3-+` `add-cbrt-cube` `flip-+` `log1p-expm1-u`
3×	`rem-log-exp`
1×	`+-commutative` `cube-mult` `unpow3` `sum-log` `sum-cubes` `sqr-pow`

Counts

4 → 115

Calls

4 calls:

4.0ms	(log (sqrt (+ N 1.0)))
4.0ms	(log (sqrt (+ N 1.0)))
4.0ms	(log (sqrt (+ N 1.0)))
17.0ms	(+ (pow (log (sqrt (+ N 1.0))) 3) (pow (log (/ (sqrt (+ N 1.0)) N)) 3))

series749.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(log (sqrt (+ N 1.0)))
81.0ms	(log (sqrt (+ N 1.0)))
80.0ms	(log (sqrt (+ N 1.0)))
507.0ms	(+ (pow (log (sqrt (+ N 1.0))) 3) (pow (log (/ (sqrt (+ N 1.0)) N)) 3))

simplify71.0ms

Algorithm

egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 2 (59.0ms)

Iter	Nodes	Cost
0	751	1151
1	2990	1080
2	5001	1069

prune388.0ms

Filtered

127 candidates to 85 candidates (66.9%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	126	1	127
Fresh	0	4	4
Picked	1	0	1
Done	0	1	1
Total	127	6	133

Merged error: 0.1b

Counts

133 → 6

regimes34.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 29.4b

bsearch35.0ms

Steps

Iters	Range		Point
9	860.9547529914067	28642596122.821114	5693.273848194081

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	14
1	25	14

end0.0ms

sample1.3s

Algorithm

intervals

Results

434.0ms	1766×	body	1280	valid
195.0ms	1241×	body	640	valid
190.0ms	8133×	body	80	nan
175.0ms	4087×	body	80	valid
60.0ms	598×	body	320	valid
19.0ms	308×	body	160	valid