Details

sample46.0ms

Algorithm

intervals

Results

14.0ms	58×	body	1280	valid
9.0ms	296×	body	80	nan
6.0ms	43×	body	640	valid
5.0ms	125×	body	80	valid
1.0ms	15×	body	320	valid
1.0ms	15×	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

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.6b

localize6.0ms

Local error

Found 2 expressions with local error:

2.1b	(log (+ N 1.0))
3.6b	(- (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))
8.0ms	(- (log (+ N 1.0)) (log N))

series136.0ms

Counts

2 → 6

Calls

2 calls:

44.0ms	(log (+ N 1.0))
92.0ms	(- (log (+ N 1.0)) (log N))

simplify124.0ms

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

prune124.0ms

Filtered

71 candidates to 43 candidates (60.6%)

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (/ 0.3333333333333333 N) 0.5)
0.1b	(fma (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5) (/ 1.0 N))
0.4b	(/ 1 (pow N 2))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

66×	`add-sqr-sqrt`
63×	`*-un-lft-identity`
61×	`add-cube-cbrt` `times-frac`
39×	`prod-diff`
13×	`fma-neg`
12×	`add-exp-log` `unpow-prod-down`
8×	`associate-/r*`
6×	`div-exp`
5×	`add-cbrt-cube` `div-inv` `add-log-exp`
4×	`unpow2` `sqr-pow`
3×	`pow1` `expm1-log1p-u` `pow-to-exp` `rec-exp` `1-exp` `pow-exp` `log1p-expm1-u` `associate-/l*`
2×	`difference-of-squares`
1×	`cbrt-undiv` `sub-neg` `flip3--` `pow-flip` `frac-2neg` `diff-log` `clear-num` `flip--` `fma-udef` `distribute-lft-out--` `inv-pow`

Counts

3 → 138

Calls

3 calls:

14.0ms	(- (/ 0.3333333333333333 N) 0.5)
0.0ms	(fma (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5) (/ 1.0 N))
4.0ms	(/ 1 (pow N 2))

series87.0ms

Counts

3 → 9

Calls

3 calls:

37.0ms	(- (/ 0.3333333333333333 N) 0.5)
34.0ms	(fma (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5) (/ 1.0 N))
16.0ms	(/ 1 (pow N 2))

simplify49.0ms

Algorithm

egg-herbie

Counts

147 → 147

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	425	1067
1	1442	713
2	5001	631

prune206.0ms

Filtered

147 candidates to 67 candidates (45.6%)

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize5.0ms

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))

series131.0ms

Counts

2 → 6

Calls

2 calls:

49.0ms	(/ (+ N 1.0) N)
83.0ms	(log (/ (+ N 1.0) N))

simplify105.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 3 (99.0ms)

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

prune121.0ms

Filtered

70 candidates to 50 candidates (71.4%)

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 4 expressions with local error:

2.1b	(log (+ N 1.0))
2.1b	(log (+ N 1.0))
2.1b	(log (+ N 1.0))
3.5b	(- (* (log (+ N 1.0)) (log (+ N 1.0))) (* (log N) (log N)))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

26×	`log-prod`
21×	`*-un-lft-identity`
11×	`add-sqr-sqrt` `add-cube-cbrt`
8×	`associate--l+`
7×	`pow1` `add-exp-log` `distribute-rgt-in` `distribute-lft-in`
6×	`log-div` `associate--r+` `add-log-exp`
5×	`distribute-lft-out`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`flip3-+` `rem-log-exp` `log-pow` `flip-+`
1×	`sub-neg` `flip3--` `fma-neg` `diff-log` `prod-diff` `flip--` `difference-of-squares`

Counts

4 → 82

Calls

4 calls:

3.0ms	(log (+ N 1.0))
2.0ms	(log (+ N 1.0))
2.0ms	(log (+ N 1.0))
8.0ms	(- (* (log (+ N 1.0)) (log (+ N 1.0))) (* (log N) (log N)))

series275.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(log (+ N 1.0))
42.0ms	(log (+ N 1.0))
47.0ms	(log (+ N 1.0))
139.0ms	(- (* (log (+ N 1.0)) (log (+ N 1.0))) (* (log N) (log N)))

simplify39.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	413	732
1	1351	650
2	5002	627

prune249.0ms

Filtered

94 candidates to 77 candidates (81.9%)

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.0b

regimes30.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 31.5b

bsearch26.0ms

Steps

Iters	Range		Point
8	6.164824567421913	81461.56837266182	13931.961951684772

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

427.0ms	1769×	body	1280	valid
188.0ms	1268×	body	640	valid
180.0ms	7974×	body	80	nan
164.0ms	4071×	body	80	valid
57.0ms	606×	body	320	valid
17.0ms	286×	body	160	valid