Details

sample53.0ms

Algorithm

intervals

Results

17.0ms	60×	body	1280	valid
10.0ms	216×	body	80	nan
7.0ms	130×	body	80	valid
7.0ms	35×	body	640	valid
3.0ms	24×	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

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: 29.5b

Counts

2 → 1

localize7.0ms

Local error

Found 2 expressions with local error:

2.3b	(- (log (+ N 1.0)) (log N))
4.4b	(log (+ N 1.0))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

13×	`*-un-lft-identity`
11×	`log-prod`
7×	`pow1` `add-sqr-sqrt`
5×	`add-cube-cbrt` `log-pow`
4×	`log-div` `associate--l+` `distribute-lft-out--`
3×	`add-exp-log` `associate--r+`
2×	`associate--l-` `flip3-+` `add-cbrt-cube` `flip-+` `distribute-lft-out` `add-log-exp`
1×	`sub-neg` `flip3--` `diff-log` `rem-log-exp` `flip--` `difference-of-squares`

Counts

2 → 41

Calls

2 calls:

6.0ms	(- (log (+ N 1.0)) (log N))
3.0ms	(log (+ N 1.0))

series138.0ms

Counts

2 → 6

Calls

2 calls:

96.0ms	(- (log (+ N 1.0)) (log N))
42.0ms	(log (+ N 1.0))

simplify53.0ms

Algorithm

egg-herbie

Counts

47 → 47

Iterations

Useful iterations: 3 (49.0ms)

Iter	Nodes	Cost
0	212	281
1	547	264
2	1874	250
3	5001	247

prune84.0ms

Filtered

47 candidates to 33 candidates (70.2%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	45	2	47
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	46	2	48

Merged error: 0.0b

Counts

48 → 2

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (+ N 1.0) N)
2.7b	(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×	`div-exp` `rem-log-exp` `div-inv` `associate-/l/` `add-log-exp`
1×	`cbrt-undiv` `log-div` `frac-2neg` `flip3-+` `clear-num` `log-pow` `flip-+`

Counts

2 → 60

Calls

2 calls:

5.0ms	(/ (+ N 1.0) N)
4.0ms	(log (/ (+ N 1.0) N))

series131.0ms

Counts

2 → 6

Calls

2 calls:

49.0ms	(/ (+ N 1.0) N)
82.0ms	(log (/ (+ N 1.0) N))

simplify101.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 2 (20.0ms)

Iter	Nodes	Cost
0	233	373
1	773	351
2	3489	339
3	5002	339

prune86.0ms

Filtered

66 candidates to 45 candidates (68.2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	65	1	66
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	65	3	68

Merged error: 0.0b

Counts

68 → 3

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (+ N 1.0) N)
0.3b	(cbrt (pow (log (/ (+ N 1.0) N)) 3))
0.4b	(pow (log (/ (+ N 1.0) N)) 3)
2.7b	(log (/ (+ N 1.0) N))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

41×	`*-un-lft-identity`
27×	`add-sqr-sqrt` `add-cube-cbrt`
24×	`times-frac`
16×	`log-prod`
14×	`cbrt-prod`
10×	`pow1` `add-exp-log`
8×	`unpow-prod-down` `cube-prod`
7×	`add-cbrt-cube` `distribute-lft-out`
5×	`log-pow`
4×	`associate-/l*` `add-log-exp`
3×	`pow-unpow` `associate-/r*`
2×	`cube-mult` `unpow3` `div-exp` `rem-log-exp` `div-inv` `associate-/l/` `sqr-pow`
1×	`cbrt-undiv` `pow-to-exp` `log-div` `pow-pow` `frac-2neg` `flip3-+` `pow1/3` `pow-exp` `clear-num` `rem-cbrt-cube` `flip-+` `rem-cube-cbrt`

Counts

4 → 108

Calls

4 calls:

5.0ms	(/ (+ N 1.0) N)
2.0ms	(cbrt (pow (log (/ (+ N 1.0) N)) 3))
2.0ms	(pow (log (/ (+ N 1.0) N)) 3)
4.0ms	(log (/ (+ N 1.0) N))

series355.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(/ (+ N 1.0) N)
84.0ms	(cbrt (pow (log (/ (+ N 1.0) N)) 3))
138.0ms	(pow (log (/ (+ N 1.0) N)) 3)
82.0ms	(log (/ (+ N 1.0) N))

simplify58.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	478	769
1	2101	733
2	5001	727

prune182.0ms

Filtered

120 candidates to 71 candidates (59.2%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	119	1	120
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	119	4	123

Merged error: 0.0b

Counts

123 → 4

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ 0.3333333333333333 N) 0.5)
0.0b	(+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N))
0.1b	(* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5))
0.5b	(/ 1 (pow N 2))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

65×	`add-sqr-sqrt`
58×	`times-frac`
45×	`*-un-lft-identity`
37×	`add-cube-cbrt`
33×	`add-exp-log`
28×	`associate-l`
23×	`unpow-prod-down`
12×	`div-exp`
11×	`add-cbrt-cube`
10×	`prod-exp`
9×	`unpow2` `unswap-sqr` `sqr-pow`
8×	`associate-/r*` `add-log-exp`
6×	`pow1` `pow-to-exp` `rec-exp` `1-exp` `associate-r` `pow-exp`
5×	`sub-neg` `flip3--` `frac-add` `flip--`
4×	`distribute-rgt-in` `frac-times` `associate-+l+` `distribute-lft-in` `associate-*r/` `difference-of-squares`
3×	`associate-/l*`
2×	`cbrt-undiv` `associate-*l/` `cbrt-unprod` `div-inv` `distribute-lft-out--`
1×	`+-commutative` `pow-flip` `frac-2neg` `flip3-+` `diff-log` `pow-prod-down` `clear-num` `sum-log` `*-commutative` `flip-+` `inv-pow`

Counts

4 → 165

Calls

4 calls:

7.0ms	(- (/ 0.3333333333333333 N) 0.5)
15.0ms	(+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N))
17.0ms	(* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5))
5.0ms	(/ 1 (pow N 2))

series159.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(- (/ 0.3333333333333333 N) 0.5)
30.0ms	(+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N))
75.0ms	(* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5))
20.0ms	(/ 1 (pow N 2))

simplify81.0ms

Algorithm

egg-herbie

Counts

177 → 177

Iterations

Useful iterations: 2 (62.0ms)

Iter	Nodes	Cost
0	597	1169
1	2754	978
2	5001	915

prune236.0ms

Filtered

177 candidates to 101 candidates (57.1%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	176	1	177
Fresh	1	0	1
Picked	0	1	1
Done	0	2	2
Total	177	4	181

Merged error: 0.0b

Counts

181 → 4

regimes24.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 29.7b

bsearch35.0ms

Steps

Iters	Range		Point
10	6.398614580632226	1668043056922.9724	7983.85988394812

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	10
1	24	10

end0.0ms

sample1.5s

Algorithm

intervals

Results

515.0ms	1770×	body	1280	valid
263.0ms	8123×	body	80	nan
236.0ms	1250×	body	640	valid
215.0ms	4039×	body	80	valid
85.0ms	647×	body	320	valid
23.0ms	294×	body	160	valid