Details

sample47.0ms

Algorithm

intervals

Results

16.0ms	66×	body	1280	valid
7.0ms	50×	body	640	valid
7.0ms	277×	body	80	nan
4.0ms	108×	body	80	valid
2.0ms	22×	body	320	valid
1.0ms	10×	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: 34.9b

localize7.0ms

Local error

Found 2 expressions with local error:

2.7b	(- (log (+ N 1.0)) (log N))
3.9b	(log (+ N 1.0))

rewrite10.0ms

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:

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

series135.0ms

Counts

2 → 6

Calls

2 calls:

91.0ms	(- (log (+ N 1.0)) (log N))
44.0ms	(log (+ N 1.0))

simplify54.0ms

Algorithm

egg-herbie

Counts

47 → 47

Iterations

Useful iterations: 3 (50.0ms)

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

prune101.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

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))
0.3b	(/ 1 (pow N 2))

rewrite85.0ms

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:

11.0ms	(- (/ 0.3333333333333333 N) 0.5)
18.0ms	(+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N))
46.0ms	(* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5))
4.0ms	(/ 1 (pow N 2))

series157.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(- (/ 0.3333333333333333 N) 0.5)
35.0ms	(+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N))
74.0ms	(* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5))
16.0ms	(/ 1 (pow N 2))

simplify75.0ms

Algorithm

egg-herbie

Counts

177 → 177

Iterations

Useful iterations: 2 (61.0ms)

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

prune294.0ms

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)
2.6b	(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×	`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:

8.0ms	(/ (+ N 1.0) N)
3.0ms	(log (/ (+ N 1.0) N))

series133.0ms

Counts

2 → 6

Calls

2 calls:

50.0ms	(/ (+ N 1.0) N)
83.0ms	(log (/ (+ N 1.0) N))

simplify100.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 2 (19.0ms)

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

prune114.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(log (/ 1 N))
3.0b	(+ (log (+ N 1.0)) (log (/ 1 N)))
3.9b	(log (+ N 1.0))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

34×	`log-prod`
27×	`*-un-lft-identity`
19×	`add-sqr-sqrt` `add-cube-cbrt`
18×	`times-frac`
13×	`associate-+r+`
10×	`pow1`
9×	`add-exp-log`
8×	`log-pow`
6×	`log-div` `distribute-lft-out`
5×	`rem-log-exp`
4×	`associate-+l+`
3×	`flip3-+` `log-rec` `add-cbrt-cube` `flip-+` `add-log-exp`
2×	`associate-+l-` `div-exp` `div-inv`
1×	`+-commutative` `associate-+r-` `rec-exp` `pow-flip` `1-exp` `unsub-neg` `sum-log` `inv-pow`

Counts

3 → 81

Calls

3 calls:

2.0ms	(log (/ 1 N))
9.0ms	(+ (log (+ N 1.0)) (log (/ 1 N)))
3.0ms	(log (+ N 1.0))

series239.0ms

Counts

3 → 9

Calls

3 calls:

115.0ms	(log (/ 1 N))
78.0ms	(+ (log (+ N 1.0)) (log (/ 1 N)))
45.0ms	(log (+ N 1.0))

simplify96.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 3 (90.0ms)

Iter	Nodes	Cost
0	324	495
1	906	452
2	3587	406
3	5001	387

prune152.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

regimes29.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 31.4b

bsearch30.0ms

Steps

Iters	Range		Point
9	251.47950061764826	4321407464.299789	5358.0336570575955

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	12
1	27	12

end0.0ms

sample1.3s

Algorithm

intervals

Results

431.0ms	1750×	body	1280	valid
196.0ms	8377×	body	80	nan
192.0ms	1261×	body	640	valid
169.0ms	4068×	body	80	valid
60.0ms	616×	body	320	valid
18.0ms	305×	body	160	valid