Details

sample44.0ms

Algorithm

intervals

Results

14.0ms	58×	body	1280	valid
7.0ms	47×	body	640	valid
6.0ms	245×	body	80	nan
5.0ms	111×	body	80	valid
3.0ms	28×	body	320	valid
1.0ms	12×	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: 33.7b

localize6.0ms

Local error

Found 2 expressions with local error:

3.2b	(log (+ N 1.0))
3.4b	(- (log (+ N 1.0)) (log N))

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:

2.0ms	(log (+ N 1.0))
6.0ms	(- (log (+ N 1.0)) (log N))

series134.0ms

Counts

2 → 6

Calls

2 calls:

43.0ms	(log (+ N 1.0))
91.0ms	(- (log (+ N 1.0)) (log N))

simplify52.0ms

Algorithm

egg-herbie

Counts

47 → 47

Iterations

Useful iterations: 3 (48.0ms)

Iter	Nodes	Cost
0	212	281
1	547	264
2	1875	250
3	5001	247

prune93.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize10.0ms

Local error

Found 3 expressions with local error:

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))
0.7b	(/ 1 (pow N 2))

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 150

Calls

3 calls:

20.0ms	(+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N))
40.0ms	(* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5))
4.0ms	(/ 1 (pow N 2))

series117.0ms

Counts

3 → 9

Calls

3 calls:

29.0ms	(+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N))
72.0ms	(* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5))
16.0ms	(/ 1 (pow N 2))

simplify74.0ms

Algorithm

egg-herbie

Counts

159 → 159

Iterations

Useful iterations: 2 (59.0ms)

Iter	Nodes	Cost
0	583	1087
1	2726	904
2	5001	841

prune246.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.1b

localize5.0ms

Local error

Found 1 expressions with local error:

3.1b	(log (/ (+ N 1.0) N))

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

16×	`log-prod`
15×	`*-un-lft-identity`
12×	`times-frac`
9×	`add-sqr-sqrt` `add-cube-cbrt`
4×	`add-exp-log`
3×	`distribute-lft-out`
2×	`pow1` `rem-log-exp`
1×	`log-div` `div-exp` `log-pow` `add-cbrt-cube` `div-inv` `add-log-exp`

Counts

1 → 27

Calls

1 calls:

5.0ms

(log (/ (+ N 1.0) N))

series81.0ms

Counts

1 → 3

Calls

1 calls:

81.0ms

(log (/ (+ N 1.0) N))

simplify59.0ms

Algorithm

egg-herbie

Counts

30 → 30

Iterations

Useful iterations: 2 (13.0ms)

Iter	Nodes	Cost
0	167	209
1	455	196
2	1964	184
3	5002	184

prune53.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.1b

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b	(log (log (/ (+ N 1.0) N)))
0.7b	(exp (log (log (/ (+ N 1.0) N))))
3.1b	(log (/ (+ N 1.0) N))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

24×	`log-prod`
20×	`*-un-lft-identity`
14×	`add-sqr-sqrt` `add-cube-cbrt`
12×	`times-frac`
8×	`pow1`
7×	`add-exp-log`
5×	`log-pow`
4×	`exp-prod` `exp-sum`
3×	`rem-log-exp` `add-cbrt-cube` `distribute-lft-out` `add-log-exp`
1×	`log-div` `div-exp` `div-inv` `rem-exp-log`

Counts

3 → 56

Calls

3 calls:

1.0ms	(log (log (/ (+ N 1.0) N)))
2.0ms	(exp (log (log (/ (+ N 1.0) N))))
3.0ms	(log (/ (+ N 1.0) N))

series313.0ms

Counts

3 → 9

Calls

3 calls:

147.0ms	(log (log (/ (+ N 1.0) N)))
84.0ms	(exp (log (log (/ (+ N 1.0) N))))
82.0ms	(log (/ (+ N 1.0) N))

simplify115.0ms

Algorithm

egg-herbie

Counts

65 → 65

Iterations

Useful iterations: 3 (109.0ms)

Iter	Nodes	Cost
0	295	470
1	944	432
2	4238	400
3	5001	394

prune118.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.1b

regimes30.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 30.9b

bsearch20.0ms

Steps

Iters	Range		Point
6	7065.8830381017015	33294.97377914132	9018.887363236374

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	10
1	24	10

end0.0ms

sample1.3s

Algorithm

intervals

Results

443.0ms	1782×	body	1280	valid
201.0ms	1317×	body	640	valid
183.0ms	8078×	body	80	nan
166.0ms	3981×	body	80	valid
66.0ms	629×	body	320	valid
18.0ms	291×	body	160	valid