Details

sample58.0ms

Algorithm

intervals

Results

17.0ms	62×	body	1280	valid
11.0ms	263×	body	80	nan
9.0ms	127×	body	80	valid
7.0ms	41×	body	640	valid
2.0ms	19×	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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.4b

localize7.0ms

Local error

Found 2 expressions with local error:

1.6b	(log (+ N 1.0))
2.5b	(- (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))

series139.0ms

Counts

2 → 6

Calls

2 calls:

40.0ms	(log (+ N 1.0))
99.0ms	(- (log (+ N 1.0)) (log N))

simplify53.0ms

Algorithm

egg-herbie

Counts

47 → 47

Iterations

Useful iterations: 3 (49.0ms)

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

prune101.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (+ N 1.0) N)
2.7b	(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))

series135.0ms

Counts

2 → 6

Calls

2 calls:

51.0ms	(/ (+ N 1.0) N)
84.0ms	(log (/ (+ N 1.0) N))

simplify99.0ms

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

prune107.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize9.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (sqrt N))
0.3b	(/ (+ N 1.0) (sqrt N))
0.4b	(* (/ 1 (sqrt N)) (/ (+ N 1.0) (sqrt N)))
16.5b	(log (* (/ 1 (sqrt N)) (/ (+ N 1.0) (sqrt N))))

rewrite68.0ms

Algorithm

rewrite-expression-head

Rules

110×	`add-sqr-sqrt`
106×	`times-frac`
96×	`*-un-lft-identity`
64×	`add-cube-cbrt`
59×	`sqrt-prod`
55×	`add-exp-log`
28×	`associate-r`
22×	`associate-l`
20×	`add-cbrt-cube`
19×	`div-exp`
16×	`prod-exp`
15×	`unswap-sqr`
13×	`distribute-lft-out`
12×	`associate-/r*`
11×	`pow1`
9×	`rem-log-exp`
7×	`associate-/l*`
6×	`cbrt-undiv`
5×	`rec-exp` `1-exp`
4×	`cbrt-unprod` `div-inv` `add-log-exp`
3×	`log-div` `pow-flip`
2×	`frac-times` `frac-2neg` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `log-pow` `associate-/l/`
1×	`log-prod` `sqrt-pow1` `flip3-+` `pow1/2` `*-commutative` `flip-+` `inv-pow`

Counts

4 → 204

Calls

4 calls:

3.0ms	(/ 1 (sqrt N))
8.0ms	(/ (+ N 1.0) (sqrt N))
36.0ms	(* (/ 1 (sqrt N)) (/ (+ N 1.0) (sqrt N)))
11.0ms	(log (* (/ 1 (sqrt N)) (/ (+ N 1.0) (sqrt N))))

series213.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(/ 1 (sqrt N))
48.0ms	(/ (+ N 1.0) (sqrt N))
47.0ms	(* (/ 1 (sqrt N)) (/ (+ N 1.0) (sqrt N)))
84.0ms	(log (* (/ 1 (sqrt N)) (/ (+ N 1.0) (sqrt N))))

simplify80.0ms

Algorithm

egg-herbie

Counts

216 → 216

Iterations

Useful iterations: 2 (65.0ms)

Iter	Nodes	Cost
0	639	1574
1	3862	1331
2	5001	1250

prune334.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize10.0ms

Local error

Found 4 expressions with local error:

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

rewrite83.0ms

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:

17.0ms	(+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N))
10.0ms	(- (/ 0.3333333333333333 N) 0.5)
44.0ms	(* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5))
4.0ms	(/ 1 (pow N 2))

series160.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N))
33.0ms	(- (/ 0.3333333333333333 N) 0.5)
76.0ms	(* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5))
21.0ms	(/ 1 (pow N 2))

simplify79.0ms

Algorithm

egg-herbie

Counts

177 → 177

Iterations

Useful iterations: 2 (61.0ms)

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

prune290.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes17.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 29.2b

bsearch38.0ms

Steps

Iters	Range		Point
9	0.817620533678417	257763.20554958374	7930.678370699702

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	10
1	24	10

end0.0ms

sample1.7s

Algorithm

intervals

Results

500.0ms	1800×	body	1280	valid
333.0ms	7979×	body	80	nan
305.0ms	4103×	body	80	valid
230.0ms	1241×	body	640	valid
76.0ms	578×	body	320	valid
25.0ms	278×	body	160	valid