Details

sample43.0ms

Algorithm

intervals

Results

13.0ms	54×	body	1280	valid
7.0ms	304×	body	80	nan
6.0ms	40×	body	640	valid
5.0ms	135×	body	80	valid
2.0ms	20×	body	320	valid
0.0ms	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: 28.5b

localize6.0ms

Local error

Found 2 expressions with local error:

2.4b	(- (log (+ N 1.0)) (log N))
3.2b	(log (+ N 1.0))

rewrite9.0ms

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

series133.0ms

Counts

2 → 6

Calls

2 calls:

89.0ms	(- (log (+ N 1.0)) (log N))
44.0ms	(log (+ N 1.0))

simplify52.0ms

Algorithm

egg-herbie

Counts

47 → 47

Iterations

Useful iterations: 3 (48.0ms)

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

prune97.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (+ N 1.0) N)
2.3b	(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))

series127.0ms

Counts

2 → 6

Calls

2 calls:

47.0ms	(/ (+ N 1.0) N)
80.0ms	(log (/ (+ N 1.0) N))

simplify98.0ms

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

prune104.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize7.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (/ (+ N 1.0) N))
0.1b	(sqrt (/ (+ N 1.0) N))
0.3b	(* (sqrt (/ (+ N 1.0) N)) (sqrt (/ (+ N 1.0) N)))
2.3b	(log (* (sqrt (/ (+ N 1.0) N)) (sqrt (/ (+ N 1.0) N))))

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

122×	`sqrt-prod`
114×	`*-un-lft-identity`
94×	`add-sqr-sqrt`
92×	`times-frac`
60×	`add-cube-cbrt`
37×	`pow1`
27×	`swap-sqr`
24×	`distribute-lft-out`
19×	`associate-r` `associate-l`
18×	`sqrt-pow1` `pow1/2`
14×	`log-pow`
10×	`sqrt-div` `pow-prod-up`
9×	`add-exp-log` `unswap-sqr`
6×	`pow-prod-down` `pow-sqr` `add-cbrt-cube` `div-inv`
4×	`rem-sqrt-square` `add-log-exp`
3×	`log-div`
2×	`pow2` `frac-times` `pow-plus` `associate-r/` `rem-log-exp` `associate-l/` `prod-exp`
1×	`log-prod` `sqrt-unprod` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 185

Calls

4 calls:

5.0ms	(sqrt (/ (+ N 1.0) N))
6.0ms	(sqrt (/ (+ N 1.0) N))
36.0ms	(* (sqrt (/ (+ N 1.0) N)) (sqrt (/ (+ N 1.0) N)))
11.0ms	(log (* (sqrt (/ (+ N 1.0) N)) (sqrt (/ (+ N 1.0) N))))

series293.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(sqrt (/ (+ N 1.0) N))
42.0ms	(sqrt (/ (+ N 1.0) N))
109.0ms	(* (sqrt (/ (+ N 1.0) N)) (sqrt (/ (+ N 1.0) N)))
97.0ms	(log (* (sqrt (/ (+ N 1.0) N)) (sqrt (/ (+ N 1.0) N))))

simplify55.0ms

Algorithm

egg-herbie

Counts

197 → 197

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	323	1241
1	1567	1138
2	5002	1114

prune336.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (pow N 3))
0.3b	(* 0.3333333333333333 (/ 1 (pow N 3)))
0.4b	(/ 1 (pow N 2))
13.2b	(- (+ (* 0.3333333333333333 (/ 1 (pow N 3))) (* 1.0 (/ 1 N))) (* 0.5 (/ 1 (pow N 2))))

rewrite92.0ms

Algorithm

rewrite-expression-head

Rules

104×	`times-frac`
89×	`add-sqr-sqrt`
73×	`*-un-lft-identity`
69×	`add-cube-cbrt`
42×	`add-exp-log`
40×	`associate-r`
35×	`unpow-prod-down`
23×	`cube-prod`
20×	`associate-/r*`
18×	`div-exp`
15×	`associate-*r/` `un-div-inv`
13×	`add-cbrt-cube` `sqr-pow`
12×	`frac-sub`
10×	`prod-exp`
9×	`pow-to-exp` `rec-exp` `1-exp` `pow-exp` `add-log-exp` `unswap-sqr`
8×	`frac-add`
7×	`cube-mult` `unpow3`
6×	`pow1` `associate-/l*`
4×	`unpow2`
3×	`cbrt-undiv` `associate-l` `div-inv`
2×	`pow-flip` `frac-2neg` `flip3-+` `diff-log` `clear-num` `cbrt-unprod` `flip-+` `inv-pow`
1×	`sub-neg` `flip3--` `pow-prod-down` `associate--l+` `sum-log` `*-commutative` `flip--`

Counts

4 → 231

Calls

4 calls:

4.0ms	(/ 1 (pow N 3))
18.0ms	(* 0.3333333333333333 (/ 1 (pow N 3)))
4.0ms	(/ 1 (pow N 2))
56.0ms	(- (+ (* 0.3333333333333333 (/ 1 (pow N 3))) (* 1.0 (/ 1 N))) (* 0.5 (/ 1 (pow N 2))))

series125.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(/ 1 (pow N 3))
36.0ms	(* 0.3333333333333333 (/ 1 (pow N 3)))
16.0ms	(/ 1 (pow N 2))
36.0ms	(- (+ (* 0.3333333333333333 (/ 1 (pow N 3))) (* 1.0 (/ 1 N))) (* 0.5 (/ 1 (pow N 2))))

simplify113.0ms

Algorithm

egg-herbie

Counts

243 → 243

Iterations

Useful iterations: 2 (96.0ms)

Iter	Nodes	Cost
0	702	1403
1	3749	1086
2	5001	1032

prune325.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0.0b

regimes15.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 29.0b

bsearch38.0ms

Steps

Iters	Range		Point
9	4043.3875059490183	556939279.5099251	8017.659518152493

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	18
1	32	18

end0.0ms

sample1.2s

Algorithm

intervals

Results

415.0ms	1731×	body	1280	valid
182.0ms	1230×	body	640	valid
178.0ms	7960×	body	80	nan
165.0ms	4129×	body	80	valid
58.0ms	614×	body	320	valid
20.0ms	296×	body	160	valid