Details

sample45.0ms

Algorithm

intervals

Results

15.0ms	66×	body	1280	valid
7.0ms	50×	body	640	valid
6.0ms	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

localize6.0ms

Local error

Found 2 expressions with local error:

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

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

22×	`*-un-lft-identity`
16×	`pow1` `add-sqr-sqrt` `prod-diff`
14×	`add-cube-cbrt` `log-pow`
11×	`log-prod`
4×	`log-div` `fma-neg` `associate--l+` `distribute-lft-out--`
3×	`add-exp-log` `associate--r+`
2×	`associate--l-` `expm1-log1p-u` `flip3-+` `add-cbrt-cube` `flip-+` `log1p-expm1-u` `distribute-lft-out` `add-log-exp`
1×	`sub-neg` `flip3--` `diff-log` `rem-log-exp` `flip--` `difference-of-squares`

Counts

2 → 65

Calls

2 calls:

7.0ms	(- (log (+ N 1.0)) (log N))
2.0ms	(log (+ N 1.0))

series134.0ms

Counts

2 → 6

Calls

2 calls:

92.0ms	(- (log (+ N 1.0)) (log N))
41.0ms	(log (+ N 1.0))

simplify122.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 3 (116.0ms)

Iter	Nodes	Cost
0	277	598
1	837	444
2	3748	347
3	5001	345

prune129.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize9.0ms

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))

rewrite125.0ms

Algorithm

rewrite-expression-head

Rules

242×	`add-sqr-sqrt`
222×	`*-un-lft-identity`
214×	`add-cube-cbrt`
202×	`times-frac`
195×	`prod-diff`
82×	`distribute-rgt-in` `associate-+l+` `distribute-lft-in`
33×	`add-exp-log`
28×	`associate-l`
23×	`unpow-prod-down`
18×	`div-inv`
13×	`fma-neg`
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×	`expm1-log1p-u` `frac-times` `associate-*r/` `log1p-expm1-u` `difference-of-squares`
3×	`associate-/l*`
2×	`cbrt-undiv` `associate-*l/` `cbrt-unprod` `distribute-lft-out--`
1×	`+-commutative` `pow-flip` `fma-def` `frac-2neg` `flip3-+` `diff-log` `pow-prod-down` `clear-num` `sum-log` `*-commutative` `flip-+` `inv-pow`

Counts

4 → 382

Calls

4 calls:

13.0ms	(- (/ 0.3333333333333333 N) 0.5)
29.0ms	(+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N))
51.0ms	(* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5))
4.0ms	(/ 1 (pow N 2))

series160.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(- (/ 0.3333333333333333 N) 0.5)
29.0ms	(+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N))
76.0ms	(* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5))
16.0ms	(/ 1 (pow N 2))

simplify120.0ms

Algorithm

egg-herbie

Counts

394 → 394

Iterations

Useful iterations: 1 (24.0ms)

Iter	Nodes	Cost
0	1036	4191
1	4558	2787
2	5001	2787

prune779.0ms

Pruning

4 alts after pruning (3 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))

rewrite14.0ms

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×	`expm1-log1p-u` `div-exp` `rem-log-exp` `log1p-expm1-u` `div-inv` `associate-/l/` `add-log-exp`
1×	`cbrt-undiv` `log-div` `frac-2neg` `flip3-+` `clear-num` `log-pow` `flip-+`

Counts

2 → 64

Calls

2 calls:

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

series130.0ms

Counts

2 → 6

Calls

2 calls:

45.0ms	(/ (+ N 1.0) N)
85.0ms	(log (/ (+ N 1.0) N))

simplify108.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 3 (97.0ms)

Iter	Nodes	Cost
0	243	383
1	808	358
2	3663	347
3	5001	344

prune116.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize6.0ms

Local error

Found 2 expressions with local error:

0.1b	(* (+ N 1.0) (/ 1 N))
8.9b	(log (* (+ N 1.0) (/ 1 N)))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-exp-log`
17×	`add-sqr-sqrt`
13×	`-un-lft-identity` `associate-r*`
11×	`times-frac`
10×	`add-cube-cbrt`
8×	`prod-exp`
7×	`pow1` `add-cbrt-cube`
6×	`log-div`
5×	`rem-log-exp`
4×	`frac-times` `flip3-+` `div-exp` `associate-l` `associate-*l/` `flip-+`
3×	`unswap-sqr`
2×	`expm1-log1p-u` `rec-exp` `1-exp` `associate-*r/` `pow-prod-down` `log-pow` `un-div-inv` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
1×	`cbrt-undiv` `log-prod` `*-commutative` `div-inv` `distribute-lft-out`

Counts

2 → 66

Calls

2 calls:

14.0ms	(* (+ N 1.0) (/ 1 N))
7.0ms	(log (* (+ N 1.0) (/ 1 N)))

series137.0ms

Counts

2 → 6

Calls

2 calls:

52.0ms	(* (+ N 1.0) (/ 1 N))
84.0ms	(log (* (+ N 1.0) (/ 1 N)))

simplify40.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	321	357
1	1504	316
2	5002	289

prune118.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

regimes23.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 31.4b

bsearch30.0ms

Steps

Iters	Range		Point
9	251.47950061764826	4321407464.299789	10602.002068345459

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	11
1	26	11

end0.0ms

sample1.2s

Algorithm

intervals

Results

415.0ms	1750×	body	1280	valid
188.0ms	1261×	body	640	valid
186.0ms	8377×	body	80	nan
161.0ms	4068×	body	80	valid
60.0ms	616×	body	320	valid
18.0ms	305×	body	160	valid