Details

sample57.0ms

Algorithm

intervals

Results

19.0ms	64×	body	1280	valid
9.0ms	268×	body	80	nan
7.0ms	33×	body	640	valid
6.0ms	118×	body	80	valid
4.0ms	31×	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: 32.3b

localize7.0ms

Local error

Found 2 expressions with local error:

2.0b	(log (+ N 1.0))
3.4b	(- (log (+ N 1.0)) (log N))

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:

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

series138.0ms

Counts

2 → 6

Calls

2 calls:

40.0ms	(log (+ N 1.0))
98.0ms	(- (log (+ N 1.0)) (log N))

simplify54.0ms

Algorithm

egg-herbie

Counts

47 → 47

Iterations

Useful iterations: 3 (50.0ms)

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

prune96.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

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))
0.2b	(/ 1 (pow N 2))

rewrite70.0ms

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:

17.0ms	(+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N))
43.0ms	(* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5))
4.0ms	(/ 1 (pow N 2))

series124.0ms

Counts

3 → 9

Calls

3 calls:

32.0ms	(+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N))
75.0ms	(* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5))
16.0ms	(/ 1 (pow N 2))

simplify73.0ms

Algorithm

egg-herbie

Counts

159 → 159

Iterations

Useful iterations: 2 (60.0ms)

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

prune249.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ 1 (pow N 2)) (/ 0.3333333333333333 N))
0.1b	(/ (/ 0.5 N) N)
0.2b	(/ 1 (pow N 2))
14.0b	(+ (* (/ 1 (pow N 2)) (/ 0.3333333333333333 N)) (- (/ 1.0 N) (/ (/ 0.5 N) N)))

rewrite141.0ms

Algorithm

rewrite-expression-head

Rules

157×	`times-frac`
130×	`add-sqr-sqrt`
93×	`*-un-lft-identity`
85×	`add-cube-cbrt`
68×	`add-exp-log`
31×	`div-exp`
28×	`associate-l`
25×	`unpow-prod-down`
23×	`add-cbrt-cube`
20×	`prod-exp`
18×	`unswap-sqr`
16×	`associate-/l*`
13×	`associate-r`
12×	`frac-add`
11×	`associate-/r*` `unpow2` `sqr-pow`
9×	`pow-to-exp` `rec-exp` `1-exp` `pow-exp` `add-log-exp`
8×	`cbrt-undiv` `div-inv`
6×	`pow1`
5×	`frac-times` `associate-r/` `associate-l/`
4×	`cbrt-unprod`
3×	`flip3--` `frac-sub` `flip--` `sub-div`
2×	`associate-+r+` `frac-2neg` `clear-num` `sum-log`
1×	`+-commutative` `associate-+r-` `sub-neg` `pow-flip` `flip3-+` `diff-log` `pow-prod-down` `*-commutative` `flip-+` `associate-/l/` `inv-pow`

Counts

4 → 249

Calls

4 calls:

20.0ms	(* (/ 1 (pow N 2)) (/ 0.3333333333333333 N))
5.0ms	(/ (/ 0.5 N) N)
4.0ms	(/ 1 (pow N 2))
100.0ms	(+ (* (/ 1 (pow N 2)) (/ 0.3333333333333333 N)) (- (/ 1.0 N) (/ (/ 0.5 N) N)))

series112.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(* (/ 1 (pow N 2)) (/ 0.3333333333333333 N))
24.0ms	(/ (/ 0.5 N) N)
16.0ms	(/ 1 (pow N 2))
35.0ms	(+ (* (/ 1 (pow N 2)) (/ 0.3333333333333333 N)) (- (/ 1.0 N) (/ (/ 0.5 N) N)))

simplify47.0ms

Algorithm

egg-herbie

Counts

261 → 261

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1184	1758
1	5002	1526

prune482.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (+ N 1.0) N)
3.6b	(log (/ (+ N 1.0) N))

rewrite15.0ms

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:

9.0ms	(/ (+ 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)
84.0ms	(log (/ (+ N 1.0) N))

simplify101.0ms

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

prune108.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

regimes21.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 32.1b

bsearch32.0ms

Steps

Iters	Range		Point
8	21.02059315853866	376494.23081693525	6620.0699010986755

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	13
1	28	13

end0.0ms

sample1.6s

Algorithm

intervals

Results

542.0ms	1727×	body	1280	valid
265.0ms	7862×	body	80	nan
250.0ms	1196×	body	640	valid
232.0ms	4138×	body	80	valid
90.0ms	646×	body	320	valid
24.0ms	293×	body	160	valid