Details

sample46.0ms

Algorithm

intervals

Results

17.0ms	60×	body	1280	valid
6.0ms	40×	body	640	valid
6.0ms	254×	body	80	nan
5.0ms	122×	body	80	valid
2.0ms	20×	body	320	valid
1.0ms	14×	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: 31.6b

localize7.0ms

Local error

Found 2 expressions with local error:

2.6b	(log (+ N 1.0))
4.1b	(- (log (+ N 1.0)) (log N))

rewrite11.0ms

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:

3.0ms	(log (+ N 1.0))
6.0ms	(- (log (+ N 1.0)) (log N))

series132.0ms

Counts

2 → 6

Calls

2 calls:

43.0ms	(log (+ N 1.0))
89.0ms	(- (log (+ N 1.0)) (log N))

simplify52.0ms

Algorithm

egg-herbie

Counts

47 → 47

Iterations

Useful iterations: 3 (47.0ms)

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: 0.2b

localize13.0ms

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))
0.4b	(/ 1 (pow N 2))

rewrite42.0ms

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:

15.0ms	(+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N))
17.0ms	(* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5))
5.0ms	(/ 1 (pow N 2))

series122.0ms

Counts

3 → 9

Calls

3 calls:

32.0ms	(+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N))
73.0ms	(* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5))
16.0ms	(/ 1 (pow N 2))

simplify70.0ms

Algorithm

egg-herbie

Counts

159 → 159

Iterations

Useful iterations: 2 (58.0ms)

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

prune249.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (log (exp (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)))) (/ 1.0 N))
0.1b	(* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5))
0.4b	(/ 1 (pow N 2))
2.1b	(log (exp (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5))))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 168

Calls

4 calls:

10.0ms	(+ (log (exp (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)))) (/ 1.0 N))
17.0ms	(* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5))
5.0ms	(/ 1 (pow N 2))
4.0ms	(log (exp (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5))))

series194.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(+ (log (exp (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)))) (/ 1.0 N))
70.0ms	(* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5))
18.0ms	(/ 1 (pow N 2))
74.0ms	(log (exp (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5))))

simplify65.0ms

Algorithm

egg-herbie

Counts

180 → 180

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	564	1216
1	2461	985
2	5002	922

prune333.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

localize16.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ 1 (pow N 2))
2.1b	(log (exp (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5))))
2.1b	(log (exp (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5))))
2.1b	(log (exp (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5))))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `times-frac`
21×	`log-prod`
13×	`add-exp-log`
12×	`unpow-prod-down` `exp-sum`
9×	`log-pow`
8×	`associate-/r*`
7×	`pow1` `add-log-exp`
6×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `div-exp` `add-cbrt-cube`
4×	`unpow2` `sqr-pow`
3×	`pow-to-exp` `rec-exp` `exp-prod` `exp-to-pow` `1-exp` `rem-log-exp` `pow-exp` `associate-/l*`
1×	`cbrt-undiv` `pow-flip` `frac-2neg` `clear-num` `div-inv` `inv-pow`

Counts

4 → 111

Calls

4 calls:

7.0ms	(/ 1 (pow N 2))
4.0ms	(log (exp (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5))))
4.0ms	(log (exp (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5))))
4.0ms	(log (exp (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5))))

series234.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(/ 1 (pow N 2))
72.0ms	(log (exp (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5))))
73.0ms	(log (exp (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5))))
73.0ms	(log (exp (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5))))

simplify36.0ms

Algorithm

egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 2 (26.0ms)

Iter	Nodes	Cost
0	228	811
1	900	627
2	5002	575

prune289.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.2b

regimes19.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 31.7b

bsearch17.0ms

Steps

Iters	Range		Point
5	4050.4462513149238	12331.842748450485	9398.860464890142

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	10
1	24	10

end0.0ms

sample1.2s

Algorithm

intervals

Results

425.0ms	1732×	body	1280	valid
188.0ms	1242×	body	640	valid
176.0ms	7827×	body	80	nan
166.0ms	4096×	body	80	valid
59.0ms	609×	body	320	valid
19.0ms	321×	body	160	valid