Details

sample47.0ms

Algorithm

intervals

Results

18.0ms	66×	body	1280	valid
6.0ms	269×	body	80	nan
6.0ms	141×	body	80	valid
4.0ms	26×	body	640	valid
1.0ms	11×	body	320	valid
1.0ms	12×	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: 26.5b

localize7.0ms

Local error

Found 2 expressions with local error:

2.5b	(- (log (+ N 1.0)) (log N))
2.9b	(log (+ N 1.0))

rewrite17.0ms

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:

11.0ms	(- (log (+ N 1.0)) (log N))
5.0ms	(log (+ N 1.0))

series128.0ms

Counts

2 → 6

Calls

2 calls:

89.0ms	(- (log (+ N 1.0)) (log N))
39.0ms	(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

prune96.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.2b

localize7.0ms

Local error

Found 2 expressions with local error:

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

rewrite24.0ms

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:

17.0ms	(/ (+ N 1.0) N)
6.0ms	(log (/ (+ N 1.0) N))

series122.0ms

Counts

2 → 6

Calls

2 calls:

45.0ms	(/ (+ N 1.0) N)
77.0ms	(log (/ (+ N 1.0) N))

simplify99.0ms

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

prune108.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.1b

localize7.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (/ (+ N 1.0) N))
0.1b	(sqrt (/ (+ N 1.0) N))
2.4b	(log (sqrt (/ (+ N 1.0) N)))
2.4b	(log (sqrt (/ (+ N 1.0) N)))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

64×	`sqrt-prod`
62×	`*-un-lft-identity`
50×	`times-frac`
44×	`add-sqr-sqrt`
38×	`add-cube-cbrt` `log-prod`
12×	`distribute-lft-out`
10×	`pow1`
6×	`add-exp-log` `log-pow`
4×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `sqrt-div` `add-cbrt-cube` `div-inv` `add-log-exp`
2×	`log-div` `rem-log-exp`

Counts

4 → 118

Calls

4 calls:

9.0ms	(sqrt (/ (+ N 1.0) N))
9.0ms	(sqrt (/ (+ N 1.0) N))
6.0ms	(log (sqrt (/ (+ N 1.0) N)))
7.0ms	(log (sqrt (/ (+ N 1.0) N)))

series306.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(sqrt (/ (+ N 1.0) N))
44.0ms	(sqrt (/ (+ N 1.0) N))
109.0ms	(log (sqrt (/ (+ N 1.0) N)))
114.0ms	(log (sqrt (/ (+ N 1.0) N)))

simplify60.0ms

Algorithm

egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 3 (50.0ms)

Iter	Nodes	Cost
0	196	964
1	456	908
2	1761	868
3	5002	860

prune306.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.1b

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (cbrt (/ (+ N 1.0) N)) (cbrt (/ (+ N 1.0) N)))
2.4b	(log (sqrt (/ (+ N 1.0) N)))
2.4b	(log (sqrt (* (cbrt (/ (+ N 1.0) N)) (cbrt (/ (+ N 1.0) N)))))
2.4b	(log (sqrt (cbrt (/ (+ N 1.0) N))))

rewrite93.0ms

Algorithm

rewrite-expression-head

Rules

118×	`*-un-lft-identity`
104×	`cbrt-prod`
90×	`times-frac`
88×	`add-sqr-sqrt`
64×	`add-cube-cbrt`
45×	`log-prod`
36×	`sqrt-prod`
25×	`swap-sqr`
24×	`pow1` `distribute-lft-out`
19×	`associate-r` `associate-l`
18×	`log-pow`
13×	`pow1/3`
12×	`sqrt-pow1`
9×	`add-exp-log` `cbrt-div` `unswap-sqr`
6×	`div-inv`
5×	`log-div` `sqrt-div`
4×	`pow-prod-down` `pow-sqr` `pow-prod-up` `add-cbrt-cube` `add-log-exp`
3×	`pow1/2` `rem-log-exp`
2×	`pow2` `frac-times` `pow-plus` `associate-r/` `associate-l/`
1×	`prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 185

Calls

4 calls:

50.0ms	(* (cbrt (/ (+ N 1.0) N)) (cbrt (/ (+ N 1.0) N)))
6.0ms	(log (sqrt (/ (+ N 1.0) N)))
20.0ms	(log (sqrt (* (cbrt (/ (+ N 1.0) N)) (cbrt (/ (+ N 1.0) N)))))
7.0ms	(log (sqrt (cbrt (/ (+ N 1.0) N))))

series646.0ms

Counts

4 → 12

Calls

4 calls:

132.0ms	(* (cbrt (/ (+ N 1.0) N)) (cbrt (/ (+ N 1.0) N)))
118.0ms	(log (sqrt (/ (+ N 1.0) N)))
193.0ms	(log (sqrt (* (cbrt (/ (+ N 1.0) N)) (cbrt (/ (+ N 1.0) N)))))
203.0ms	(log (sqrt (cbrt (/ (+ N 1.0) N))))

simplify65.0ms

Algorithm

egg-herbie

Counts

197 → 197

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	594	2040
1	1747	1930
2	5002	1843

prune628.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

regimes84.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 29.2b

bsearch20.0ms

Steps

Iters	Range		Point
5	7732.291311132395	19335.207415959976	8430.538053514889

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	18
1	33	18

end0.0ms

sample1.3s

Algorithm

intervals

Results

429.0ms	1748×	body	1280	valid
185.0ms	7894×	body	80	nan
182.0ms	1195×	body	640	valid
172.0ms	4112×	body	80	valid
61.0ms	614×	body	320	valid
20.0ms	331×	body	160	valid