Details

sample70.0ms

Algorithm

intervals

Results

21.0ms	54×	body	1280	valid
13.0ms	268×	body	80	nan
11.0ms	133×	body	80	valid
10.0ms	43×	body	640	valid
3.0ms	16×	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: 28.7b

localize6.0ms

Local error

Found 2 expressions with local error:

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

rewrite10.0ms

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))

series140.0ms

Counts

2 → 6

Calls

2 calls:

46.0ms	(log (+ N 1.0))
94.0ms	(- (log (+ N 1.0)) (log N))

simplify52.0ms

Algorithm

egg-herbie

Counts

47 → 47

Iterations

Useful iterations: 3 (48.0ms)

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

prune112.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (+ N 1.0) N)
3.0b	(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×	`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)
4.0ms	(log (/ (+ N 1.0) N))

series136.0ms

Counts

2 → 6

Calls

2 calls:

51.0ms	(/ (+ N 1.0) N)
85.0ms	(log (/ (+ N 1.0) N))

simplify100.0ms

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

prune124.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (/ (+ N 1.0) N))
0.3b	(cbrt (/ (+ N 1.0) N))
3.1b	(log (cbrt (/ (+ N 1.0) N)))
3.1b	(log (cbrt (/ (+ N 1.0) N)))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

64×	`cbrt-prod`
62×	`*-un-lft-identity`
48×	`times-frac`
38×	`add-sqr-sqrt` `add-cube-cbrt` `log-prod`
12×	`distribute-lft-out`
6×	`pow1` `add-exp-log`
4×	`cbrt-div` `pow1/3` `log-pow` `add-cbrt-cube` `div-inv` `add-log-exp`
2×	`log-div` `rem-log-exp`

Counts

4 → 110

Calls

4 calls:

3.0ms	(cbrt (/ (+ N 1.0) N))
3.0ms	(cbrt (/ (+ N 1.0) N))
4.0ms	(log (cbrt (/ (+ N 1.0) N)))
4.0ms	(log (cbrt (/ (+ N 1.0) N)))

series686.0ms

Counts

4 → 12

Calls

4 calls:

128.0ms	(cbrt (/ (+ N 1.0) N))
135.0ms	(cbrt (/ (+ N 1.0) N))
206.0ms	(log (cbrt (/ (+ N 1.0) N)))
217.0ms	(log (cbrt (/ (+ N 1.0) N)))

simplify106.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 3 (95.0ms)

Iter	Nodes	Cost
0	267	1056
1	755	996
2	3236	966
3	5001	948

prune372.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (/ 1 (sqrt N)))
0.5b	(cbrt (/ (+ N 1.0) (sqrt N)))
2.8b	(+ (log (cbrt (/ 1 (sqrt N)))) (log (cbrt (/ (+ N 1.0) (sqrt N)))))
3.1b	(log (cbrt (/ (+ N 1.0) N)))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

116×	`cbrt-prod`
105×	`*-un-lft-identity`
96×	`times-frac`
75×	`log-prod`
71×	`add-sqr-sqrt` `add-cube-cbrt`
42×	`sqrt-prod`
31×	`associate-+r+`
25×	`associate-+l+`
20×	`distribute-lft-out`
9×	`pow1`
8×	`log-pow`
5×	`add-exp-log` `cbrt-div` `pow1/3` `div-inv`
4×	`add-cbrt-cube` `add-log-exp`
3×	`log-div`
1×	`+-commutative` `associate-+l-` `associate-+r-` `flip3-+` `rem-log-exp` `sum-log` `flip-+`

Counts

4 → 172

Calls

4 calls:

3.0ms	(cbrt (/ 1 (sqrt N)))
4.0ms	(cbrt (/ (+ N 1.0) (sqrt N)))
19.0ms	(+ (log (cbrt (/ 1 (sqrt N)))) (log (cbrt (/ (+ N 1.0) (sqrt N)))))
4.0ms	(log (cbrt (/ (+ N 1.0) N)))

series742.0ms

Counts

4 → 12

Calls

4 calls:

160.0ms	(cbrt (/ 1 (sqrt N)))
133.0ms	(cbrt (/ (+ N 1.0) (sqrt N)))
243.0ms	(+ (log (cbrt (/ 1 (sqrt N)))) (log (cbrt (/ (+ N 1.0) (sqrt N)))))
207.0ms	(log (cbrt (/ (+ N 1.0) N)))

simplify63.0ms

Algorithm

egg-herbie

Counts

184 → 184

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	748	1922
1	1991	1858
2	5001	1800

prune684.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

regimes57.0ms

Accuracy

99.7% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 29.1b

bsearch1.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	14
1	27	14

end0.0ms

sample2.0s

Algorithm

intervals

Results

585.0ms	1737×	body	1280	valid
405.0ms	7994×	body	80	nan
352.0ms	4115×	body	80	valid
283.0ms	1212×	body	640	valid
107.0ms	646×	body	320	valid
32.0ms	290×	body	160	valid