Details

sample42.0ms

Algorithm

intervals

Results

14.0ms	55×	body	1280	valid
6.0ms	38×	body	640	valid
6.0ms	251×	body	80	nan
6.0ms	134×	body	80	valid
2.0ms	16×	body	320	valid
1.0ms	13×	body	160	valid

simplify8.0ms

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: 28.3b

localize6.0ms

Local error

Found 2 expressions with local error:

2.5b	(- (log (+ N 1.0)) (log N))
3.5b	(log (+ N 1.0))

rewrite20.0ms

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:

14.0ms	(- (log (+ N 1.0)) (log N))
4.0ms	(log (+ N 1.0))

series123.0ms

Counts

2 → 6

Calls

2 calls:

86.0ms	(- (log (+ N 1.0)) (log N))
37.0ms	(log (+ N 1.0))

simplify121.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 3 (115.0ms)

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

prune165.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize5.0ms

Local error

Found 2 expressions with local error:

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

rewrite25.0ms

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:

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

series122.0ms

Counts

2 → 6

Calls

2 calls:

46.0ms	(/ (+ N 1.0) N)
76.0ms	(log (/ (+ N 1.0) N))

simplify104.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 3 (98.0ms)

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

prune159.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize8.0ms

Local error

Found 4 expressions with local error:

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

rewrite27.0ms

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×	`expm1-log1p-u` `cbrt-div` `pow1/3` `log-pow` `add-cbrt-cube` `log1p-expm1-u` `div-inv` `add-log-exp`
2×	`log-div` `rem-log-exp`

Counts

4 → 118

Calls

4 calls:

5.0ms	(cbrt (/ (+ N 1.0) N))
5.0ms	(cbrt (/ (+ N 1.0) N))
6.0ms	(log (cbrt (/ (+ N 1.0) N)))
6.0ms	(log (cbrt (/ (+ N 1.0) N)))

series594.0ms

Counts

4 → 12

Calls

4 calls:

114.0ms	(cbrt (/ (+ N 1.0) N))
108.0ms	(cbrt (/ (+ N 1.0) N))
181.0ms	(log (cbrt (/ (+ N 1.0) N)))
190.0ms	(log (cbrt (/ (+ N 1.0) N)))

simplify106.0ms

Algorithm

egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 3 (95.0ms)

Iter	Nodes	Cost
0	278	1088
1	803	1024
2	3528	998
3	5002	962

prune545.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (/ (sqrt (+ N 1.0)) N))
2.4b	(log (cbrt (/ (+ N 1.0) N)))
2.7b	(+ (log (cbrt (/ (sqrt (+ N 1.0)) 1))) (log (cbrt (/ (sqrt (+ N 1.0)) N))))
3.3b	(log (cbrt (/ (sqrt (+ N 1.0)) 1)))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

116×	`cbrt-prod`
107×	`*-un-lft-identity`
103×	`log-prod`
96×	`times-frac`
73×	`add-sqr-sqrt` `add-cube-cbrt`
48×	`sqrt-prod`
28×	`associate-+l+` `associate-+r+`
20×	`distribute-lft-out`
12×	`log-pow`
11×	`pow1`
6×	`add-exp-log` `pow1/3`
5×	`cbrt-div` `fma-def` `div-inv`
4×	`expm1-log1p-u` `log-div` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`rem-log-exp`
1×	`+-commutative` `associate-+l-` `associate-+r-` `flip3-+` `sum-log` `flip-+`

Counts

4 → 190

Calls

4 calls:

9.0ms	(cbrt (/ (sqrt (+ N 1.0)) N))
6.0ms	(log (cbrt (/ (+ N 1.0) N)))
24.0ms	(+ (log (cbrt (/ (sqrt (+ N 1.0)) 1))) (log (cbrt (/ (sqrt (+ N 1.0)) N))))
7.0ms	(log (cbrt (/ (sqrt (+ N 1.0)) 1)))

series646.0ms

Counts

4 → 12

Calls

4 calls:

116.0ms	(cbrt (/ (sqrt (+ N 1.0)) N))
183.0ms	(log (cbrt (/ (+ N 1.0) N)))
244.0ms	(+ (log (cbrt (/ (sqrt (+ N 1.0)) 1))) (log (cbrt (/ (sqrt (+ N 1.0)) N))))
104.0ms	(log (cbrt (/ (sqrt (+ N 1.0)) 1)))

simplify72.0ms

Algorithm

egg-herbie

Counts

202 → 202

Iterations

Useful iterations: 2 (53.0ms)

Iter	Nodes	Cost
0	839	2231
1	2527	2091
2	5001	2032

prune1.1s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

regimes28.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 29.0b

bsearch32.0ms

Steps

Iters	Range		Point
8	357.62882370262366	15234496.061427226	7470.929670082821

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	10
1	24	10

end0.0ms

sample1.3s

Algorithm

intervals

Results

436.0ms	1769×	body	1280	valid
205.0ms	8056×	body	80	nan
189.0ms	1227×	body	640	valid
177.0ms	4116×	body	80	valid
58.0ms	579×	body	320	valid
19.0ms	309×	body	160	valid