Details

sample66.0ms

Algorithm

intervals

Results

18.0ms	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

localize7.0ms

Local error

Found 2 expressions with local error:

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

rewrite12.0ms

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:

2.0ms	(log (+ N 1.0))
7.0ms	(- (log (+ N 1.0)) (log N))

series145.0ms

Counts

2 → 6

Calls

2 calls:

43.0ms	(log (+ N 1.0))
102.0ms	(- (log (+ N 1.0)) (log N))

simplify125.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 3 (119.0ms)

Iter	Nodes	Cost
0	277	598
1	837	444
2	3748	347
3	5001	343

prune138.0ms

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×	`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:

8.0ms	(/ (+ N 1.0) N)
4.0ms	(log (/ (+ N 1.0) N))

series137.0ms

Counts

2 → 6

Calls

2 calls:

48.0ms	(/ (+ N 1.0) N)
89.0ms	(log (/ (+ N 1.0) N))

simplify112.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 3 (101.0ms)

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

prune126.0ms

Pruning

5 alts after pruning (4 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)))

rewrite19.0ms

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:

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)))

series708.0ms

Counts

4 → 12

Calls

4 calls:

132.0ms	(cbrt (/ (+ N 1.0) N))
138.0ms	(cbrt (/ (+ N 1.0) N))
215.0ms	(log (cbrt (/ (+ N 1.0) N)))
222.0ms	(log (cbrt (/ (+ N 1.0) N)))

simplify117.0ms

Algorithm

egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 3 (98.0ms)

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

prune376.0ms

Pruning

5 alts after pruning (4 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)))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

116×	`cbrt-prod`
106×	`*-un-lft-identity`
96×	`times-frac`
75×	`log-prod`
72×	`add-sqr-sqrt` `add-cube-cbrt`
42×	`sqrt-prod`
31×	`associate-+r+`
25×	`associate-+l+`
20×	`distribute-lft-out`
10×	`pow1` `log-pow`
6×	`pow1/3`
5×	`add-exp-log` `cbrt-div` `fma-def` `div-inv`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`log-div`
1×	`+-commutative` `associate-+l-` `associate-+r-` `flip3-+` `rem-log-exp` `sum-log` `flip-+`

Counts

4 → 185

Calls

4 calls:

3.0ms	(cbrt (/ 1 (sqrt N)))
4.0ms	(cbrt (/ (+ N 1.0) (sqrt N)))
15.0ms	(+ (log (cbrt (/ 1 (sqrt N)))) (log (cbrt (/ (+ N 1.0) (sqrt N)))))
4.0ms	(log (cbrt (/ (+ N 1.0) N)))

series777.0ms

Counts

4 → 12

Calls

4 calls:

164.0ms	(cbrt (/ 1 (sqrt N)))
129.0ms	(cbrt (/ (+ N 1.0) (sqrt N)))
258.0ms	(+ (log (cbrt (/ 1 (sqrt N)))) (log (cbrt (/ (+ N 1.0) (sqrt N)))))
226.0ms	(log (cbrt (/ (+ N 1.0) N)))

simplify67.0ms

Algorithm

egg-herbie

Counts

197 → 197

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	773	1967
1	2103	1898
2	5001	1846

prune725.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

regimes58.0ms

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	24	13
1	24	13

end0.0ms

sample1.9s

Algorithm

intervals

Results

579.0ms	1737×	body	1280	valid
396.0ms	7994×	body	80	nan
346.0ms	4115×	body	80	valid
279.0ms	1212×	body	640	valid
102.0ms	646×	body	320	valid
31.0ms	290×	body	160	valid