Details

sample43.0ms

Algorithm

intervals

Results

13.0ms	52×	body	1280	valid
7.0ms	276×	body	80	nan
6.0ms	139×	body	80	valid
4.0ms	28×	body	640	valid
3.0ms	27×	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: 26.8b

localize7.0ms

Local error

Found 2 expressions with local error:

2.6b	(- (log (+ N 1.0)) (log N))
3.2b	(log (+ N 1.0))

rewrite13.0ms

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:

8.0ms	(- (log (+ N 1.0)) (log N))
3.0ms	(log (+ N 1.0))

series142.0ms

Counts

2 → 6

Calls

2 calls:

95.0ms	(- (log (+ N 1.0)) (log N))
47.0ms	(log (+ N 1.0))

simplify123.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 3 (116.0ms)

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

prune139.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(log (log (+ N 1.0)))
0.7b	(exp (log (log (+ N 1.0))))
3.2b	(log (+ N 1.0))
22.5b	(- (exp (log (log (+ N 1.0)))) (log N))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

36×	`log-prod`
31×	`*-un-lft-identity`
30×	`add-sqr-sqrt`
28×	`prod-diff`
26×	`add-cube-cbrt`
25×	`exp-sum`
22×	`pow1`
18×	`log-pow`
7×	`fma-neg`
6×	`add-exp-log`
5×	`add-log-exp`
4×	`expm1-log1p-u` `exp-prod` `add-cbrt-cube` `log1p-expm1-u`
3×	`associate--r+`
2×	`log-div` `rem-log-exp` `distribute-lft-out--` `difference-of-squares`
1×	`sub-neg` `flip3--` `flip3-+` `diff-log` `flip--` `flip-+` `rem-exp-log` `distribute-lft-out`

Counts

4 → 106

Calls

4 calls:

2.0ms	(log (log (+ N 1.0)))
2.0ms	(exp (log (log (+ N 1.0))))
2.0ms	(log (+ N 1.0))
14.0ms	(- (exp (log (log (+ N 1.0)))) (log N))

series273.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(log (log (+ N 1.0)))
41.0ms	(exp (log (log (+ N 1.0))))
47.0ms	(log (+ N 1.0))
95.0ms	(- (exp (log (log (+ N 1.0)))) (log N))

simplify55.0ms

Algorithm

egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	448	1188
1	1481	809
2	5001	615

prune216.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma 0.3333333333333333 (/ 1 (pow N 3)) (/ 1.0 N))
0.2b	(/ 1 (pow N 3))
0.4b	(/ 1 (pow N 2))
15.0b	(fma (- 0.5) (/ 1 (pow N 2)) (fma 0.3333333333333333 (/ 1 (pow N 3)) (/ 1.0 N)))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

60×	`times-frac`
46×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
24×	`unpow-prod-down`
22×	`add-exp-log`
20×	`associate-/r*`
12×	`cube-prod` `div-exp`
8×	`add-cbrt-cube` `sqr-pow`
6×	`pow-to-exp` `rec-exp` `1-exp` `pow-exp` `associate-/l*`
4×	`pow1` `expm1-log1p-u` `cube-mult` `unpow3` `log1p-expm1-u` `unpow2` `add-log-exp`
2×	`cbrt-undiv` `pow-flip` `frac-2neg` `clear-num` `fma-udef` `div-inv` `inv-pow`

Counts

4 → 154

Calls

4 calls:

0.0ms	(fma 0.3333333333333333 (/ 1 (pow N 3)) (/ 1.0 N))
5.0ms	(/ 1 (pow N 3))
4.0ms	(/ 1 (pow N 2))
0.0ms	(fma (- 0.5) (/ 1 (pow N 2)) (fma 0.3333333333333333 (/ 1 (pow N 3)) (/ 1.0 N)))

series173.0ms

Counts

4 → 12

Calls

4 calls:

85.0ms	(fma 0.3333333333333333 (/ 1 (pow N 3)) (/ 1.0 N))
37.0ms	(/ 1 (pow N 3))
16.0ms	(/ 1 (pow N 2))
35.0ms	(fma (- 0.5) (/ 1 (pow N 2)) (fma 0.3333333333333333 (/ 1 (pow N 3)) (/ 1.0 N)))

simplify54.0ms

Algorithm

egg-herbie

Counts

166 → 166

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	348	793
1	1771	580
2	5001	557

prune252.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes19.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 30.6b

bsearch34.0ms

Steps

Iters	Range		Point
9	2.027436157277799	7103758.057079569	3926.442943372092

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	14
1	27	14

end0.0ms

sample1.3s

Algorithm

intervals

Results

465.0ms	1832×	body	1280	valid
206.0ms	1279×	body	640	valid
185.0ms	7781×	body	80	nan
171.0ms	3993×	body	80	valid
63.0ms	603×	body	320	valid
19.0ms	293×	body	160	valid