Details

sample42.0ms

Algorithm

intervals

Results

10.0ms	43×	body	1280	valid
6.0ms	293×	body	80	nan
6.0ms	141×	body	80	valid
6.0ms	39×	body	640	valid
2.0ms	17×	body	320	valid
1.0ms	16×	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: 27.0b

localize6.0ms

Local error

Found 2 expressions with local error:

2.2b	(log (+ N 1.0))
4.2b	(- (log (+ N 1.0)) (log N))

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:

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

series140.0ms

Counts

2 → 6

Calls

2 calls:

46.0ms	(log (+ N 1.0))
93.0ms	(- (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

prune127.0ms

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)
4.3b	(log (/ (+ N 1.0) N))

rewrite28.0ms

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:

20.0ms	(/ (+ N 1.0) N)
6.0ms	(log (/ (+ N 1.0) N))

series128.0ms

Counts

2 → 6

Calls

2 calls:

46.0ms	(/ (+ N 1.0) N)
82.0ms	(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

prune122.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 4 expressions with local error:

2.2b	(log (+ N 1.0))
2.2b	(log (+ N 1.0))
2.2b	(log (+ N 1.0))
26.8b	(fma (* (cbrt (log (+ N 1.0))) (cbrt (log (+ N 1.0)))) (cbrt (log (+ N 1.0))) (log (/ 1 N)))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

13×	`*-un-lft-identity`
12×	`log-prod`
7×	`pow1` `add-exp-log` `add-sqr-sqrt` `add-cube-cbrt`
6×	`log-div`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`flip3-+` `rem-log-exp` `log-pow` `flip-+` `distribute-lft-out`
1×	`fma-udef`

Counts

4 → 61

Calls

4 calls:

4.0ms	(log (+ N 1.0))
4.0ms	(log (+ N 1.0))
4.0ms	(log (+ N 1.0))
0.0ms	(fma (* (cbrt (log (+ N 1.0))) (cbrt (log (+ N 1.0)))) (cbrt (log (+ N 1.0))) (log (/ 1 N)))

series526.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(log (+ N 1.0))
45.0ms	(log (+ N 1.0))
40.0ms	(log (+ N 1.0))
400.0ms	(fma (* (cbrt (log (+ N 1.0))) (cbrt (log (+ N 1.0)))) (cbrt (log (+ N 1.0))) (log (/ 1 N)))

simplify48.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	435	668
1	1865	598
2	5002	583

prune244.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

2.2b	(log (+ N 1.0))
26.8b	(fma (* (cbrt (log (+ N 1.0))) (cbrt (log (+ N 1.0)))) (cbrt (log (+ N 1.0))) (log (/ 1 N)))
26.8b	(fma (* (cbrt (log (+ N 1.0))) (cbrt (log (+ N 1.0)))) (cbrt (log (+ N 1.0))) (log (/ 1 N)))
26.8b	(fma (* (cbrt (log (+ N 1.0))) (cbrt (log (+ N 1.0)))) (cbrt (log (+ N 1.0))) (log (/ 1 N)))

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

7×	`*-un-lft-identity`
5×	`pow1` `add-exp-log` `add-sqr-sqrt` `add-cube-cbrt`
4×	`expm1-log1p-u` `log-prod` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`fma-udef`
2×	`log-div`
1×	`flip3-+` `rem-log-exp` `log-pow` `flip-+` `distribute-lft-out`

Counts

4 → 47

Calls

4 calls:

4.0ms	(log (+ N 1.0))
0.0ms	(fma (* (cbrt (log (+ N 1.0))) (cbrt (log (+ N 1.0)))) (cbrt (log (+ N 1.0))) (log (/ 1 N)))
0.0ms	(fma (* (cbrt (log (+ N 1.0))) (cbrt (log (+ N 1.0)))) (cbrt (log (+ N 1.0))) (log (/ 1 N)))
0.0ms	(fma (* (cbrt (log (+ N 1.0))) (cbrt (log (+ N 1.0)))) (cbrt (log (+ N 1.0))) (log (/ 1 N)))

series1.3s

Counts

4 → 12

Calls

4 calls:

45.0ms	(log (+ N 1.0))
405.0ms	(fma (* (cbrt (log (+ N 1.0))) (cbrt (log (+ N 1.0)))) (cbrt (log (+ N 1.0))) (log (/ 1 N)))
405.0ms	(fma (* (cbrt (log (+ N 1.0))) (cbrt (log (+ N 1.0)))) (cbrt (log (+ N 1.0))) (log (/ 1 N)))
396.0ms	(fma (* (cbrt (log (+ N 1.0))) (cbrt (log (+ N 1.0)))) (cbrt (log (+ N 1.0))) (log (/ 1 N)))

simplify49.0ms

Algorithm

egg-herbie

Counts

59 → 59

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	435	1212
1	1865	1090
2	5002	1045

prune305.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

regimes22.0ms

Accuracy

100% (0.0b remaining)

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

bsearch31.0ms

Steps

Iters	Range		Point
10	177.7519823634673	3845520655822.575	8816.358696954578

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	9
1	21	9

end0.0ms

sample1.3s

Algorithm

intervals

Results

417.0ms	1744×	body	1280	valid
188.0ms	7890×	body	80	nan
184.0ms	1226×	body	640	valid
169.0ms	4117×	body	80	valid
61.0ms	613×	body	320	valid
20.0ms	300×	body	160	valid