Details

sample50.0ms

Algorithm

intervals

Results

15.0ms	56×	body	1280	valid
8.0ms	46×	body	640	valid
7.0ms	241×	body	80	nan
6.0ms	125×	body	80	valid
2.0ms	20×	body	320	valid
1.0ms	9×	body	160	valid

simplify4.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	9	4
1	10	4
2	10	4

prune3.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 30.5b

Counts

2 → 1

localize11.0ms

Local error

Found 2 expressions with local error:

2.8b	(log (+ N 1.0))
2.8b	(- (log (+ N 1.0)) (log N))

rewrite11.0ms

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:

4.0ms	(log (+ N 1.0))
6.0ms	(- (log (+ N 1.0)) (log N))

series140.0ms

Counts

2 → 6

Calls

2 calls:

41.0ms	(log (+ N 1.0))
98.0ms	(- (log (+ N 1.0)) (log N))

simplify51.0ms

Algorithm

egg-herbie

Counts

47 → 47

Iterations

Useful iterations: 3 (47.0ms)

Iter	Nodes	Cost
0	212	281
1	547	264
2	1875	250
3	5002	247

prune128.0ms

Filtered

47 candidates to 33 candidates (70.2%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	44	3	47
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	45	3	48

Merged error: 0.0b

Counts

48 → 3

localize4.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (+ N 1.0) N)
2.7b	(log (/ (+ N 1.0) N))

rewrite11.0ms

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:

5.0ms	(/ (+ N 1.0) N)
4.0ms	(log (/ (+ N 1.0) N))

series140.0ms

Counts

2 → 6

Calls

2 calls:

53.0ms	(/ (+ N 1.0) N)
86.0ms	(log (/ (+ N 1.0) N))

simplify98.0ms

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

prune133.0ms

Filtered

66 candidates to 45 candidates (68.2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	66	0	66
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	66	3	69

Merged error: 0.0b

Counts

69 → 3

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N))
0.1b	(* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5))
0.6b	(/ 1 (pow N 2))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

59×	`add-sqr-sqrt`
57×	`times-frac`
42×	`*-un-lft-identity`
36×	`add-cube-cbrt`
32×	`add-exp-log`
28×	`associate-l`
23×	`unpow-prod-down`
12×	`div-exp`
10×	`prod-exp` `add-cbrt-cube`
9×	`unpow2` `unswap-sqr` `sqr-pow`
8×	`associate-/r*`
6×	`pow-to-exp` `rec-exp` `1-exp` `associate-r` `pow-exp`
5×	`pow1` `frac-add` `add-log-exp`
4×	`distribute-rgt-in` `frac-times` `sub-neg` `associate-+l+` `flip3--` `distribute-lft-in` `associate-*r/` `flip--`
3×	`associate-/l*`
2×	`cbrt-undiv` `associate-*l/` `cbrt-unprod` `div-inv` `difference-of-squares`
1×	`+-commutative` `pow-flip` `frac-2neg` `flip3-+` `pow-prod-down` `clear-num` `sum-log` `*-commutative` `flip-+` `distribute-lft-out--` `inv-pow`

Counts

3 → 150

Calls

3 calls:

15.0ms	(+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N))
16.0ms	(* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5))
5.0ms	(/ 1 (pow N 2))

series132.0ms

Counts

3 → 9

Calls

3 calls:

31.0ms	(+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N))
80.0ms	(* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5))
21.0ms	(/ 1 (pow N 2))

simplify71.0ms

Algorithm

egg-herbie

Counts

159 → 159

Iterations

Useful iterations: 2 (58.0ms)

Iter	Nodes	Cost
0	583	1075
1	2726	892
2	5001	829

prune302.0ms

Filtered

159 candidates to 89 candidates (56.0%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	159	0	159
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	159	3	162

Merged error: 0.0b

Counts

162 → 3

localize16.0ms

Local error

Found 4 expressions with local error:

2.8b	(- (pow (log (+ N 1.0)) 3) (pow (log N) 3))
2.8b	(log (+ N 1.0))
2.8b	(log (+ N 1.0))
2.8b	(log (+ N 1.0))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-sqr-sqrt` `*-un-lft-identity`
24×	`unpow-prod-down` `cube-prod`
23×	`pow1`
19×	`log-pow`
17×	`distribute-lft-out--`
16×	`difference-of-squares`
12×	`log-prod`
8×	`sqr-pow`
7×	`add-exp-log` `add-cube-cbrt`
6×	`log-div` `add-log-exp`
4×	`add-cbrt-cube`
3×	`flip3-+` `rem-log-exp` `flip-+` `distribute-lft-out`
1×	`difference-cubes` `sub-neg` `flip3--` `diff-log` `flip--`

Counts

4 → 91

Calls

4 calls:

13.0ms	(- (pow (log (+ N 1.0)) 3) (pow (log N) 3))
3.0ms	(log (+ N 1.0))
3.0ms	(log (+ N 1.0))
3.0ms	(log (+ N 1.0))

series328.0ms

Counts

4 → 12

Calls

4 calls:

196.0ms	(- (pow (log (+ N 1.0)) 3) (pow (log N) 3))
43.0ms	(log (+ N 1.0))
47.0ms	(log (+ N 1.0))
43.0ms	(log (+ N 1.0))

simplify49.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	480	888
1	1809	857
2	5001	844

prune459.0ms

Filtered

103 candidates to 66 candidates (64.1%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	102	1	103
Fresh	0	0	0
Picked	1	0	1
Done	0	2	2
Total	103	3	106

Merged error: 0.0b

Counts

106 → 3

regimes34.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 29.2b

bsearch37.0ms

Steps

Iters	Range		Point
9	911.8039404667869	114238954.84408061	7257.543954629768

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	10
1	24	10

end0.0ms

sample1.5s

Algorithm

intervals

Results

487.0ms	1779×	body	1280	valid
230.0ms	7953×	body	80	nan
211.0ms	1205×	body	640	valid
194.0ms	4091×	body	80	valid
72.0ms	620×	body	320	valid
22.0ms	305×	body	160	valid

Details

sample50.0ms

simplify4.0ms

prune3.0ms

localize11.0ms

rewrite11.0ms

series140.0ms

simplify51.0ms

prune128.0ms

localize4.0ms

rewrite11.0ms

series140.0ms

simplify98.0ms

prune133.0ms

localize9.0ms

rewrite42.0ms

series132.0ms

simplify71.0ms

prune302.0ms

localize16.0ms

rewrite28.0ms

series328.0ms

simplify49.0ms

prune459.0ms

regimes34.0ms

bsearch37.0ms

simplify1.0ms

end0.0ms

sample1.5s

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