Details

analyze2.0ms

Algorithm

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
50%	50%	0%	2
50%	25%	25%	3
50%	0%	50%	4

sample40.0ms

Algorithm

intervals

Results

18.0ms	63×	body	1280	valid
8.0ms	44×	body	640	valid
6.0ms	122×	body	80	valid
2.0ms	18×	body	320	valid
1.0ms	9×	body	160	valid

simplify4.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	71	7
1	71	7

prune3.0ms

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: 31.2b

Counts

2 → 1

localize7.0ms

Local error

Found 2 expressions with local error:

2.0b	(log (+ N 1.0))
2.1b	(- (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 → 40

Calls

2 calls:

3.0ms	(log (+ N 1.0))
7.0ms	(- (log (+ N 1.0)) (log N))

series10.0ms

Counts

2 → 6

Calls

2 calls:

3.0ms	(log (+ N 1.0))
7.0ms	(- (log (+ N 1.0)) (log N))

simplify43.0ms

Algorithm

egg-herbie

Counts

46 → 46

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5481	434

prune85.0ms

Filtered

35 candidates to 46 candidates (-31.4%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	42	4	46
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	43	4	47

Merged error: 0.1b

Counts

47 → 4

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ 1.0 N) (/ 0.5 (* N N)))
0.5b	(/ 0.3333333333333333 (pow N 3))
0.6b	(/ 0.5 (* N N))
12.0b	(+ (/ 0.3333333333333333 (pow N 3)) (- (/ 1.0 N) (/ 0.5 (* N N))))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

43×	`times-frac`
41×	`add-sqr-sqrt`
38×	`*-un-lft-identity`
31×	`add-cube-cbrt`
14×	`add-exp-log`
13×	`associate-/r*`
12×	`unpow-prod-down` `cube-prod`
11×	`add-cbrt-cube` `add-log-exp`
6×	`associate-/l*`
5×	`div-exp`
4×	`pow1` `cube-mult` `unpow3` `difference-of-squares` `sqr-pow`
3×	`cbrt-undiv` `frac-add`
2×	`sub-neg` `flip3--` `frac-2neg` `diff-log` `clear-num` `sum-log` `frac-sub` `flip--` `div-inv` `distribute-lft-out` `distribute-lft-out--`
1×	`+-commutative` `pow-to-exp` `associate-+r-` `associate-+r+` `flip3-+` `pow-exp` `prod-exp` `cbrt-unprod` `flip-+`

Counts

4 → 122

Calls

4 calls:

9.0ms	(- (/ 1.0 N) (/ 0.5 (* N N)))
5.0ms	(/ 0.3333333333333333 (pow N 3))
4.0ms	(/ 0.5 (* N N))
30.0ms	(+ (/ 0.3333333333333333 (pow N 3)) (- (/ 1.0 N) (/ 0.5 (* N N))))

series16.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(- (/ 1.0 N) (/ 0.5 (* N N)))
3.0ms	(/ 0.3333333333333333 (pow N 3))
3.0ms	(/ 0.5 (* N N))
4.0ms	(+ (/ 0.3333333333333333 (pow N 3)) (- (/ 1.0 N) (/ 0.5 (* N N))))

simplify32.0ms

Algorithm

egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 0 (22.0ms)

Iter	Nodes	Cost
0	5101	1475

prune163.0ms

Filtered

82 candidates to 134 candidates (-63.4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	132	2	134
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	132	6	138

Merged error: 0.1b

Counts

138 → 6

localize14.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ (sqrt 0.5) N)
0.5b	(/ (sqrt 0.5) N)
0.5b	(/ 0.3333333333333333 (pow N 3))
12.0b	(+ (/ 0.3333333333333333 (pow N 3)) (* (+ (/ (sqrt 0.5) N) (sqrt (/ 1.0 N))) (- (sqrt (/ 1.0 N)) (/ (sqrt 0.5) N))))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

72×	`times-frac`
59×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
24×	`sqrt-prod`
19×	`frac-add`
18×	`associate-/r*`
15×	`associate-/l*`
13×	`add-exp-log`
12×	`unpow-prod-down` `cube-prod`
10×	`add-cbrt-cube`
9×	`frac-times`
8×	`sqrt-div`
6×	`add-log-exp`
5×	`flip3-+` `div-exp` `flip-+`
4×	`pow1` `cube-mult` `flip3--` `unpow3` `frac-sub` `flip--` `sqr-pow`
3×	`cbrt-undiv` `frac-2neg` `associate-r/` `associate-l/` `clear-num` `div-inv`
2×	`sub-neg` `associate-+r+`
1×	`+-commutative` `distribute-rgt-in` `pow-to-exp` `distribute-lft-in` `pow-exp` `sum-log`

Counts

4 → 171

Calls

4 calls:

4.0ms	(/ (sqrt 0.5) N)
4.0ms	(/ (sqrt 0.5) N)
7.0ms	(/ 0.3333333333333333 (pow N 3))
18.0ms	(+ (/ 0.3333333333333333 (pow N 3)) (* (+ (/ (sqrt 0.5) N) (sqrt (/ 1.0 N))) (- (sqrt (/ 1.0 N)) (/ (sqrt 0.5) N))))

series20.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(/ (sqrt 0.5) N)
4.0ms	(/ (sqrt 0.5) N)
3.0ms	(/ 0.3333333333333333 (pow N 3))
9.0ms	(+ (/ 0.3333333333333333 (pow N 3)) (* (+ (/ (sqrt 0.5) N) (sqrt (/ 1.0 N))) (- (sqrt (/ 1.0 N)) (/ (sqrt 0.5) N))))

simplify63.0ms

Algorithm

egg-herbie

Counts

183 → 183

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5062	2527

prune390.0ms

Filtered

118 candidates to 183 candidates (-55.1%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	183	0	183
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	183	6	189

Merged error: 0.1b

Counts

189 → 6

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (+ N 1.0) N)
1.9b	(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))

series8.0ms

Counts

2 → 6

Calls

2 calls:

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

simplify40.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	4970	619
1	4970	619

prune78.0ms

Filtered

48 candidates to 66 candidates (-37.5%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	63	3	66
Fresh	2	1	3
Picked	1	0	1
Done	0	2	2
Total	66	6	72

Merged error: 0.0b

Counts

72 → 6

regimes44.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 31.9b

bsearch11.0ms

Steps

Iters	Range		Point
8	4032.9232090851956	15890396.227721306	8715.354544935088

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	37	25
1	37	25

end0.0ms

sample1.1s

Algorithm

intervals

Results

489.0ms	1725×	body	1280	valid
239.0ms	1281×	body	640	valid
208.0ms	4117×	body	80	valid
71.0ms	584×	body	320	valid
22.0ms	293×	body	160	valid

Details

analyze2.0ms

sample40.0ms

simplify4.0ms

prune3.0ms

localize7.0ms

rewrite11.0ms

series10.0ms

simplify43.0ms

prune85.0ms

localize10.0ms

rewrite52.0ms

series16.0ms

simplify32.0ms

prune163.0ms

localize14.0ms

rewrite39.0ms

series20.0ms

simplify63.0ms

prune390.0ms

localize5.0ms

rewrite11.0ms

series8.0ms

simplify40.0ms

prune78.0ms

regimes44.0ms

bsearch11.0ms

simplify1.0ms

end0.0ms

sample1.1s

Profiling