Details

analyze269.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
6.2%	93.6%	0.2%	5
6.2%	68.6%	25.1%	6
6.2%	49.9%	43.9%	7
6.2%	35.9%	57.9%	8
6.2%	25.3%	68.4%	9
6.2%	20.1%	73.7%	10
6.2%	15.7%	78.1%	11
6.2%	12%	81.7%	12
6.2%	9%	84.8%	13
6.2%	7.5%	86.3%	14

sample137.0ms

Algorithm

intervals

Results

61.0ms	150×	body	640	valid
31.0ms	325×	body	80	nan
16.0ms	55×	body	320	valid
4.0ms	23×	body	160	valid
2.0ms	25×	body	80	valid
1.0ms	3×	body	1280	valid

simplify26.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	51	19
1	156	19
2	907	19
3	5001	19

prune6.0ms

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: 4.7b

Counts

2 → 1

localize23.0ms

Local error

Found 4 expressions with local error:

2.2b	(- (sqrt (+ x 1.0)) (sqrt x))
2.9b	(- (sqrt (+ y 1.0)) (sqrt y))
3.1b	(- (sqrt (+ t 1.0)) (sqrt t))
3.2b	(- (sqrt (+ z 1.0)) (sqrt z))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

36×	`add-sqr-sqrt`
32×	`*-un-lft-identity` `sqrt-prod`
16×	`difference-of-squares`
12×	`distribute-lft-out--` `add-log-exp`
4×	`pow1` `add-exp-log` `add-cube-cbrt` `sub-neg` `flip3--` `diff-log` `add-cbrt-cube` `flip--` `distribute-lft-out`

Counts

4 → 76

Calls

4 calls:

8.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
8.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
7.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
8.0ms	(- (sqrt (+ z 1.0)) (sqrt z))

series37.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
9.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
9.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
9.0ms	(- (sqrt (+ z 1.0)) (sqrt z))

simplify64.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 1 (15.0ms)

Iter	Nodes	Cost
0	692	864
1	2941	824
2	5001	824

prune256.0ms

Filtered

60 candidates to 88 candidates (-46.7%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	81	7	88
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	82	7	89

Merged error: 3.0b

Counts

89 → 7

localize33.0ms

Local error

Found 4 expressions with local error:

1.7b	(+ y (- 1.0 y))
2.2b	(- (sqrt (+ x 1.0)) (sqrt x))
3.1b	(- (sqrt (+ t 1.0)) (sqrt t))
3.2b	(- (sqrt (+ z 1.0)) (sqrt z))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

30×	`*-un-lft-identity`
28×	`add-sqr-sqrt`
24×	`sqrt-prod`
15×	`add-log-exp`
12×	`difference-of-squares`
10×	`distribute-lft-out--`
5×	`distribute-lft-out`
4×	`pow1` `add-exp-log` `add-cube-cbrt` `sub-neg` `diff-log` `add-cbrt-cube`
3×	`flip3--` `flip--`
2×	`associate-+r+` `sum-log`
1×	`+-commutative` `associate-+r-` `flip3-+` `flip-+`

Counts

4 → 74

Calls

4 calls:

6.0ms	(+ y (- 1.0 y))
8.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
8.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
8.0ms	(- (sqrt (+ z 1.0)) (sqrt z))

series30.0ms

Counts

4 → 12

Calls

4 calls:

1.0ms	(+ y (- 1.0 y))
9.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
10.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
10.0ms	(- (sqrt (+ z 1.0)) (sqrt z))

simplify57.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 1 (13.0ms)

Iter	Nodes	Cost
0	604	708
1	2432	673
2	5001	673

prune244.0ms

Filtered

59 candidates to 86 candidates (-45.8%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	82	4	86
Fresh	1	5	6
Picked	1	0	1
Done	0	0	0
Total	84	9	93

Merged error: 2.2b

Counts

93 → 9

localize25.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1.0 (+ (sqrt (+ y 1.0)) (sqrt y)))
2.2b	(- (sqrt (+ x 1.0)) (sqrt x))
3.1b	(- (sqrt (+ t 1.0)) (sqrt t))
3.2b	(- (sqrt (+ z 1.0)) (sqrt z))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

64×	`*-un-lft-identity`
40×	`sqrt-prod`
39×	`add-sqr-sqrt`
19×	`distribute-lft-out`
18×	`times-frac`
15×	`add-cube-cbrt`
12×	`difference-of-squares`
10×	`add-log-exp`
9×	`distribute-lft-out--`
6×	`add-exp-log` `associate-/r*` `add-cbrt-cube`
4×	`pow1`
3×	`sub-neg` `flip3--` `diff-log` `flip--` `associate-/l*`
2×	`associate-/r/`
1×	`cbrt-undiv` `frac-2neg` `flip3-+` `div-exp` `clear-num` `flip-+` `div-inv`

Counts

4 → 98

Calls

4 calls:

9.0ms	(/ 1.0 (+ (sqrt (+ y 1.0)) (sqrt y)))
8.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
9.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
8.0ms	(- (sqrt (+ z 1.0)) (sqrt z))

series40.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(/ 1.0 (+ (sqrt (+ y 1.0)) (sqrt y)))
11.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
9.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
9.0ms	(- (sqrt (+ z 1.0)) (sqrt z))

simplify88.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 2 (70.0ms)

Iter	Nodes	Cost
0	813	1083
1	3571	1022
2	5003	1005

prune397.0ms

Filtered

72 candidates to 110 candidates (-52.8%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	104	6	110
Fresh	3	5	8
Picked	1	0	1
Done	0	0	0
Total	108	11	119

Merged error: 2.2b

Counts

119 → 11

localize36.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1.0 (+ (sqrt (+ y 1.0)) (sqrt y)))
2.2b	(+ t (- 1.0 t))
2.2b	(- (sqrt (+ x 1.0)) (sqrt x))
3.2b	(- (sqrt (+ z 1.0)) (sqrt z))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

62×	`*-un-lft-identity`
32×	`sqrt-prod`
31×	`add-sqr-sqrt`
20×	`distribute-lft-out`
18×	`times-frac`
15×	`add-cube-cbrt`
13×	`add-log-exp`
8×	`difference-of-squares`
7×	`distribute-lft-out--`
6×	`add-exp-log` `associate-/r*` `add-cbrt-cube`
4×	`pow1`
3×	`sub-neg` `diff-log` `associate-/l*`
2×	`associate-+r+` `flip3--` `flip3-+` `sum-log` `associate-/r/` `flip--` `flip-+`
1×	`cbrt-undiv` `+-commutative` `associate-+r-` `frac-2neg` `div-exp` `clear-num` `div-inv`

Counts

4 → 96

Calls

4 calls:

11.0ms	(/ 1.0 (+ (sqrt (+ y 1.0)) (sqrt y)))
6.0ms	(+ t (- 1.0 t))
9.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
9.0ms	(- (sqrt (+ z 1.0)) (sqrt z))

series38.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(/ 1.0 (+ (sqrt (+ y 1.0)) (sqrt y)))
1.0ms	(+ t (- 1.0 t))
11.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
11.0ms	(- (sqrt (+ z 1.0)) (sqrt z))

simplify74.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 2 (63.0ms)

Iter	Nodes	Cost
0	722	927
1	3053	871
2	5001	854

prune239.0ms

Filtered

70 candidates to 108 candidates (-54.3%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	107	1	108
Fresh	1	9	10
Picked	1	0	1
Done	0	0	0
Total	109	10	119

Merged error: 1.3b

Counts

119 → 10

regimes1.2s

Accuracy

0% (0.8b remaining)

Error of 2.7b against oracle of 1.9b and baseline of 2.7b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	21
1	35	21

end0.0ms

analyze380.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
6.2%	93.6%	0.2%	5
6.2%	68.6%	25.1%	6
6.2%	49.9%	43.9%	7
6.2%	35.9%	57.9%	8
6.2%	25.3%	68.4%	9
6.2%	20.1%	73.7%	10
6.2%	15.7%	78.1%	11
6.2%	12%	81.7%	12
6.2%	9%	84.8%	13
6.2%	7.5%	86.3%	14

sample4.3s

Algorithm

intervals

Results

2.1s	5188×	body	640	valid
1.0s	9643×	body	80	nan
485.0ms	1581×	body	320	valid
98.0ms	491×	body	160	valid
70.0ms	130×	body	1280	valid
65.0ms	610×	body	80	valid

Details

analyze269.0ms

sample137.0ms

simplify26.0ms

prune6.0ms

localize23.0ms

rewrite35.0ms

series37.0ms

simplify64.0ms

prune256.0ms

localize33.0ms

rewrite32.0ms

series30.0ms

simplify57.0ms

prune244.0ms

localize25.0ms

rewrite38.0ms

series40.0ms

simplify88.0ms

prune397.0ms

localize36.0ms

rewrite39.0ms

series38.0ms

simplify74.0ms

prune239.0ms

regimes1.2s

bsearch0.0ms

simplify2.0ms

end0.0ms

analyze380.0ms

sample4.3s

Profiling