Details

analyze273.0ms

Algorithm: search

sample140.0ms

Algorithm

intervals

Results

66.0ms	173×	body	640	valid
33.0ms	330×	body	80	nan
14.0ms	42×	body	320	valid
3.0ms	17×	body	160	valid
3.0ms	6×	body	1280	valid
2.0ms	18×	body	80	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

prune5.0ms

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: 6.1b

Counts

2 → 1

localize22.0ms

Local error

Found 4 expressions with local error:

1.8b	(- (sqrt (+ t 1.0)) (sqrt t))
2.5b	(- (sqrt (+ z 1.0)) (sqrt z))
2.6b	(- (sqrt (+ x 1.0)) (sqrt x))
3.1b	(- (sqrt (+ y 1.0)) (sqrt y))

rewrite31.0ms

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:

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

series41.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
10.0ms	(- (sqrt (+ z 1.0)) (sqrt z))
10.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
12.0ms	(- (sqrt (+ y 1.0)) (sqrt y))

simplify66.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 1 (15.0ms)

Iter	Nodes	Cost
0	692	864
1	2941	824
2	5002	824

prune239.0ms

Filtered

60 candidates to 88 candidates (-46.7%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	82	6	88
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	83	6	89

Merged error: 5.4b

Counts

89 → 6

localize26.0ms

Local error

Found 4 expressions with local error:

1.7b	(+ z (- 1.0 z))
1.8b	(- (sqrt (+ t 1.0)) (sqrt t))
2.6b	(- (sqrt (+ x 1.0)) (sqrt x))
3.1b	(- (sqrt (+ y 1.0)) (sqrt y))

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:

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

series29.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify57.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 1 (13.0ms)

Iter	Nodes	Cost
0	601	708
1	2432	673
2	5001	673

prune226.0ms

Filtered

59 candidates to 86 candidates (-45.8%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	83	3	86
Fresh	1	4	5
Picked	1	0	1
Done	0	0	0
Total	85	7	92

Merged error: 4.2b

Counts

92 → 7

localize28.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1.0 (+ (sqrt (+ z 1.0)) (sqrt z)))
1.8b	(- (sqrt (+ t 1.0)) (sqrt t))
2.6b	(- (sqrt (+ x 1.0)) (sqrt x))
3.1b	(- (sqrt (+ y 1.0)) (sqrt y))

rewrite34.0ms

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

series42.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(/ 1.0 (+ (sqrt (+ z 1.0)) (sqrt z)))
14.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
10.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
10.0ms	(- (sqrt (+ y 1.0)) (sqrt y))

simplify76.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 2 (64.0ms)

Iter	Nodes	Cost
0	813	1082
1	3573	1020
2	5002	1003

prune303.0ms

Filtered

72 candidates to 110 candidates (-52.8%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	107	3	110
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	107	10	117

Merged error: 4.2b

Counts

117 → 10

localize27.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (/ 1.0 (sqrt (+ (sqrt (+ z 1.0)) (sqrt z)))) (sqrt (+ (sqrt (+ z 1.0)) (sqrt z))))
1.8b	(- (sqrt (+ t 1.0)) (sqrt t))
2.6b	(- (sqrt (+ x 1.0)) (sqrt x))
3.1b	(- (sqrt (+ y 1.0)) (sqrt y))

rewrite83.0ms

Algorithm

rewrite-expression-head

Rules

701×	`*-un-lft-identity`
664×	`sqrt-prod`
567×	`times-frac`
259×	`distribute-lft-out`
256×	`add-sqr-sqrt`
232×	`add-cube-cbrt`
33×	`associate-/l*`
22×	`sqrt-div` `associate-/r/`
12×	`difference-of-squares`
11×	`flip3-+` `flip-+` `div-inv`
10×	`add-log-exp`
9×	`add-exp-log` `associate-/r*` `add-cbrt-cube` `distribute-lft-out--`
4×	`pow1`
3×	`cbrt-undiv` `sub-neg` `flip3--` `diff-log` `div-exp` `flip--`
1×	`frac-2neg` `clear-num` `associate-/l/`

Counts

4 → 413

Calls

4 calls:

29.0ms	(/ (/ 1.0 (sqrt (+ (sqrt (+ z 1.0)) (sqrt z)))) (sqrt (+ (sqrt (+ z 1.0)) (sqrt z))))
8.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
7.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
7.0ms	(- (sqrt (+ y 1.0)) (sqrt y))

series46.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(/ (/ 1.0 (sqrt (+ (sqrt (+ z 1.0)) (sqrt z)))) (sqrt (+ (sqrt (+ z 1.0)) (sqrt z))))
10.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
17.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
10.0ms	(- (sqrt (+ y 1.0)) (sqrt y))

simplify100.0ms

Algorithm

egg-herbie

Counts

425 → 425

Iterations

Useful iterations: 1 (31.0ms)

Iter	Nodes	Cost
0	1404	8412
1	5001	7358

prune732.0ms

Filtered

135 candidates to 425 candidates (-214.8%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	423	2	425
Fresh	0	8	8
Picked	1	0	1
Done	0	1	1
Total	424	11	435

Merged error: 4.2b

Counts

435 → 11

regimes1.2s

Accuracy

0% (1.1b remaining)

Error of 3.9b against oracle of 2.8b and baseline of 3.9b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	20
1	33	20

end0.0ms

analyze286.0ms

Algorithm: search

sample4.1s

Algorithm

intervals

Results

2.0s	5218×	body	640	valid
980.0ms	10071×	body	80	nan
467.0ms	1615×	body	320	valid
87.0ms	456×	body	160	valid
67.0ms	132×	body	1280	valid
60.0ms	579×	body	80	valid

Details

analyze273.0ms

sample140.0ms

simplify26.0ms

prune5.0ms

localize22.0ms

rewrite31.0ms

series41.0ms

simplify66.0ms

prune239.0ms

localize26.0ms

rewrite32.0ms

series29.0ms

simplify57.0ms

prune226.0ms

localize28.0ms

rewrite34.0ms

series42.0ms

simplify76.0ms

prune303.0ms

localize27.0ms

rewrite83.0ms

series46.0ms

simplify100.0ms

prune732.0ms

regimes1.2s

bsearch0.0ms

simplify2.0ms

end0.0ms

analyze286.0ms

sample4.1s

Profiling