Details

sample572.0ms

Algorithm

intervals

Results

320.0ms	3361×	body	80	nan
65.0ms	167×	body	640	valid
15.0ms	52×	body	320	valid
2.0ms	12×	body	160	valid
2.0ms	22×	body	80	valid
1.0ms	3×	body	1280	valid

simplify27.0ms

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: 5.8b

Counts

2 → 1

localize27.0ms

Local error

Found 4 expressions with local error:

2.8b	(- (sqrt (+ z 1.0)) (sqrt z))
3.6b	(- (sqrt (+ t 1.0)) (sqrt t))
3.7b	(- (sqrt (+ x 1.0)) (sqrt x))
4.2b	(- (sqrt (+ y 1.0)) (sqrt y))

rewrite33.0ms

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

series37.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify65.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 1 (15.0ms)

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

prune262.0ms

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: 4.5b

Counts

89 → 7

localize26.0ms

Local error

Found 4 expressions with local error:

2.6b	(+ x (- 1.0 x))
2.8b	(- (sqrt (+ z 1.0)) (sqrt z))
3.6b	(- (sqrt (+ t 1.0)) (sqrt t))
4.2b	(- (sqrt (+ y 1.0)) (sqrt y))

rewrite30.0ms

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

series30.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify55.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 1 (13.0ms)

Iter	Nodes	Cost
0	602	708
1	2429	673
2	5002	673

prune242.0ms

Filtered

59 candidates to 86 candidates (-45.8%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	82	4	86
Fresh	2	4	6
Picked	1	0	1
Done	0	0	0
Total	85	8	93

Merged error: 3.5b

Counts

93 → 8

localize26.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
2.8b	(- (sqrt (+ z 1.0)) (sqrt z))
3.6b	(- (sqrt (+ t 1.0)) (sqrt t))
4.2b	(- (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 (+ x 1.0)) (sqrt x)))
7.0ms	(- (sqrt (+ z 1.0)) (sqrt z))
7.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
8.0ms	(- (sqrt (+ y 1.0)) (sqrt y))

series40.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
12.0ms	(- (sqrt (+ z 1.0)) (sqrt z))
9.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
10.0ms	(- (sqrt (+ y 1.0)) (sqrt y))

simplify75.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 2 (63.0ms)

Iter	Nodes	Cost
0	816	1082
1	3586	1020
2	5002	1003

prune309.0ms

Filtered

72 candidates to 110 candidates (-52.8%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	104	6	110
Fresh	3	4	7
Picked	1	0	1
Done	0	0	0
Total	108	10	118

Merged error: 3.5b

Counts

118 → 10

localize27.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
1.9b	(+ z (- 1.0 z))
3.6b	(- (sqrt (+ t 1.0)) (sqrt t))
4.2b	(- (sqrt (+ y 1.0)) (sqrt y))

rewrite32.0ms

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:

9.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
5.0ms	(+ z (- 1.0 z))
7.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
8.0ms	(- (sqrt (+ y 1.0)) (sqrt y))

series30.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify67.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 2 (56.0ms)

Iter	Nodes	Cost
0	725	926
1	3068	869
2	5001	852

prune242.0ms

Filtered

70 candidates to 108 candidates (-54.3%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	106	2	108
Fresh	3	6	9
Picked	1	0	1
Done	0	0	0
Total	110	8	118

Merged error: 2.2b

Counts

118 → 8

regimes1.0s

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	21
1	35	21

end0.0ms

sample1.0s

Algorithm

intervals

Results

596.0ms	6137×	body	80	nan
116.0ms	297×	body	640	valid
26.0ms	89×	body	320	valid
5.0ms	26×	body	160	valid
3.0ms	6×	body	1280	valid
3.0ms	30×	body	80	valid

Details

sample572.0ms

simplify27.0ms

prune6.0ms

localize27.0ms

rewrite33.0ms

series37.0ms

simplify65.0ms

prune262.0ms

localize26.0ms

rewrite30.0ms

series30.0ms

simplify55.0ms

prune242.0ms

localize26.0ms

rewrite34.0ms

series40.0ms

simplify75.0ms

prune309.0ms

localize27.0ms

rewrite32.0ms

series30.0ms

simplify67.0ms

prune242.0ms

regimes1.0s

bsearch0.0ms

simplify1.0ms

end0.0ms

sample1.0s

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