Details

analyze13.0ms (0.4%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
75%	25%	0%	4
87.5%	12.5%	0%	5
93.7%	6.2%	0%	6
96.8%	3.1%	0%	7
98.4%	1.6%	0%	8
99.2%	0.8%	0%	9
99.6%	0.4%	0%	10
99.8%	0.2%	0%	11
99.9%	0.1%	0%	12
99.9%	0%	0%	13
99.9%	0%	0.1%	14

sample22.0ms (0.7%)

Algorithm

1×

intervals

Results

14.0ms

256×

body

valid

simplify714.0ms (21.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (81.0ms)

Iter	Nodes	Cost
0	4811	6
1	4811	6

prune9.0ms (0.3%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 27.9b

Counts

2 → 1

localize7.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b	(* (pow x 2.0) 2)
27.1b	(sqrt (* (pow x 2.0) 2))

rewrite12.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
7×	`add-exp-log` `associate-l`
5×	`add-cube-cbrt` `*-un-lft-identity`
4×	`unpow-prod-down` `add-cbrt-cube`
3×	`pow1` `associate-r` `prod-exp` `unswap-sqr`
2×	`add-log-exp` `sqr-pow`
1×	`pow-to-exp` `sqrt-pow1` `pow1/2` `pow-exp` `sqrt-prod` `*-commutative` `cbrt-unprod`

Counts

2 → 35

Calls

2 calls:

5.0ms	(sqrt (* (pow x 2.0) 2))
5.0ms	(* (pow x 2.0) 2)

series156.0ms (4.8%)

Counts

2 → 6

Calls

2 calls:

91.0ms	(sqrt (* (pow x 2.0) 2))
65.0ms	(* (pow x 2.0) 2)

simplify62.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

41 → 41

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4905	307
1	4905	307

prune103.0ms (3.1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	35	6	41
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	35	7	42

Merged error: 14.0b

Counts

42 → 7

localize10.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.2b	(* (pow x 2.0) (sqrt 2))
0.3b	(* (* (pow x 2.0) (sqrt 2)) (sqrt 2))
27.1b	(sqrt (* (* (pow x 2.0) (sqrt 2)) (sqrt 2)))

rewrite22.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`add-sqr-sqrt`
18×	`add-exp-log`
12×	`associate-r`
10×	`prod-exp` `sqrt-prod` `add-cbrt-cube`
9×	`add-cube-cbrt` `*-un-lft-identity`
8×	`pow1` `associate-l`
6×	`unswap-sqr`
5×	`unpow-prod-down`
4×	`cbrt-unprod`
3×	`add-log-exp` `sqr-pow`
2×	`pow-to-exp` `sqrt-pow1` `pow-prod-down` `pow-exp` `*-commutative`
1×	`pow1/2`

Counts

3 → 64

Calls

3 calls:

7.0ms	(* (* (pow x 2.0) (sqrt 2)) (sqrt 2))
6.0ms	(* (pow x 2.0) (sqrt 2))
6.0ms	(sqrt (* (* (pow x 2.0) (sqrt 2)) (sqrt 2)))

series204.0ms (6.2%)

Counts

3 → 9

Calls

3 calls:

71.0ms	(* (* (pow x 2.0) (sqrt 2)) (sqrt 2))
66.0ms	(sqrt (* (* (pow x 2.0) (sqrt 2)) (sqrt 2)))
66.0ms	(* (pow x 2.0) (sqrt 2))

simplify63.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	5409	586

prune169.0ms (5.2%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	72	1	73
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	73	7	80

Merged error: 14.0b

Counts

80 → 7

localize8.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.2b	(* (pow x 2.0) (sqrt 2))
0.3b	(* (sqrt (* (pow x 2.0) (sqrt 2))) (sqrt (sqrt 2)))
27.1b	(sqrt (* (pow x 2.0) (sqrt 2)))

rewrite22.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

27×	`add-sqr-sqrt`
20×	`sqrt-prod`
15×	`associate-r`
11×	`add-cube-cbrt` `-un-lft-identity` `associate-l*`
10×	`add-exp-log`
9×	`unswap-sqr`
8×	`pow1`
7×	`add-cbrt-cube`
5×	`unpow-prod-down`
4×	`prod-exp`
3×	`sqrt-pow1` `pow1/2` `pow-prod-down` `add-log-exp` `sqr-pow`
2×	`*-commutative` `cbrt-unprod`
1×	`pow-to-exp` `sqrt-unprod` `pow-exp`

Counts

3 → 71

Calls

3 calls:

10.0ms	(* (sqrt (* (pow x 2.0) (sqrt 2))) (sqrt (sqrt 2)))
6.0ms	(* (pow x 2.0) (sqrt 2))
4.0ms	(sqrt (* (pow x 2.0) (sqrt 2)))

series201.0ms (6.1%)

Counts

3 → 9

Calls

3 calls:

69.0ms	(sqrt (* (pow x 2.0) (sqrt 2)))
67.0ms	(* (pow x 2.0) (sqrt 2))
65.0ms	(* (sqrt (* (pow x 2.0) (sqrt 2))) (sqrt (sqrt 2)))

simplify61.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	5439	812

prune220.0ms (6.7%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	77	3	80
Fresh	2	2	4
Picked	1	0	1
Done	0	2	2
Total	80	7	87

Merged error: 13.9b

Counts

87 → 7

localize8.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.2b	(* (sqrt (pow x 2.0)) (sqrt (sqrt 2)))
0.3b	(* (* (sqrt (pow x 2.0)) (sqrt (sqrt 2))) (sqrt (sqrt 2)))
27.0b	(sqrt (pow x 2.0))

rewrite28.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

53×	`sqrt-prod`
37×	`add-sqr-sqrt`
18×	`associate-r`
14×	`add-cube-cbrt` `*-un-lft-identity`
12×	`unswap-sqr`
11×	`associate-l`
10×	`pow1` `add-exp-log` `unpow-prod-down` `add-cbrt-cube`
7×	`pow-prod-down`
6×	`pow1/2` `sqr-pow`
4×	`prod-exp` `cbrt-unprod`
3×	`rem-sqrt-square` `sqrt-unprod` `add-log-exp`
2×	`*-commutative`
1×	`sqrt-pow1`

Counts

3 → 89

Calls

3 calls:

11.0ms	(* (* (sqrt (pow x 2.0)) (sqrt (sqrt 2))) (sqrt (sqrt 2)))
9.0ms	(* (sqrt (pow x 2.0)) (sqrt (sqrt 2)))
2.0ms	(sqrt (pow x 2.0))

series195.0ms (6%)

Counts

3 → 9

Calls

3 calls:

67.0ms	(* (sqrt (pow x 2.0)) (sqrt (sqrt 2)))
67.0ms	(* (* (sqrt (pow x 2.0)) (sqrt (sqrt 2))) (sqrt (sqrt 2)))
60.0ms	(sqrt (pow x 2.0))

simplify49.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	4861	955
1	4861	955

prune262.0ms (8%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	94	4	98
Fresh	3	1	4
Picked	1	0	1
Done	0	2	2
Total	98	7	105

Merged error: 0.1b

Counts

105 → 7

regimes126.0ms (3.8%)

Accuracy

Total 0.3b remaining (71%)

Threshold costs 0.3b (71%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	14
1	12	14

end0.0ms (0%)

sample522.0ms (16%)

Algorithm

1×

intervals

Results

418.0ms

8000×

body

valid

Details

analyze13.0ms (0.4%)

sample22.0ms (0.7%)

simplify714.0ms (21.8%)

prune9.0ms (0.3%)

localize7.0ms (0.2%)

rewrite12.0ms (0.4%)

series156.0ms (4.8%)

simplify62.0ms (1.9%)

prune103.0ms (3.1%)

localize10.0ms (0.3%)

rewrite22.0ms (0.7%)

series204.0ms (6.2%)

simplify63.0ms (1.9%)

prune169.0ms (5.2%)

localize8.0ms (0.3%)

rewrite22.0ms (0.7%)

series201.0ms (6.1%)

simplify61.0ms (1.9%)

prune220.0ms (6.7%)

localize8.0ms (0.3%)

rewrite28.0ms (0.9%)

series195.0ms (6%)

simplify49.0ms (1.5%)

prune262.0ms (8%)

regimes126.0ms (3.8%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample522.0ms (16%)

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