Details

analyze43.0ms (2.5%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	74.9%	25.1%	4
18.7%	56.2%	25.1%	5
28.1%	34.3%	37.6%	6
34.3%	28.1%	37.6%	7
39%	17.2%	43.8%	8
41%	13.7%	45.4%	9
43.1%	8.4%	48.5%	10
44%	6.7%	49.3%	11
45%	4.1%	50.8%	12
45.4%	3.3%	51.2%	13
45.9%	2.1%	52%	14

sample14.0ms (0.8%)

Algorithm

1×

intervals

Results

7.0ms	256×	body	80	valid
0.0ms	5×	body	80	nan
0.0ms	2×	body	80	invalid

simplify7.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (6.0ms)

Iter	Nodes	Cost
0	225	8
1	225	8

prune5.0ms (0.3%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 0.1b

Counts

2 → 1

localize9.0ms (0.5%)

Local error

Found 1 expressions with local error:

0.2b	(* y (sqrt x))

rewrite5.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
6×	`associate-r`
4×	`add-cube-cbrt` `*-un-lft-identity` `sqrt-prod`
3×	`pow1` `add-exp-log` `associate-l` `add-cbrt-cube`
2×	`unswap-sqr`
1×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `add-log-exp`

Counts

1 → 22

Calls

1 calls:

5.0ms

(* y (sqrt x))

series7.0ms (0.4%)

Counts

1 → 3

Calls

1 calls:

6.0ms

(* y (sqrt x))

simplify40.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

25 → 25

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5051	174

prune47.0ms (2.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	21	4	25
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	21	5	26

Merged error: 0.0b

Counts

26 → 5

localize8.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.1b	(sqrt (sqrt x))
0.1b	(sqrt (sqrt x))
0.2b	(* y (sqrt (sqrt x)))
0.3b	(* (* y (sqrt (sqrt x))) (sqrt (sqrt x)))

rewrite21.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

41×	`sqrt-prod`
25×	`add-sqr-sqrt`
18×	`associate-r`
15×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
11×	`add-exp-log` `add-cbrt-cube`
8×	`sqrt-pow1`
4×	`rem-sqrt-square` `pow1/2` `associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `add-log-exp`
3×	`unswap-sqr`
2×	`*-commutative`

Counts

4 → 88

Calls

4 calls:

9.0ms	(* (* y (sqrt (sqrt x))) (sqrt (sqrt x)))
6.0ms	(* y (sqrt (sqrt x)))
2.0ms	(sqrt (sqrt x))
2.0ms	(sqrt (sqrt x))

series49.0ms (2.9%)

Counts

4 → 12

Calls

4 calls:

16.0ms	(sqrt (sqrt x))
14.0ms	(sqrt (sqrt x))
11.0ms	(* y (sqrt (sqrt x)))
7.0ms	(* (* y (sqrt (sqrt x))) (sqrt (sqrt x)))

simplify53.0ms (3.1%)

Algorithm

1×	egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5020	626

prune126.0ms (7.4%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	98	2	100
Fresh	1	2	3
Picked	1	0	1
Done	0	1	1
Total	100	5	105

Merged error: 0b

Counts

105 → 5

localize12.0ms (0.7%)

Local error

Found 4 expressions with local error:

0.2b	(* y (sqrt (sqrt x)))
0.3b	(* (* y (sqrt (sqrt x))) (cbrt (pow (sqrt (sqrt x)) 3)))
0.6b	(cbrt (pow (sqrt (sqrt x)) 3))
0.7b	(pow (sqrt (sqrt x)) 3)

rewrite36.0ms (2.1%)

Algorithm

1×	rewrite-expression-head

Rules

66×	`sqrt-prod`
48×	`cbrt-prod`
36×	`add-sqr-sqrt` `associate-r`
30×	`add-cube-cbrt` `*-un-lft-identity`
27×	`unpow-prod-down` `cube-prod`
14×	`pow1`
12×	`add-exp-log`
10×	`add-cbrt-cube`
5×	`pow-pow`
4×	`sqrt-pow1` `associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `add-log-exp`
3×	`cube-mult` `pow-unpow` `unpow3` `unswap-sqr` `sqr-pow`
2×	`pow1/2` `*-commutative`
1×	`pow-to-exp` `pow1/3` `pow-exp` `sqrt-pow2` `rem-cbrt-cube` `rem-cube-cbrt`

Counts

4 → 141

Calls

4 calls:

13.0ms	(* (* y (sqrt (sqrt x))) (cbrt (pow (sqrt (sqrt x)) 3)))
6.0ms	(* y (sqrt (sqrt x)))
4.0ms	(pow (sqrt (sqrt x)) 3)
4.0ms	(cbrt (pow (sqrt (sqrt x)) 3))

series51.0ms (3%)

Counts

4 → 12

Calls

4 calls:

19.0ms	(pow (sqrt (sqrt x)) 3)
14.0ms	(cbrt (pow (sqrt (sqrt x)) 3))
10.0ms	(* y (sqrt (sqrt x)))
7.0ms	(* (* y (sqrt (sqrt x))) (cbrt (pow (sqrt (sqrt x)) 3)))

simplify59.0ms (3.4%)

Algorithm

1×	egg-herbie

Counts

153 → 153

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4879	1054
1	4879	1054

prune226.0ms (13.2%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	153	0	153
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	153	5	158

Merged error: 0b

Counts

158 → 5

localize13.0ms (0.7%)

Local error

Found 4 expressions with local error:

0.1b	(sqrt (sqrt (sqrt x)))
0.2b	(* y (* (sqrt (sqrt x)) (sqrt (sqrt (sqrt x)))))
0.3b	(* (* y (* (sqrt (sqrt x)) (sqrt (sqrt (sqrt x))))) (sqrt (sqrt (sqrt x))))
0.3b	(* (sqrt (sqrt x)) (sqrt (sqrt (sqrt x))))

rewrite52.0ms (3.1%)

Algorithm

1×	rewrite-expression-head

Rules

99×	`sqrt-prod`
49×	`add-sqr-sqrt`
42×	`sqrt-pow1`
38×	`pow1`
25×	`associate-r`
20×	`add-exp-log` `add-cbrt-cube`
19×	`add-cube-cbrt` `*-un-lft-identity`
16×	`pow1/2`
14×	`pow-prod-down`
13×	`associate-l`
12×	`unswap-sqr`
10×	`prod-exp` `pow-prod-up` `cbrt-unprod`
4×	`add-log-exp`
3×	`rem-sqrt-square` `pow3` `*-commutative`
1×	`sqrt-unprod`

Counts

4 → 135

Calls

4 calls:

19.0ms	(* (* y (* (sqrt (sqrt x)) (sqrt (sqrt (sqrt x))))) (sqrt (sqrt (sqrt x))))
13.0ms	(* y (* (sqrt (sqrt x)) (sqrt (sqrt (sqrt x)))))
12.0ms	(* (sqrt (sqrt x)) (sqrt (sqrt (sqrt x))))
3.0ms	(sqrt (sqrt (sqrt x)))

series63.0ms (3.7%)

Counts

4 → 12

Calls

4 calls:

22.0ms	(* (sqrt (sqrt x)) (sqrt (sqrt (sqrt x))))
18.0ms	(* y (* (sqrt (sqrt x)) (sqrt (sqrt (sqrt x)))))
15.0ms	(sqrt (sqrt (sqrt x)))
7.0ms	(* (* y (* (sqrt (sqrt x)) (sqrt (sqrt (sqrt x))))) (sqrt (sqrt (sqrt x))))

simplify51.0ms (3%)

Algorithm

1×	egg-herbie

Counts

147 → 147

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	4966	1155
1	4966	1155

prune182.0ms (10.7%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	146	1	147
Fresh	1	1	2
Picked	0	1	1
Done	0	2	2
Total	147	5	152

Merged error: 0b

Counts

152 → 5

regimes135.0ms (7.9%)

Accuracy

Total 0.1b remaining (65.6%)

Threshold costs 0.1b (65.6%)

bsearch0.0ms (0%)

simplify1.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	8
1	19	8

end0.0ms (0%)

sample393.0ms (23%)

Algorithm

1×

intervals

Results

245.0ms	7999×	body	80	valid
5.0ms	59×	body	80	invalid
4.0ms	141×	body	80	nan
0.0ms	1×	body	640	valid

Details

analyze43.0ms (2.5%)

sample14.0ms (0.8%)

simplify7.0ms (0.4%)

prune5.0ms (0.3%)

localize9.0ms (0.5%)

rewrite5.0ms (0.3%)

series7.0ms (0.4%)

simplify40.0ms (2.3%)

prune47.0ms (2.8%)

localize8.0ms (0.5%)

rewrite21.0ms (1.2%)

series49.0ms (2.9%)

simplify53.0ms (3.1%)

prune126.0ms (7.4%)

localize12.0ms (0.7%)

rewrite36.0ms (2.1%)

series51.0ms (3%)

simplify59.0ms (3.4%)

prune226.0ms (13.2%)

localize13.0ms (0.7%)

rewrite52.0ms (3.1%)

series63.0ms (3.7%)

simplify51.0ms (3%)

prune182.0ms (10.7%)

regimes135.0ms (7.9%)

bsearch0.0ms (0%)

simplify1.0ms (0.1%)

end0.0ms (0%)

sample393.0ms (23%)

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