Details

analyze70.0ms (4.6%)

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
25%	74.9%	0.1%	4
25%	74.9%	0.1%	5
43.7%	50%	6.3%	6
43.7%	43.7%	12.6%	7
59.3%	26.5%	14.1%	8
59.3%	22.6%	18%	9
67.1%	13.7%	19.2%	10
67.1%	11.5%	21.4%	11
71%	6.9%	22%	12
71%	5.8%	23.2%	13
73%	3.5%	23.5%	14

sample14.0ms (0.9%)

Algorithm

1×

intervals

Results

7.0ms	256×	body	80	valid
0.0ms	1×	body	80	nan

simplify3.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	6	6
1	6	6

prune5.0ms (0.3%)

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: 24.1b

Counts

2 → 1

localize4.0ms (0.3%)

Local error

Found 2 expressions with local error:

0.0b	(+ (* x x) y)
22.3b	(sqrt (+ (* x x) y))

rewrite8.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

4×	`add-sqr-sqrt` `add-log-exp`
3×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `sqrt-prod`
2×	`add-exp-log` `flip3-+` `sqrt-div` `add-cbrt-cube` `flip-+`
1×	`+-commutative` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `sum-log`

Counts

2 → 26

Calls

2 calls:

4.0ms	(sqrt (+ (* x x) y))
4.0ms	(+ (* x x) y)

series9.0ms (0.6%)

Counts

2 → 6

Calls

2 calls:

6.0ms	(sqrt (+ (* x x) y))
4.0ms	(+ (* x x) y)

simplify55.0ms (3.6%)

Algorithm

1×	egg-herbie

Counts

32 → 32

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4926	260
1	4926	260

prune48.0ms (3.1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	29	3	32
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	29	4	33

Merged error: 0b

Counts

33 → 4

localize8.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt (sqrt (+ (* x x) y)))
0.5b	(* (sqrt (sqrt (+ (* x x) y))) (sqrt (sqrt (+ (* x x) y))))
22.3b	(sqrt (+ (* x x) y))
22.3b	(sqrt (+ (* x x) y))

rewrite35.0ms (2.3%)

Algorithm

1×	rewrite-expression-head

Rules

82×	`sqrt-prod`
54×	`add-sqr-sqrt`
38×	`sqrt-pow1`
32×	`sqrt-div`
31×	`pow1`
20×	`add-cube-cbrt` `*-un-lft-identity` `pow1/2`
15×	`swap-sqr`
9×	`flip3-+` `associate-r` `associate-l` `pow-prod-up` `flip-+` `unswap-sqr`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow-prod-down` `pow-sqr`
4×	`frac-times` `rem-sqrt-square` `add-log-exp`
2×	`associate-r/` `associate-l/`
1×	`pow2` `pow-plus` `sqrt-unprod` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 134

Calls

4 calls:

15.0ms	(* (sqrt (sqrt (+ (* x x) y))) (sqrt (sqrt (+ (* x x) y))))
5.0ms	(sqrt (sqrt (+ (* x x) y)))
4.0ms	(sqrt (+ (* x x) y))
4.0ms	(sqrt (+ (* x x) y))

series35.0ms (2.3%)

Counts

4 → 12

Calls

4 calls:

17.0ms	(sqrt (sqrt (+ (* x x) y)))
6.0ms	(* (sqrt (sqrt (+ (* x x) y))) (sqrt (sqrt (+ (* x x) y))))
6.0ms	(sqrt (+ (* x x) y))
6.0ms	(sqrt (+ (* x x) y))

simplify72.0ms (4.7%)

Algorithm

1×	egg-herbie

Counts

146 → 146

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	5028	1345

prune166.0ms (10.8%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	146	0	146
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	146	4	150

Merged error: 0b

Counts

150 → 4

localize5.0ms (0.3%)

Local error

Found 1 expressions with local error:

0.2b	(* y (/ 1/2 x))

rewrite8.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
13×	`associate-r`
10×	`times-frac`
9×	`add-cube-cbrt` `*-un-lft-identity`
6×	`add-exp-log` `add-cbrt-cube`
3×	`pow1` `associate-l`
2×	`prod-exp` `cbrt-unprod` `unswap-sqr`
1×	`cbrt-undiv` `associate-r/` `div-exp` `pow-prod-down` `-commutative` `div-inv` `add-log-exp`

Counts

1 → 32

Calls

1 calls:

6.0ms

(* y (/ 1/2 x))

series4.0ms (0.2%)

Counts

1 → 3

Calls

1 calls:

4.0ms

(* y (/ 1/2 x))

simplify55.0ms (3.6%)

Algorithm

1×	egg-herbie

Counts

35 → 35

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4960	229
1	4960	229

prune50.0ms (3.3%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	35	0	35
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	35	4	39

Merged error: 0b

Counts

39 → 4

localize5.0ms (0.3%)

Local error

Found 1 expressions with local error:

0.2b	(* y (/ -1/2 x))

rewrite8.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
13×	`associate-r`
10×	`times-frac`
9×	`add-cube-cbrt` `*-un-lft-identity`
6×	`add-exp-log` `add-cbrt-cube`
3×	`pow1` `associate-l`
2×	`prod-exp` `cbrt-unprod` `unswap-sqr`
1×	`cbrt-undiv` `associate-r/` `div-exp` `pow-prod-down` `-commutative` `div-inv` `add-log-exp`

Counts

1 → 32

Calls

1 calls:

7.0ms

(* y (/ -1/2 x))

series4.0ms (0.2%)

Counts

1 → 3

Calls

1 calls:

3.0ms

(* y (/ -1/2 x))

simplify66.0ms (4.3%)

Algorithm

1×	egg-herbie

Counts

35 → 35

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	5360	230

prune46.0ms (3%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	35	0	35
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	35	4	39

Merged error: 0b

Counts

39 → 4

regimes324.0ms (21.2%)

Accuracy

Total 0.1b remaining (98.4%)

Threshold costs 0.1b (98.4%)

bsearch20.0ms (1.3%)

Steps

Iters	Range		Point
6	7.812714832008245e+99	9.242818628972127e+100	8.662991656120997e+100
8	-6.974863825994112e+154	-9.256716772661227e+150	-1.3543668959932148e+154

simplify1.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	33	28
1	33	28

end0.0ms (0%)

sample405.0ms (26.4%)

Algorithm

1×

intervals

Results

244.0ms	8000×	body	80	valid
5.0ms	167×	body	80	nan

Details

analyze70.0ms (4.6%)

sample14.0ms (0.9%)

simplify3.0ms (0.2%)

prune5.0ms (0.3%)

localize4.0ms (0.3%)

rewrite8.0ms (0.5%)

series9.0ms (0.6%)

simplify55.0ms (3.6%)

prune48.0ms (3.1%)

localize8.0ms (0.5%)

rewrite35.0ms (2.3%)

series35.0ms (2.3%)

simplify72.0ms (4.7%)

prune166.0ms (10.8%)

localize5.0ms (0.3%)

rewrite8.0ms (0.5%)

series4.0ms (0.2%)

simplify55.0ms (3.6%)

prune50.0ms (3.3%)

localize5.0ms (0.3%)

rewrite8.0ms (0.5%)

series4.0ms (0.2%)

simplify66.0ms (4.3%)

prune46.0ms (3%)

regimes324.0ms (21.2%)

bsearch20.0ms (1.3%)

simplify1.0ms (0.1%)

end0.0ms (0%)

sample405.0ms (26.4%)

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