Details

analyze163.0ms (7.9%)

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%	99.9%	0.1%	4
0%	99.9%	0.1%	5
25%	74.9%	0.1%	6
34.3%	40.6%	25.1%	7
35.9%	39%	25.1%	8
42.1%	32.8%	25.1%	9
42.9%	19.5%	37.6%	10
43.3%	19.1%	37.6%	11
45%	17.5%	37.6%	12
45.1%	10.3%	44.6%	13
45.2%	10.2%	44.6%	14

sample20.0ms (1%)

Algorithm

1×

intervals

Results

9.0ms	256×	body	80	valid
1.0ms	38×	body	80	nan
1.0ms	15×	body	80	invalid

simplify4.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	105	10
1	105	10

prune6.0ms (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: 0.1b

Counts

2 → 1

localize7.0ms (0.4%)

Local error

Found 1 expressions with local error:

0.2b	(* y (sqrt z))

rewrite8.0ms (0.4%)

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:

7.0ms

(* y (sqrt z))

series7.0ms (0.3%)

Counts

1 → 3

Calls

1 calls:

7.0ms

(* y (sqrt z))

simplify47.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

25 → 25

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4978	172
1	4978	172

prune48.0ms (2.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	22	3	25
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	22	4	26

Merged error: 0.0b

Counts

26 → 4

localize10.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.1b	(sqrt (sqrt z))
0.1b	(sqrt (sqrt z))
0.3b	(* y (sqrt (sqrt z)))
0.3b	(* (* y (sqrt (sqrt z))) (sqrt (sqrt z)))

rewrite21.0ms (1%)

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 z))) (sqrt (sqrt z)))
6.0ms	(* y (sqrt (sqrt z)))
2.0ms	(sqrt (sqrt z))
2.0ms	(sqrt (sqrt z))

series47.0ms (2.3%)

Counts

4 → 12

Calls

4 calls:

15.0ms	(sqrt (sqrt z))
14.0ms	(sqrt (sqrt z))
11.0ms	(* y (sqrt (sqrt z)))
7.0ms	(* (* y (sqrt (sqrt z))) (sqrt (sqrt z)))

simplify45.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5286	622

prune150.0ms (7.3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	96	4	100
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	97	7	104

Merged error: 0b

Counts

104 → 7

localize18.0ms (0.9%)

Local error

Found 3 expressions with local error:

0.1b	(sqrt (sqrt z))
0.3b	(* y (sqrt (sqrt z)))
0.3b	(* (* y (sqrt (sqrt z))) (pow z 1/4))

rewrite18.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 69

Calls

3 calls:

8.0ms	(* (* y (sqrt (sqrt z))) (pow z 1/4))
6.0ms	(* y (sqrt (sqrt z)))
2.0ms	(sqrt (sqrt z))

series38.0ms (1.8%)

Counts

3 → 9

Calls

3 calls:

15.0ms	(sqrt (sqrt z))
13.0ms	(* (* y (sqrt (sqrt z))) (pow z 1/4))
10.0ms	(* y (sqrt (sqrt z)))

simplify31.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	5060	624

prune139.0ms (6.8%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	78	0	78
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	78	7	85

Merged error: 0b

Counts

85 → 7

localize14.0ms (0.7%)

Local error

Found 4 expressions with local error:

0.3b	(* (* (* y (sqrt (sqrt z))) (fabs (cbrt (sqrt z)))) (sqrt (cbrt (sqrt z))))
0.3b	(* (* y (sqrt (sqrt z))) (fabs (cbrt (sqrt z))))
0.5b	(cbrt (sqrt z))
0.5b	(cbrt (sqrt z))

rewrite23.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`pow1` `add-exp-log` `cbrt-prod` `sqrt-prod` `add-cbrt-cube`
15×	`associate-r`
13×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`add-log-exp`
2×	`pow1/3` `associate-l` `*-commutative`

Counts

4 → 76

Calls

4 calls:

11.0ms	(* (* (* y (sqrt (sqrt z))) (fabs (cbrt (sqrt z)))) (sqrt (cbrt (sqrt z))))
6.0ms	(* (* y (sqrt (sqrt z))) (fabs (cbrt (sqrt z))))
2.0ms	(cbrt (sqrt z))
2.0ms	(cbrt (sqrt z))

series67.0ms (3.3%)

Counts

4 → 12

Calls

4 calls:

19.0ms	(* (* (* y (sqrt (sqrt z))) (fabs (cbrt (sqrt z)))) (sqrt (cbrt (sqrt z))))
17.0ms	(cbrt (sqrt z))
16.0ms	(* (* y (sqrt (sqrt z))) (fabs (cbrt (sqrt z))))
15.0ms	(cbrt (sqrt z))

simplify31.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	4946	981
1	4946	981

prune117.0ms (5.7%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	88	0	88
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	88	7	95

Merged error: 0b

Counts

95 → 7

regimes454.0ms (22.1%)

Accuracy

Total 0.1b remaining (78.3%)

Threshold costs 0.1b (78.3%)

bsearch0.0ms (0%)

simplify1.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	10
1	13	10

end0.0ms (0%)

sample520.0ms (25.3%)

Algorithm

1×

intervals

Results

286.0ms	8000×	body	80	valid
37.0ms	1076×	body	80	nan
15.0ms	428×	body	80	invalid

Details

analyze163.0ms (7.9%)

sample20.0ms (1%)

simplify4.0ms (0.2%)

prune6.0ms (0.3%)

localize7.0ms (0.4%)

rewrite8.0ms (0.4%)

series7.0ms (0.3%)

simplify47.0ms (2.3%)

prune48.0ms (2.3%)

localize10.0ms (0.5%)

rewrite21.0ms (1%)

series47.0ms (2.3%)

simplify45.0ms (2.2%)

prune150.0ms (7.3%)

localize18.0ms (0.9%)

rewrite18.0ms (0.9%)

series38.0ms (1.8%)

simplify31.0ms (1.5%)

prune139.0ms (6.8%)

localize14.0ms (0.7%)

rewrite23.0ms (1.1%)

series67.0ms (3.3%)

simplify31.0ms (1.5%)

prune117.0ms (5.7%)

regimes454.0ms (22.1%)

bsearch0.0ms (0%)

simplify1.0ms (0.1%)

end0.0ms (0%)

sample520.0ms (25.3%)

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