Details

analyze281.0ms (16.4%)

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
0%	99.9%	0.1%	6
15.6%	84.3%	0.1%	7
29.6%	70.2%	0.1%	8
36.7%	60.1%	3.3%	9
43.3%	49.5%	7.2%	10
52.1%	39.2%	8.7%	11
57.6%	31.1%	11.3%	12
60.6%	25.6%	13.8%	13
65.2%	20.4%	14.4%	14

sample15.0ms (0.9%)

Algorithm

1×

intervals

Results

7.0ms	256×	body	80	valid
0.0ms	16×	body	80	invalid

simplify14.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (13.0ms)

Iter	Nodes	Cost
0	345	9
1	345	9

prune7.0ms (0.4%)

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: 0.0b

Counts

2 → 1

localize6.0ms (0.4%)

Local error

Found 2 expressions with local error:

0.0b	(* (- 1.0 x) y)
0.0b	(+ (* (- 1.0 x) y) (* x z))

rewrite12.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
6×	`*-un-lft-identity`
5×	`associate-l`
4×	`pow1` `add-exp-log` `add-cube-cbrt` `add-cbrt-cube` `add-log-exp`
3×	`associate-r`
2×	`associate-*l/`
1×	`+-commutative` `flip3--` `flip3-+` `pow-prod-down` `prod-exp` `sum-log` `*-commutative` `flip--` `cbrt-unprod` `flip-+` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

2 → 33

Calls

2 calls:

6.0ms	(+ (* (- 1.0 x) y) (* x z))
6.0ms	(* (- 1.0 x) y)

series12.0ms (0.7%)

Counts

2 → 6

Calls

2 calls:

8.0ms	(+ (* (- 1.0 x) y) (* x z))
4.0ms	(* (- 1.0 x) y)

simplify55.0ms (3.2%)

Algorithm

1×	egg-herbie

Counts

39 → 39

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4979	345
1	4979	345

prune58.0ms (3.4%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	37	2	39
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	37	3	40

Merged error: 0.0b

Counts

40 → 3

localize8.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt (- 1.0 x))
0.0b	(+ (* (sqrt (- 1.0 x)) (* y (sqrt (- 1.0 x)))) (* x z))
0.1b	(* y (sqrt (- 1.0 x)))
0.1b	(* (sqrt (- 1.0 x)) (* y (sqrt (- 1.0 x))))

rewrite36.0ms (2.1%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`add-sqr-sqrt`
16×	`*-un-lft-identity` `sqrt-div` `sqrt-prod`
12×	`pow1`
11×	`add-exp-log` `associate-l` `add-cbrt-cube`
10×	`add-cube-cbrt` `associate-*r/`
9×	`associate-r`
8×	`flip3--` `flip--`
6×	`add-log-exp`
4×	`frac-times` `pow-prod-down` `prod-exp` `cbrt-unprod`
3×	`distribute-lft-out--` `difference-of-squares`
2×	`associate-l/` `-commutative` `unswap-sqr`
1×	`+-commutative` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `sum-log` `flip-+`

Counts

4 → 85

Calls

4 calls:

13.0ms	(+ (* (sqrt (- 1.0 x)) (* y (sqrt (- 1.0 x)))) (* x z))
11.0ms	(* (sqrt (- 1.0 x)) (* y (sqrt (- 1.0 x))))
6.0ms	(* y (sqrt (- 1.0 x)))
3.0ms	(sqrt (- 1.0 x))

series24.0ms (1.4%)

Counts

4 → 12

Calls

4 calls:

8.0ms	(* y (sqrt (- 1.0 x)))
8.0ms	(+ (* (sqrt (- 1.0 x)) (* y (sqrt (- 1.0 x)))) (* x z))
5.0ms	(* (sqrt (- 1.0 x)) (* y (sqrt (- 1.0 x))))
3.0ms	(sqrt (- 1.0 x))

simplify36.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	5060	1021

prune177.0ms (10.3%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	97	0	97
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	97	3	100

Merged error: 0.0b

Counts

100 → 3

localize9.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt (- 1.0 x))
0.0b	(* (sqrt (- 1.0 x)) (sqrt y))
0.0b	(* (sqrt (- 1.0 x)) (sqrt y))
0.2b	(* (* (sqrt (- 1.0 x)) (sqrt y)) (* (sqrt (- 1.0 x)) (sqrt y)))

rewrite40.0ms (2.3%)

Algorithm

1×	rewrite-expression-head

Rules

68×	`pow1`
41×	`pow-prod-down`
36×	`add-sqr-sqrt`
29×	`sqrt-prod`
21×	`sqrt-pow1` `pow1/2`
20×	`add-exp-log` `add-cbrt-cube`
19×	`*-un-lft-identity`
18×	`sqrt-div` `associate-*l/`
17×	`associate-l`
13×	`add-cube-cbrt` `associate-r`
10×	`prod-exp` `cbrt-unprod`
9×	`flip3--` `flip--`
8×	`pow-prod-up` `unswap-sqr`
7×	`sqrt-unprod`
6×	`pow-sqr`
4×	`frac-times` `add-log-exp`
3×	`*-commutative` `distribute-lft-out--` `difference-of-squares`
2×	`pow-plus` `associate-*r/`
1×	`pow2` `rem-sqrt-square` `swap-sqr` `rem-square-sqrt`

Counts

4 → 137

Calls

4 calls:

17.0ms	(* (* (sqrt (- 1.0 x)) (sqrt y)) (* (sqrt (- 1.0 x)) (sqrt y)))
8.0ms	(* (sqrt (- 1.0 x)) (sqrt y))
8.0ms	(* (sqrt (- 1.0 x)) (sqrt y))
3.0ms	(sqrt (- 1.0 x))

series33.0ms (1.9%)

Counts

4 → 12

Calls

4 calls:

12.0ms	(* (sqrt (- 1.0 x)) (sqrt y))
12.0ms	(* (sqrt (- 1.0 x)) (sqrt y))
5.0ms	(* (* (sqrt (- 1.0 x)) (sqrt y)) (* (sqrt (- 1.0 x)) (sqrt y)))
3.0ms	(sqrt (- 1.0 x))

simplify36.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

149 → 149

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	5049	1291

prune271.0ms (15.8%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	149	0	149
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	149	3	152

Merged error: 0.0b

Counts

152 → 3

regimes170.0ms (9.9%)

Accuracy

Total 0.0b remaining (16.3%)

Threshold costs 0.0b (16.3%)

bsearch0.0ms (0%)

simplify1.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	21	9
1	21	9

end0.0ms (0%)

sample412.0ms (24%)

Algorithm

1×

intervals

Results

226.0ms	8000×	body	80	valid
17.0ms	649×	body	80	invalid

Details

analyze281.0ms (16.4%)

sample15.0ms (0.9%)

simplify14.0ms (0.8%)

prune7.0ms (0.4%)

localize6.0ms (0.4%)

rewrite12.0ms (0.7%)

series12.0ms (0.7%)

simplify55.0ms (3.2%)

prune58.0ms (3.4%)

localize8.0ms (0.5%)

rewrite36.0ms (2.1%)

series24.0ms (1.4%)

simplify36.0ms (2.1%)

prune177.0ms (10.3%)

localize9.0ms (0.5%)

rewrite40.0ms (2.3%)

series33.0ms (1.9%)

simplify36.0ms (2.1%)

prune271.0ms (15.8%)

regimes170.0ms (9.9%)

bsearch0.0ms (0%)

simplify1.0ms (0.1%)

end0.0ms (0%)

sample412.0ms (24%)

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