Details

analyze67.0ms (3.8%)

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
25%	74.9%	0.1%	5
50%	50%	0.1%	6
56.2%	37.5%	6.3%	7
68.7%	25%	6.3%	8
71.8%	18.7%	9.5%	9
78%	12.5%	9.5%	10
79.6%	9.4%	11%	11
82.7%	6.2%	11%	12
83.6%	4.6%	11.8%	13
85.1%	3.1%	11.8%	14

sample14.0ms (0.8%)

Algorithm

1×

intervals

Results

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

simplify24.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	642	11
1	642	11

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: 0.0b

Counts

2 → 1

localize7.0ms (0.4%)

Local error

Found 2 expressions with local error:

0.0b	(* x (- y 1.0))
0.0b	(- (* x (- y 1.0)) (* y 0.5))

rewrite13.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

2 → 37

Calls

2 calls:

6.0ms	(* x (- y 1.0))
6.0ms	(- (* x (- y 1.0)) (* y 0.5))

series9.0ms (0.5%)

Counts

2 → 6

Calls

2 calls:

5.0ms	(- (* x (- y 1.0)) (* y 0.5))
4.0ms	(* x (- y 1.0))

simplify50.0ms (2.8%)

Algorithm

1×	egg-herbie

Counts

43 → 43

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4944	375
1	4944	375

prune69.0ms (3.9%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	40	3	43
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	40	4	44

Merged error: 0.0b

Counts

44 → 4

localize11.0ms (0.6%)

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (- (* x (- y 1.0)) (* y 0.5))) (cbrt (- (* x (- y 1.0)) (* y 0.5))))
0.6b	(cbrt (- (* x (- y 1.0)) (* y 0.5)))
0.6b	(cbrt (- (* x (- y 1.0)) (* y 0.5)))
0.6b	(cbrt (- (* x (- y 1.0)) (* y 0.5)))

rewrite36.0ms (2%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
18×	`cbrt-div`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`flip3--` `pow1/3` `flip--`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l`
4×	`frac-times` `add-cbrt-cube` `add-log-exp` `unswap-sqr`
2×	`associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 87

Calls

4 calls:

16.0ms	(* (cbrt (- (* x (- y 1.0)) (* y 0.5))) (cbrt (- (* x (- y 1.0)) (* y 0.5))))
6.0ms	(cbrt (- (* x (- y 1.0)) (* y 0.5)))
6.0ms	(cbrt (- (* x (- y 1.0)) (* y 0.5)))
6.0ms	(cbrt (- (* x (- y 1.0)) (* y 0.5)))

series82.0ms (4.6%)

Counts

4 → 12

Calls

4 calls:

25.0ms	(* (cbrt (- (* x (- y 1.0)) (* y 0.5))) (cbrt (- (* x (- y 1.0)) (* y 0.5))))
20.0ms	(cbrt (- (* x (- y 1.0)) (* y 0.5)))
18.0ms	(cbrt (- (* x (- y 1.0)) (* y 0.5)))
18.0ms	(cbrt (- (* x (- y 1.0)) (* y 0.5)))

simplify66.0ms (3.7%)

Algorithm

1×	egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	5026	1971

prune281.0ms (15.7%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	99	0	99
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	99	4	103

Merged error: 0.0b

Counts

103 → 4

localize9.0ms (0.5%)

Local error

Found 3 expressions with local error:

0.0b	(- (* (sqrt x) (* (- y 1.0) (sqrt x))) (* y 0.5))
0.0b	(* (- y 1.0) (sqrt x))
0.2b	(* (sqrt x) (* (- y 1.0) (sqrt x)))

rewrite28.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
11×	`associate-l`
10×	`pow1` `add-exp-log` `*-un-lft-identity` `add-cbrt-cube`
8×	`add-cube-cbrt`
7×	`associate-r` `sqrt-prod`
5×	`add-log-exp`
4×	`pow-prod-down` `associate-*l/` `prod-exp` `cbrt-unprod`
3×	`flip3--` `flip--`
2×	`associate-r/` `-commutative` `unswap-sqr`
1×	`sub-neg` `diff-log` `distribute-lft-out--` `difference-of-squares`

Counts

3 → 60

Calls

3 calls:

10.0ms	(- (* (sqrt x) (* (- y 1.0) (sqrt x))) (* y 0.5))
9.0ms	(* (sqrt x) (* (- y 1.0) (sqrt x)))
7.0ms	(* (- y 1.0) (sqrt x))

series21.0ms (1.2%)

Counts

3 → 9

Calls

3 calls:

9.0ms	(- (* (sqrt x) (* (- y 1.0) (sqrt x))) (* y 0.5))
6.0ms	(* (sqrt x) (* (- y 1.0) (sqrt x)))
6.0ms	(* (- y 1.0) (sqrt x))

simplify59.0ms (3.3%)

Algorithm

1×	egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4959	632
1	4959	632

prune98.0ms (5.5%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	68	1	69
Fresh	0	1	1
Picked	1	0	1
Done	0	2	2
Total	69	4	73

Merged error: 0b

Counts

73 → 4

localize11.0ms (0.6%)

Local error

Found 4 expressions with local error:

0.1b	(sqrt (sqrt x))
0.1b	(sqrt (sqrt x))
0.2b	(* (sqrt (sqrt x)) (* (* (sqrt x) (- y 1.0)) (sqrt (sqrt x))))
0.2b	(* (* (sqrt x) (- y 1.0)) (sqrt (sqrt x)))

rewrite33.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Rules

38×	`sqrt-prod`
22×	`pow1`
18×	`add-exp-log` `add-sqr-sqrt` `add-cbrt-cube`
14×	`add-cube-cbrt` `*-un-lft-identity`
10×	`associate-r` `associate-l`
9×	`pow-prod-down` `prod-exp` `cbrt-unprod`
8×	`sqrt-pow1`
6×	`associate-*r/`
4×	`rem-sqrt-square` `pow1/2` `associate-*l/` `add-log-exp`
2×	`flip3--` `*-commutative` `flip--`

Counts

4 → 93

Calls

4 calls:

14.0ms	(* (sqrt (sqrt x)) (* (* (sqrt x) (- y 1.0)) (sqrt (sqrt x))))
12.0ms	(* (* (sqrt x) (- y 1.0)) (sqrt (sqrt x)))
2.0ms	(sqrt (sqrt x))
2.0ms	(sqrt (sqrt x))

series54.0ms (3%)

Counts

4 → 12

Calls

4 calls:

20.0ms	(* (* (sqrt x) (- y 1.0)) (sqrt (sqrt x)))
14.0ms	(sqrt (sqrt x))
14.0ms	(sqrt (sqrt x))
6.0ms	(* (sqrt (sqrt x)) (* (* (sqrt x) (- y 1.0)) (sqrt (sqrt x))))

simplify66.0ms (3.7%)

Algorithm

1×	egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	5073	772

prune144.0ms (8.1%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	105	0	105
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	105	4	109

Merged error: 0b

Counts

109 → 4

regimes161.0ms (9%)

Accuracy

Total 0.0b remaining (40.5%)

Threshold costs 0.0b (40.5%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	47	11
1	47	11

end0.0ms (0%)

sample362.0ms (20.3%)

Algorithm

1×

intervals

Results

230.0ms	7990×	body	80	valid
2.0ms	74×	body	80	invalid
0.0ms	4×	body	640	valid
0.0ms	2×	body	1280	valid
0.0ms	2×	body	320	valid
0.0ms	2×	body	160	valid

Details

analyze67.0ms (3.8%)

sample14.0ms (0.8%)

simplify24.0ms (1.4%)

prune5.0ms (0.3%)

localize7.0ms (0.4%)

rewrite13.0ms (0.7%)

series9.0ms (0.5%)

simplify50.0ms (2.8%)

prune69.0ms (3.9%)

localize11.0ms (0.6%)

rewrite36.0ms (2%)

series82.0ms (4.6%)

simplify66.0ms (3.7%)

prune281.0ms (15.7%)

localize9.0ms (0.5%)

rewrite28.0ms (1.6%)

series21.0ms (1.2%)

simplify59.0ms (3.3%)

prune98.0ms (5.5%)

localize11.0ms (0.6%)

rewrite33.0ms (1.8%)

series54.0ms (3%)

simplify66.0ms (3.7%)

prune144.0ms (8.1%)

regimes161.0ms (9%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample362.0ms (20.3%)

Profiling