Details

analyze3.0ms (0.3%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
75%	25%	0%	4
87.5%	12.5%	0%	5
93.7%	6.2%	0%	6
96.8%	3.1%	0%	7
98.4%	1.6%	0%	8
99.2%	0.8%	0%	9
99.6%	0.4%	0%	10
99.8%	0.2%	0%	11
99.9%	0.1%	0%	12
99.9%	0%	0%	13
99.9%	0%	0.1%	14

sample15.0ms (1.5%)

Algorithm

1×

intervals

Results

9.0ms

256×

body

valid

simplify3.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	12	6
1	12	6

prune5.0ms (0.5%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 29.9b

Counts

2 → 1

localize4.0ms (0.4%)

Local error

Found 1 expressions with local error:

28.9b

(sqrt (* x (+ x x)))

rewrite5.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

4×	`pow1`
2×	`sqrt-pow1` `sqrt-div` `associate-*r/`
1×	`add-exp-log` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `flip3-+` `pow1/2` `pow-prod-down` `sqrt-prod` `add-cbrt-cube` `flip-+` `add-log-exp`

Counts

1 → 13

Calls

1 calls:

5.0ms

(sqrt (* x (+ x x)))

series4.0ms (0.4%)

Counts

1 → 3

Calls

1 calls:

4.0ms

(sqrt (* x (+ x x)))

simplify51.0ms (5%)

Algorithm

1×	egg-herbie

Counts

16 → 16

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4818	91
1	4818	91

prune35.0ms (3.4%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	12	4	16
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	12	5	17

Merged error: 0.2b

Counts

17 → 5

localize5.0ms (0.5%)

Local error

Found 1 expressions with local error:

0.5b	(* x (sqrt 2))

rewrite5.0ms (0.5%)

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

(* x (sqrt 2))

series4.0ms (0.4%)

Counts

1 → 3

Calls

1 calls:

4.0ms

(* x (sqrt 2))

simplify28.0ms (2.8%)

Algorithm

1×	egg-herbie

Counts

25 → 25

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	4888	133
1	4888	133

prune57.0ms (5.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	22	3	25
Fresh	0	3	3
Picked	1	0	1
Done	0	1	1
Total	23	7	30

Merged error: 0.1b

Counts

30 → 7

localize7.0ms (0.7%)

Local error

Found 2 expressions with local error:

0.1b	(* x (* (cbrt (sqrt 2)) (cbrt (sqrt 2))))
0.3b	(* (* x (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (cbrt (sqrt 2)))

rewrite20.0ms (2%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

2 → 46

Calls

2 calls:

11.0ms	(* (* x (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (cbrt (sqrt 2)))
8.0ms	(* x (* (cbrt (sqrt 2)) (cbrt (sqrt 2))))

series40.0ms (3.9%)

Counts

2 → 6

Calls

2 calls:

35.0ms	(* x (* (cbrt (sqrt 2)) (cbrt (sqrt 2))))
4.0ms	(* (* x (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (cbrt (sqrt 2)))

simplify49.0ms (4.8%)

Algorithm

1×	egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5150	361

prune131.0ms (12.9%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	51	1	52
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	51	8	59

Merged error: 0.1b

Counts

59 → 8

localize8.0ms (0.7%)

Local error

Found 2 expressions with local error:

0.2b	(* x (sqrt (sqrt 2)))
0.2b	(* (* x (sqrt (sqrt 2))) (sqrt (sqrt 2)))

rewrite18.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

2 → 50

Calls

2 calls:

10.0ms	(* (* x (sqrt (sqrt 2))) (sqrt (sqrt 2)))
6.0ms	(* x (sqrt (sqrt 2)))

series11.0ms (1.1%)

Counts

2 → 6

Calls

2 calls:

6.0ms	(* x (sqrt (sqrt 2)))
4.0ms	(* (* x (sqrt (sqrt 2))) (sqrt (sqrt 2)))

simplify59.0ms (5.8%)

Algorithm

1×	egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	5070	343

prune117.0ms (11.5%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	55	1	56
Fresh	1	4	5
Picked	1	0	1
Done	0	2	2
Total	57	7	64

Merged error: 0.1b

Counts

64 → 7

regimes47.0ms (4.6%)

Accuracy

Total 0.2b remaining (63%)

Threshold costs 0.2b (63%)

bsearch14.0ms (1.3%)

Steps

Iters	Range		Point
11	-3.0183957739187235e-302	1.300418255857306e-287	-2.8491681377424e-310

simplify1.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	40	21
1	40	21

end0.0ms (0%)

sample268.0ms (26.4%)

Algorithm

1×

intervals

Results

179.0ms	8000×	body	80	valid
0.0ms	1×	body	80	invalid

Details

analyze3.0ms (0.3%)

sample15.0ms (1.5%)

simplify3.0ms (0.3%)

prune5.0ms (0.5%)

localize4.0ms (0.4%)

rewrite5.0ms (0.5%)

series4.0ms (0.4%)

simplify51.0ms (5%)

prune35.0ms (3.4%)

localize5.0ms (0.5%)

rewrite5.0ms (0.5%)

series4.0ms (0.4%)

simplify28.0ms (2.8%)

prune57.0ms (5.7%)

localize7.0ms (0.7%)

rewrite20.0ms (2%)

series40.0ms (3.9%)

simplify49.0ms (4.8%)

prune131.0ms (12.9%)

localize8.0ms (0.7%)

rewrite18.0ms (1.7%)

series11.0ms (1.1%)

simplify59.0ms (5.8%)

prune117.0ms (11.5%)

regimes47.0ms (4.6%)

bsearch14.0ms (1.3%)

simplify1.0ms (0.1%)

end0.0ms (0%)

sample268.0ms (26.4%)

Profiling