Details

analyze296.0ms (14.8%)

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
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
12.5%	87.4%	0.1%	7
25%	74.9%	0.1%	8
31.2%	64%	4.8%	9
31.2%	42.1%	26.7%	10
35.9%	37.1%	27.1%	11
38.2%	32.2%	29.6%	12
47.8%	21.6%	30.6%	13
50.2%	19%	30.8%	14

sample17.0ms (0.8%)

Algorithm

1×

intervals

Results

8.0ms	256×	body	80	valid
0.0ms	12×	body	80	invalid

simplify3.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	40	9
1	40	9

prune9.0ms (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 → 2

localize7.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.0b	(+ (* x y) (* z z))
0.0b	(+ (+ (* x y) (* z z)) (* z z))
0.1b	(+ (+ (+ (* x y) (* z z)) (* z z)) (* z z))

rewrite19.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`add-log-exp`
10×	`sum-log`
3×	`pow1` `add-exp-log` `+-commutative` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `flip3-+` `add-cbrt-cube` `flip-+`
2×	`associate-+l+`

Counts

3 → 38

Calls

3 calls:

9.0ms	(+ (+ (+ (* x y) (* z z)) (* z z)) (* z z))
6.0ms	(+ (+ (* x y) (* z z)) (* z z))
4.0ms	(+ (* x y) (* z z))

series35.0ms (1.7%)

Counts

3 → 9

Calls

3 calls:

14.0ms	(+ (+ (* x y) (* z z)) (* z z))
12.0ms	(+ (+ (+ (* x y) (* z z)) (* z z)) (* z z))
9.0ms	(+ (* x y) (* z z))

simplify49.0ms (2.4%)

Algorithm

1×	egg-herbie

Counts

47 → 47

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4862	519
1	4862	519

prune71.0ms (3.5%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	44	3	47
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	45	4	49

Merged error: 0.0b

Counts

49 → 4

localize6.0ms (0.3%)

Local error

Found 2 expressions with local error:

0.0b	(+ (* x y) (* z (* z 3)))
0.2b	(* z (* z 3))

rewrite9.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`pow1` `add-exp-log` `add-cbrt-cube`
4×	`add-log-exp`
3×	`add-sqr-sqrt` `add-cube-cbrt` `-un-lft-identity` `associate-l*` `pow-prod-down` `prod-exp` `cbrt-unprod`
1×	`+-commutative` `flip3-+` `associate-r` `sum-log` `*-commutative` `flip-+`

Counts

2 → 29

Calls

2 calls:

5.0ms	(* z (* z 3))
4.0ms	(+ (* x y) (* z (* z 3)))

series14.0ms (0.7%)

Counts

2 → 6

Calls

2 calls:

11.0ms	(+ (* x y) (* z (* z 3)))
3.0ms	(* z (* z 3))

simplify32.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

35 → 35

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	5454	285

prune63.0ms (3.1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	34	1	35
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	34	5	39

Merged error: 0b

Counts

39 → 5

localize9.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.1b	(+ (+ (* (sqrt (+ (* x y) (* z z))) (sqrt (+ (* x y) (* z z)))) (* z z)) (* z z))
0.1b	(* (sqrt (+ (* x y) (* z z))) (sqrt (+ (* x y) (* z z))))
2.2b	(sqrt (+ (* x y) (* z z)))
2.2b	(sqrt (+ (* x y) (* z z)))

rewrite36.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
24×	`sqrt-prod`
21×	`pow1`
16×	`sqrt-div`
14×	`add-cube-cbrt` `*-un-lft-identity`
10×	`sqrt-pow1` `pow1/2`
9×	`flip3-+` `flip-+` `add-log-exp`
8×	`swap-sqr`
6×	`add-exp-log` `associate-r` `associate-l` `add-cbrt-cube`
5×	`pow-prod-up`
4×	`frac-times` `unswap-sqr`
3×	`pow-prod-down` `sum-log` `pow-sqr`
2×	`rem-sqrt-square` `associate-r/` `associate-l/`
1×	`+-commutative` `pow2` `associate-+l+` `pow-plus` `sqrt-unprod` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 100

Calls

4 calls:

14.0ms	(+ (+ (* (sqrt (+ (* x y) (* z z))) (sqrt (+ (* x y) (* z z)))) (* z z)) (* z z))
11.0ms	(* (sqrt (+ (* x y) (* z z))) (sqrt (+ (* x y) (* z z))))
4.0ms	(sqrt (+ (* x y) (* z z)))
4.0ms	(sqrt (+ (* x y) (* z z)))

series55.0ms (2.8%)

Counts

4 → 12

Calls

4 calls:

16.0ms	(sqrt (+ (* x y) (* z z)))
16.0ms	(sqrt (+ (* x y) (* z z)))
14.0ms	(+ (+ (* (sqrt (+ (* x y) (* z z))) (sqrt (+ (* x y) (* z z)))) (* z z)) (* z z))
9.0ms	(* (sqrt (+ (* x y) (* z z))) (sqrt (+ (* x y) (* z z))))

simplify55.0ms (2.8%)

Algorithm

1×	egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4970	1205
1	4970	1205

prune139.0ms (6.9%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	112	0	112
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	112	5	117

Merged error: 0b

Counts

117 → 5

localize9.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.2b	(* z (* z 3))
0.3b	(* (sqrt (+ (* x y) (* z (* z 3)))) (sqrt (+ (* x y) (* z (* z 3)))))
2.2b	(sqrt (+ (* x y) (* z (* z 3))))
2.2b	(sqrt (+ (* x y) (* z (* z 3))))

rewrite29.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
26×	`pow1`
24×	`sqrt-prod`
16×	`sqrt-div`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`add-exp-log` `add-cbrt-cube`
10×	`sqrt-pow1` `pow1/2`
9×	`associate-l`
8×	`flip3-+` `swap-sqr` `flip-+`
7×	`associate-r`
6×	`pow-prod-down`
5×	`pow-prod-up`
4×	`frac-times` `prod-exp` `cbrt-unprod` `add-log-exp` `unswap-sqr`
3×	`pow-sqr`
2×	`rem-sqrt-square` `associate-r/` `associate-l/` `*-commutative`
1×	`pow2` `pow-plus` `sqrt-unprod` `rem-square-sqrt`

Counts

4 → 105

Calls

4 calls:

11.0ms	(* (sqrt (+ (* x y) (* z (* z 3)))) (sqrt (+ (* x y) (* z (* z 3)))))
7.0ms	(* z (* z 3))
4.0ms	(sqrt (+ (* x y) (* z (* z 3))))
4.0ms	(sqrt (+ (* x y) (* z (* z 3))))

series56.0ms (2.8%)

Counts

4 → 12

Calls

4 calls:

20.0ms	(sqrt (+ (* x y) (* z (* z 3))))
20.0ms	(sqrt (+ (* x y) (* z (* z 3))))
12.0ms	(* (sqrt (+ (* x y) (* z (* z 3)))) (sqrt (+ (* x y) (* z (* z 3)))))
3.0ms	(* z (* z 3))

simplify57.0ms (2.8%)

Algorithm

1×	egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4945	1340
1	4945	1340

prune197.0ms (9.8%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	117	0	117
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	117	5	122

Merged error: 0b

Counts

122 → 5

regimes256.0ms (12.7%)

Accuracy

Total 0.1b remaining (81%)

Threshold costs 0.1b (81%)

bsearch0.0ms (0%)

simplify1.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	9
1	12	9

end0.0ms (0%)

sample477.0ms (23.8%)

Algorithm

1×

intervals

Results

272.0ms	8000×	body	80	valid
15.0ms	457×	body	80	invalid

Details

analyze296.0ms (14.8%)

sample17.0ms (0.8%)

simplify3.0ms (0.2%)

prune9.0ms (0.4%)

localize7.0ms (0.3%)

rewrite19.0ms (0.9%)

series35.0ms (1.7%)

simplify49.0ms (2.4%)

prune71.0ms (3.5%)

localize6.0ms (0.3%)

rewrite9.0ms (0.5%)

series14.0ms (0.7%)

simplify32.0ms (1.6%)

prune63.0ms (3.1%)

localize9.0ms (0.5%)

rewrite36.0ms (1.8%)

series55.0ms (2.8%)

simplify55.0ms (2.8%)

prune139.0ms (6.9%)

localize9.0ms (0.4%)

rewrite29.0ms (1.5%)

series56.0ms (2.8%)

simplify57.0ms (2.8%)

prune197.0ms (9.8%)

regimes256.0ms (12.7%)

bsearch0.0ms (0%)

simplify1.0ms (0.1%)

end0.0ms (0%)

sample477.0ms (23.8%)

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