Details

analyze3.0ms (0.2%)

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

sample11.0ms (0.8%)

Algorithm

1×

intervals

Results

6.0ms

256×

body

valid

simplify3.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	12	6
1	12	6

prune7.0ms (0.5%)

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: 27.9b

Counts

2 → 2

localize4.0ms (0.3%)

Local error

Found 1 expressions with local error:

27.1b

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

rewrite5.0ms (0.4%)

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 (0.3%)

Counts

1 → 3

Calls

1 calls:

4.0ms

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

simplify60.0ms (4.5%)

Algorithm

1×	egg-herbie

Counts

16 → 16

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4818	91
1	4818	91

prune41.0ms (3%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	11	5	16
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	12	6	18

Merged error: 0.1b

Counts

18 → 6

localize4.0ms (0.3%)

Local error

Found 2 expressions with local error:

0.0b	(+ (* x x) (* x x))
27.1b	(sqrt (+ (* x x) (* x x)))

rewrite9.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`sqrt-prod`
4×	`add-sqr-sqrt` `add-log-exp`
3×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
2×	`add-exp-log` `distribute-rgt-out` `flip3-+` `count-2` `sqrt-div` `add-cbrt-cube` `flip-+` `distribute-lft-out`
1×	`+-commutative` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `sum-log`

Counts

2 → 32

Calls

2 calls:

4.0ms	(+ (* x x) (* x x))
4.0ms	(sqrt (+ (* x x) (* x x)))

series7.0ms (0.6%)

Counts

2 → 6

Calls

2 calls:

4.0ms	(sqrt (+ (* x x) (* x x)))
3.0ms	(+ (* x x) (* x x))

simplify77.0ms (5.7%)

Algorithm

1×	egg-herbie

Counts

38 → 38

Iterations

Useful iterations: 0 (73.0ms)

Iter	Nodes	Cost
0	4793	222
1	4793	222

prune53.0ms (4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	37	1	38
Fresh	1	4	5
Picked	0	1	1
Done	0	0	0
Total	38	6	44

Merged error: 0.1b

Counts

44 → 6

localize6.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.1b	(sqrt (sqrt (* x (+ x x))))
0.5b	(* (sqrt (sqrt (* x (+ x x)))) (sqrt (sqrt (* x (+ x x)))))
27.1b	(sqrt (* x (+ x x)))
27.1b	(sqrt (* x (+ x x)))

rewrite39.0ms (2.9%)

Algorithm

1×	rewrite-expression-head

Rules

84×	`sqrt-pow1`
71×	`pow1`
33×	`sqrt-prod`
32×	`sqrt-div`
26×	`add-sqr-sqrt`
25×	`pow-prod-down`
22×	`pow1/2`
20×	`associate-*r/`
14×	`pow-prod-up`
13×	`add-cube-cbrt` `*-un-lft-identity`
9×	`flip3-+` `swap-sqr` `flip-+`
8×	`pow-sqr`
7×	`associate-r` `associate-l`
6×	`add-exp-log` `add-cbrt-cube`
4×	`frac-times` `add-log-exp` `unswap-sqr`
2×	`associate-*l/`
1×	`pow2` `rem-sqrt-square` `pow-plus` `sqrt-unprod` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 124

Calls

4 calls:

17.0ms	(* (sqrt (sqrt (* x (+ x x)))) (sqrt (sqrt (* x (+ x x)))))
8.0ms	(sqrt (sqrt (* x (+ x x))))
5.0ms	(sqrt (* x (+ x x)))
4.0ms	(sqrt (* x (+ x x)))

series17.0ms (1.3%)

Counts

4 → 12

Calls

4 calls:

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

simplify81.0ms (6%)

Algorithm

1×	egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 0 (71.0ms)

Iter	Nodes	Cost
0	4895	929
1	4895	929

prune166.0ms (12.3%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	135	1	136
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	135	7	142

Merged error: 0.1b

Counts

142 → 7

localize8.0ms (0.6%)

Local error

Found 4 expressions with local error:

0.2b	(sqrt (cbrt (* x (+ x x))))
0.3b	(* (fabs (cbrt (* x (+ x x)))) (sqrt (cbrt (* x (+ x x)))))
28.0b	(cbrt (* x (+ x x)))
28.0b	(cbrt (* x (+ x x)))

rewrite19.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`add-sqr-sqrt`
10×	`associate-*r/`
9×	`sqrt-prod`
8×	`add-cube-cbrt` `cbrt-div` `*-un-lft-identity`
7×	`pow1` `associate-r`
6×	`add-exp-log` `add-cbrt-cube`
4×	`cbrt-prod` `flip3-+` `sqrt-div` `flip-+` `add-log-exp`
3×	`pow1/3` `associate-l`
2×	`sqrt-pow1` `unswap-sqr`
1×	`rem-sqrt-square` `pow1/2` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 64

Calls

4 calls:

6.0ms	(* (fabs (cbrt (* x (+ x x)))) (sqrt (cbrt (* x (+ x x)))))
5.0ms	(cbrt (* x (+ x x)))
4.0ms	(cbrt (* x (+ x x)))
2.0ms	(sqrt (cbrt (* x (+ x x))))

series120.0ms (8.9%)

Counts

4 → 12

Calls

4 calls:

36.0ms	(* (fabs (cbrt (* x (+ x x)))) (sqrt (cbrt (* x (+ x x)))))
29.0ms	(cbrt (* x (+ x x)))
27.0ms	(cbrt (* x (+ x x)))
27.0ms	(sqrt (cbrt (* x (+ x x))))

simplify53.0ms (3.9%)

Algorithm

1×	egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4774	795
1	4774	795

prune90.0ms (6.6%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	76	0	76
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	76	7	83

Merged error: 0.1b

Counts

83 → 7

regimes176.0ms (13.1%)

Accuracy

Total 0.2b remaining (57.9%)

Threshold costs 0.2b (57.9%)

bsearch12.0ms (0.9%)

Steps

Iters	Range		Point
9	-4.0303509276913107e-308	1.978313196859493e-301	-3.9001145064361e-310

simplify1.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	37	16
1	37	16

end0.0ms (0%)

sample272.0ms (20.2%)

Algorithm

1×

intervals

Results

182.0ms

8000×

body

valid

Details

analyze3.0ms (0.2%)

sample11.0ms (0.8%)

simplify3.0ms (0.2%)

prune7.0ms (0.5%)

localize4.0ms (0.3%)

rewrite5.0ms (0.4%)

series4.0ms (0.3%)

simplify60.0ms (4.5%)

prune41.0ms (3%)

localize4.0ms (0.3%)

rewrite9.0ms (0.7%)

series7.0ms (0.6%)

simplify77.0ms (5.7%)

prune53.0ms (4%)

localize6.0ms (0.5%)

rewrite39.0ms (2.9%)

series17.0ms (1.3%)

simplify81.0ms (6%)

prune166.0ms (12.3%)

localize8.0ms (0.6%)

rewrite19.0ms (1.4%)

series120.0ms (8.9%)

simplify53.0ms (3.9%)

prune90.0ms (6.6%)

regimes176.0ms (13.1%)

bsearch12.0ms (0.9%)

simplify1.0ms (0.1%)

end0.0ms (0%)

sample272.0ms (20.2%)

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