Details

analyze92.0ms (6.8%)

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
25%	74.9%	0.1%	4
25%	74.9%	0.1%	5
43.7%	50%	6.3%	6
43.7%	43.7%	12.6%	7
59.3%	26.5%	14.1%	8
59.3%	22.6%	18%	9
67.1%	13.7%	19.2%	10
67.1%	11.5%	21.4%	11
71%	6.9%	22%	12
71%	5.8%	23.2%	13
73%	3.5%	23.5%	14

sample16.0ms (1.2%)

Algorithm

1×

intervals

Results

9.0ms	256×	body	80	valid
0.0ms	5×	body	80	nan

simplify3.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	6	6
1	6	6

prune5.0ms (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: 23.4b

Counts

2 → 1

localize5.0ms (0.3%)

Local error

Found 1 expressions with local error:

21.8b

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

rewrite4.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

3×	`add-sqr-sqrt` `sqrt-prod`
2×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `sqrt-div`
1×	`add-exp-log` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `add-cbrt-cube` `flip-+` `add-log-exp`

Counts

1 → 15

Calls

1 calls:

4.0ms

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

series6.0ms (0.4%)

Counts

1 → 3

Calls

1 calls:

6.0ms

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

simplify56.0ms (4.1%)

Algorithm

1×	egg-herbie

Counts

18 → 18

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4926	159
1	4926	159

prune35.0ms (2.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	15	3	18
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	15	4	19

Merged error: 0b

Counts

19 → 4

localize8.0ms (0.6%)

Local error

Found 3 expressions with local error:

0.2b	(pow (sqrt (+ (* x x) y)) 3)
21.8b	(sqrt (+ (* x x) y))
33.8b	(cbrt (pow (sqrt (+ (* x x) y)) 3))

rewrite17.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`cbrt-prod`
15×	`add-sqr-sqrt` `sqrt-prod`
14×	`add-cube-cbrt` `*-un-lft-identity`
12×	`unpow-prod-down` `cube-prod`
6×	`pow1` `sqrt-div`
4×	`add-exp-log` `cube-div` `add-cbrt-cube`
3×	`pow-unpow` `pow-pow` `flip3-+` `flip-+` `add-log-exp`
2×	`cube-mult` `cbrt-div` `sqrt-pow1` `pow1/2` `unpow3` `sqr-pow`
1×	`pow-to-exp` `rem-sqrt-square` `pow1/3` `pow-exp` `sqrt-pow2` `rem-cbrt-cube` `rem-cube-cbrt`

Counts

3 → 78

Calls

3 calls:

6.0ms	(cbrt (pow (sqrt (+ (* x x) y)) 3))
5.0ms	(pow (sqrt (+ (* x x) y)) 3)
4.0ms	(sqrt (+ (* x x) y))

series18.0ms (1.3%)

Counts

3 → 9

Calls

3 calls:

6.0ms	(pow (sqrt (+ (* x x) y)) 3)
6.0ms	(cbrt (pow (sqrt (+ (* x x) y)) 3))
5.0ms	(sqrt (+ (* x x) y))

simplify54.0ms (4%)

Algorithm

1×	egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4937	843
1	4937	843

prune116.0ms (8.6%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	87	0	87
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	87	4	91

Merged error: 0b

Counts

91 → 4

localize5.0ms (0.3%)

Local error

Found 2 expressions with local error:

0.0b	(+ x (* 1/2 (/ y x)))
0.0b	(* 1/2 (/ y x))

rewrite10.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`add-sqr-sqrt`
13×	`associate-r`
10×	`add-cube-cbrt` `*-un-lft-identity` `times-frac`
7×	`add-exp-log` `add-cbrt-cube`
4×	`pow1` `add-log-exp`
3×	`associate-l`
2×	`prod-exp` `cbrt-unprod` `unswap-sqr`
1×	`cbrt-undiv` `+-commutative` `flip3-+` `associate-r/` `div-exp` `pow-prod-down` `sum-log` `-commutative` `flip-+` `div-inv`

Counts

2 → 43

Calls

2 calls:

6.0ms	(* 1/2 (/ y x))
3.0ms	(+ x (* 1/2 (/ y x)))

series7.0ms (0.5%)

Counts

2 → 6

Calls

2 calls:

4.0ms	(+ x (* 1/2 (/ y x)))
3.0ms	(* 1/2 (/ y x))

simplify34.0ms (2.5%)

Algorithm

1×	egg-herbie

Counts

49 → 49

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	4999	372
1	4999	372

prune59.0ms (4.3%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	49	0	49
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	49	4	53

Merged error: 0b

Counts

53 → 4

localize5.0ms (0.3%)

Local error

Found 2 expressions with local error:

0.0b	(- (* y (/ -1/2 x)) x)
0.2b	(* y (/ -1/2 x))

rewrite14.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`add-sqr-sqrt`
13×	`associate-r`
10×	`add-cube-cbrt` `*-un-lft-identity` `times-frac`
7×	`add-exp-log` `add-cbrt-cube`
4×	`pow1` `add-log-exp`
3×	`associate-l`
2×	`prod-exp` `cbrt-unprod` `unswap-sqr`
1×	`cbrt-undiv` `sub-neg` `flip3--` `diff-log` `associate-r/` `div-exp` `pow-prod-down` `-commutative` `flip--` `div-inv`

Counts

2 → 43

Calls

2 calls:

8.0ms	(* y (/ -1/2 x))
5.0ms	(- (* y (/ -1/2 x)) x)

series9.0ms (0.6%)

Counts

2 → 6

Calls

2 calls:

5.0ms	(- (* y (/ -1/2 x)) x)
3.0ms	(* y (/ -1/2 x))

simplify41.0ms (3%)

Algorithm

1×	egg-herbie

Counts

49 → 49

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5315	373

prune63.0ms (4.7%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	49	0	49
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	49	4	53

Merged error: 0b

Counts

53 → 4

regimes318.0ms (23.5%)

Accuracy

Total 0.0b remaining (85%)

Threshold costs 0.0b (85%)

bsearch21.0ms (1.6%)

Steps

Iters	Range		Point
7	1.4372210532027569e+135	8.320137619080135e+136	6.947391960525683e+136
9	-4.8280070932576916e+154	-5.881222518501429e+146	-1.1516046553453194e+154

simplify1.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	33	28
1	33	28

end0.0ms (0%)

sample331.0ms (24.5%)

Algorithm

1×

intervals

Results

200.0ms	8000×	body	80	valid
3.0ms	152×	body	80	nan

Details

analyze92.0ms (6.8%)

sample16.0ms (1.2%)

simplify3.0ms (0.2%)

prune5.0ms (0.4%)

localize5.0ms (0.3%)

rewrite4.0ms (0.3%)

series6.0ms (0.4%)

simplify56.0ms (4.1%)

prune35.0ms (2.6%)

localize8.0ms (0.6%)

rewrite17.0ms (1.3%)

series18.0ms (1.3%)

simplify54.0ms (4%)

prune116.0ms (8.6%)

localize5.0ms (0.3%)

rewrite10.0ms (0.7%)

series7.0ms (0.5%)

simplify34.0ms (2.5%)

prune59.0ms (4.3%)

localize5.0ms (0.3%)

rewrite14.0ms (1%)

series9.0ms (0.6%)

simplify41.0ms (3%)

prune63.0ms (4.7%)

regimes318.0ms (23.5%)

bsearch21.0ms (1.6%)

simplify1.0ms (0.1%)

end0.0ms (0%)

sample331.0ms (24.5%)

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