Details

analyze559.0ms (12.1%)

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
3.1%	90.5%	6.3%	6
4.7%	85.9%	9.5%	7
21.1%	64%	14.9%	8
23.4%	58.9%	17.7%	9
27.7%	51.3%	21%	10
28.9%	48.5%	22.6%	11
31.1%	44.4%	24.5%	12
31.7%	42.9%	25.4%	13
32.7%	41%	26.3%	14

sample68.0ms (1.5%)

Algorithm

1×

intervals

Results

28.0ms	53×	body	1280	valid
12.0ms	42×	body	640	valid
7.0ms	131×	body	80	valid
4.0ms	19×	body	320	valid
3.0ms	9×	body	640	invalid
1.0ms	11×	body	160	valid
1.0ms	6×	body	320	invalid
1.0ms	6×	body	160	invalid
0.0ms	8×	body	80	invalid
0.0ms	1×	body	1280	invalid
0.0ms	5×	body	80	nan

simplify38.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	4985	9
1	4985	9

prune6.0ms (0.1%)

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: 9.8b

Counts

2 → 1

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(/ (pow (/ x (+ x y)) x) x)
0.0b	(/ x (+ x y))
5.6b	(pow (/ x (+ x y)) x)

rewrite30.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

138×	`times-frac`
118×	`*-un-lft-identity`
90×	`unpow-prod-down`
80×	`add-sqr-sqrt` `add-cube-cbrt`
25×	`associate-/l*`
19×	`distribute-lft-out`
16×	`add-exp-log`
12×	`associate-/r/`
7×	`div-exp` `associate-/r*` `add-cbrt-cube` `div-inv`
6×	`flip3-+` `flip-+`
5×	`sqr-pow`
4×	`pow1` `pow-exp`
3×	`pow-unpow` `add-log-exp`
2×	`cbrt-undiv` `pow-to-exp` `frac-2neg` `clear-num`
1×	`pow-pow`

Counts

3 → 172

Calls

3 calls:

11.0ms	(/ (pow (/ x (+ x y)) x) x)
6.0ms	(pow (/ x (+ x y)) x)
5.0ms	(/ x (+ x y))

series47.0ms (1%)

Counts

3 → 9

Calls

3 calls:

21.0ms	(pow (/ x (+ x y)) x)
20.0ms	(/ (pow (/ x (+ x y)) x) x)
5.0ms	(/ x (+ x y))

simplify60.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

181 → 181

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5011	2849

prune230.0ms (5%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	174	7	181
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	175	7	182

Merged error: 0.3b

Counts

182 → 7

localize19.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
1.2b	(pow (/ (cbrt x) (cbrt (+ x y))) x)
1.7b	(pow (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ x y)) (cbrt (+ x y)))) x)

rewrite33.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

61×	`unpow-prod-down`
51×	`cbrt-prod`
48×	`*-un-lft-identity`
43×	`times-frac`
36×	`add-sqr-sqrt` `add-cube-cbrt`
20×	`add-exp-log`
14×	`cbrt-div`
10×	`associate-/r/`
7×	`flip3-+` `pow-exp` `flip-+`
6×	`pow1` `pow-unpow` `distribute-lft-out`
5×	`div-exp`
4×	`frac-times` `prod-exp` `add-cbrt-cube` `add-log-exp`
2×	`pow-to-exp` `pow-pow` `pow1/3` `associate-r/` `associate-l/` `div-inv` `sqr-pow`

Counts

4 → 116

Calls

4 calls:

15.0ms	(pow (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ x y)) (cbrt (+ x y)))) x)
10.0ms	(pow (/ (cbrt x) (cbrt (+ x y))) x)
1.0ms	(cbrt x)
1.0ms	(cbrt x)

series108.0ms (2.3%)

Counts

4 → 12

Calls

4 calls:

35.0ms	(pow (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ x y)) (cbrt (+ x y)))) x)
29.0ms	(pow (/ (cbrt x) (cbrt (+ x y))) x)
22.0ms	(cbrt x)
22.0ms	(cbrt x)

simplify263.0ms (5.7%)

Algorithm

1×	egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4936	2335
1	4936	2335

prune198.0ms (4.3%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	127	1	128
Fresh	2	4	6
Picked	1	0	1
Done	0	0	0
Total	130	5	135

Merged error: 0.3b

Counts

135 → 5

localize15.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
1.2b	(pow (/ (cbrt x) (cbrt (+ x y))) x)
2.9b	(log (/ (cbrt x) (cbrt (+ x y))))

rewrite32.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

96×	`cbrt-prod`
85×	`*-un-lft-identity`
84×	`times-frac`
61×	`add-sqr-sqrt` `add-cube-cbrt`
48×	`unpow-prod-down` `log-prod`
12×	`distribute-lft-out`
10×	`add-exp-log`
6×	`pow1`
4×	`cbrt-div` `associate-/r/` `add-cbrt-cube` `add-log-exp`
3×	`pow-unpow`
2×	`flip3-+` `pow1/3` `div-exp` `rem-log-exp` `pow-exp` `flip-+` `div-inv`
1×	`pow-to-exp` `log-div` `pow-pow` `log-pow` `sqr-pow`

Counts

4 → 144

Calls

4 calls:

15.0ms	(pow (/ (cbrt x) (cbrt (+ x y))) x)
8.0ms	(log (/ (cbrt x) (cbrt (+ x y))))
1.0ms	(cbrt x)
1.0ms	(cbrt x)

series94.0ms (2%)

Counts

4 → 12

Calls

4 calls:

26.0ms	(pow (/ (cbrt x) (cbrt (+ x y))) x)
24.0ms	(cbrt x)
23.0ms	(log (/ (cbrt x) (cbrt (+ x y))))
21.0ms	(cbrt x)

simplify65.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

156 → 156

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4804	2360
1	4804	2360

prune297.0ms (6.4%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	156	0	156
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	156	5	161

Merged error: 0.3b

Counts

161 → 5

localize17.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.5b	(cbrt (+ x y))
0.5b	(cbrt (+ x y))
0.5b	(cbrt (+ x y))
22.7b	(pow (* (/ 1 (* (cbrt (+ x y)) (cbrt (+ x y)))) (/ x (cbrt (+ x y)))) x)

rewrite30.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

50×	`add-exp-log`
20×	`prod-exp`
15×	`div-exp` `pow-exp`
14×	`*-un-lft-identity`
12×	`cbrt-prod`
8×	`add-sqr-sqrt` `add-cube-cbrt`
7×	`pow1`
6×	`cbrt-div`
4×	`rec-exp` `1-exp` `add-cbrt-cube` `add-log-exp`
3×	`pow-unpow` `flip3-+` `pow1/3` `flip-+` `distribute-lft-out`
2×	`pow-pow`
1×	`pow-to-exp` `unpow-prod-down` `pow-prod-down` `sqr-pow`

Counts

4 → 72

Calls

4 calls:

20.0ms	(pow (* (/ 1 (* (cbrt (+ x y)) (cbrt (+ x y)))) (/ x (cbrt (+ x y)))) x)
3.0ms	(cbrt (+ x y))
3.0ms	(cbrt (+ x y))
3.0ms	(cbrt (+ x y))

series115.0ms (2.5%)

Counts

4 → 12

Calls

4 calls:

33.0ms	(cbrt (+ x y))
31.0ms	(cbrt (+ x y))
30.0ms	(cbrt (+ x y))
20.0ms	(pow (* (/ 1 (* (cbrt (+ x y)) (cbrt (+ x y)))) (/ x (cbrt (+ x y)))) x)

simplify48.0ms (1%)

Algorithm

1×	egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	4965	1070
1	4965	1070

prune119.0ms (2.6%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	84	0	84
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	84	5	89

Merged error: 0.3b

Counts

89 → 5

regimes104.0ms (2.2%)

Accuracy

Total 3.3b remaining (70.7%)

Threshold costs 0b (0%)

bsearch145.0ms (3.1%)

Steps

Iters	Range		Point
10	2.0205711676386665e+153	7.322388177837852e+168	1.0720527371918883e+168
10	2.0177397367920753e+90	6.657304916560063e+103	2.5779544643503928e+94
11	6.520422951244181e-19	3.740006215103466e+19	124.59949045110731

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	100
1	42	100

end0.0ms (0%)

sample1.9s (40.6%)

Algorithm

1×

intervals

Results

736.0ms	1484×	body	1280	valid
360.0ms	1200×	body	640	valid
236.0ms	4300×	body	80	valid
133.0ms	668×	body	320	valid
76.0ms	267×	body	640	invalid
43.0ms	348×	body	160	valid
35.0ms	80×	body	1280	invalid
32.0ms	171×	body	320	invalid
12.0ms	103×	body	160	invalid
9.0ms	154×	body	80	invalid
7.0ms	177×	body	80	nan

Details

analyze559.0ms (12.1%)

sample68.0ms (1.5%)

simplify38.0ms (0.8%)

prune6.0ms (0.1%)

localize6.0ms (0.1%)

rewrite30.0ms (0.6%)

series47.0ms (1%)

simplify60.0ms (1.3%)

prune230.0ms (5%)

localize19.0ms (0.4%)

rewrite33.0ms (0.7%)

series108.0ms (2.3%)

simplify263.0ms (5.7%)

prune198.0ms (4.3%)

localize15.0ms (0.3%)

rewrite32.0ms (0.7%)

series94.0ms (2%)

simplify65.0ms (1.4%)

prune297.0ms (6.4%)

localize17.0ms (0.4%)

rewrite30.0ms (0.7%)

series115.0ms (2.5%)

simplify48.0ms (1%)

prune119.0ms (2.6%)

regimes104.0ms (2.2%)

bsearch145.0ms (3.1%)

simplify2.0ms (0%)

end0.0ms (0%)

sample1.9s (40.6%)

Profiling