Details

analyze3.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
50%	50%	0%	2
50%	25%	25%	3
62.5%	12.5%	25%	4
68.7%	6.2%	25%	5
71.8%	3.1%	25%	6
73.4%	1.6%	25%	7
74.2%	0.8%	25%	8
74.6%	0.4%	25%	9
74.8%	0.2%	25%	10
74.9%	0.1%	25%	11
74.9%	0%	25%	12
74.9%	0%	25%	13
74.9%	0%	25%	14

sample12.0ms (0.4%)

Algorithm

1×

intervals

Results

7.0ms

256×

body

valid

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	8	8
1	8	8

prune4.0ms (0.1%)

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: 0.2b

Counts

2 → 1

localize5.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(sqrt (+ x 1.0))
0.0b	(+ 1.0 (sqrt (+ x 1.0)))
0.1b	(/ x (+ 1.0 (sqrt (+ x 1.0))))

rewrite21.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`*-un-lft-identity`
14×	`add-sqr-sqrt`
13×	`add-cube-cbrt`
12×	`times-frac`
6×	`distribute-lft-out`
5×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
4×	`pow1` `associate-/r*` `sqrt-prod`
3×	`flip3-+` `flip-+` `associate-/l*`
2×	`sqrt-div` `associate-/r/`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

3 → 61

Calls

3 calls:

9.0ms	(+ 1.0 (sqrt (+ x 1.0)))
7.0ms	(/ x (+ 1.0 (sqrt (+ x 1.0))))
3.0ms	(sqrt (+ x 1.0))

series25.0ms (0.7%)

Counts

3 → 9

Calls

3 calls:

16.0ms	(/ x (+ 1.0 (sqrt (+ x 1.0))))
4.0ms	(+ 1.0 (sqrt (+ x 1.0)))
4.0ms	(sqrt (+ x 1.0))

simplify25.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 0 (17.0ms)

Iter	Nodes	Cost
0	4963	1021
1	4963	1021

prune141.0ms (4.1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	67	3	70
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	67	4	71

Merged error: 0b

Counts

71 → 4

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ 1.0 (sqrt (+ x 1.0))))
0.0b	(sqrt (+ 1.0 (sqrt (+ x 1.0))))
0.3b	(/ x (sqrt (+ 1.0 (sqrt (+ x 1.0)))))
0.4b	(/ (/ x (sqrt (+ 1.0 (sqrt (+ x 1.0))))) (sqrt (+ 1.0 (sqrt (+ x 1.0)))))

rewrite59.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Rules

378×	`times-frac`
306×	`*-un-lft-identity`
232×	`sqrt-prod`
192×	`add-sqr-sqrt`
190×	`add-cube-cbrt`
58×	`distribute-lft-out`
30×	`associate-/l*`
24×	`sqrt-div`
20×	`associate-/r/`
14×	`associate-/r*`
12×	`flip3-+` `flip-+`
11×	`add-exp-log` `add-cbrt-cube`
10×	`div-inv`
6×	`pow1`
4×	`cbrt-undiv` `div-exp` `add-log-exp`
2×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num`
1×	`associate-/l/`

Counts

4 → 317

Calls

4 calls:

20.0ms	(/ (/ x (sqrt (+ 1.0 (sqrt (+ x 1.0))))) (sqrt (+ 1.0 (sqrt (+ x 1.0)))))
8.0ms	(/ x (sqrt (+ 1.0 (sqrt (+ x 1.0)))))
6.0ms	(sqrt (+ 1.0 (sqrt (+ x 1.0))))
6.0ms	(sqrt (+ 1.0 (sqrt (+ x 1.0))))

series69.0ms (2%)

Counts

4 → 12

Calls

4 calls:

29.0ms	(/ x (sqrt (+ 1.0 (sqrt (+ x 1.0)))))
16.0ms	(/ (/ x (sqrt (+ 1.0 (sqrt (+ x 1.0))))) (sqrt (+ 1.0 (sqrt (+ x 1.0)))))
13.0ms	(sqrt (+ 1.0 (sqrt (+ x 1.0))))
10.0ms	(sqrt (+ 1.0 (sqrt (+ x 1.0))))

simplify76.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

329 → 329

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5484	8179

prune1.3s (37.6%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	329	0	329
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	329	4	333

Merged error: 0b

Counts

333 → 4

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.4b	(* (/ (cbrt x) (sqrt (+ 1.0 (sqrt (+ x 1.0))))) (cbrt x))
0.6b	(cbrt x)
0.6b	(cbrt x)
0.6b	(cbrt x)

rewrite29.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

64×	`add-sqr-sqrt`
50×	`times-frac`
48×	`-un-lft-identity` `associate-l*`
42×	`cbrt-prod`
36×	`add-cube-cbrt`
28×	`sqrt-prod`
10×	`unswap-sqr`
9×	`add-exp-log`
6×	`pow1` `associate-r` `add-cbrt-cube` `distribute-lft-out`
4×	`add-log-exp`
3×	`pow1/3`
2×	`sqrt-div` `prod-exp` `associate-/r/` `cbrt-unprod`
1×	`cbrt-undiv` `flip3-+` `div-exp` `pow-prod-down` `associate-l/` `-commutative` `flip-+` `div-inv`

Counts

4 → 111

Calls

4 calls:

21.0ms	(* (/ (cbrt x) (sqrt (+ 1.0 (sqrt (+ x 1.0))))) (cbrt x))
1.0ms	(cbrt x)
1.0ms	(cbrt x)
1.0ms	(cbrt x)

series109.0ms (3.2%)

Counts

4 → 12

Calls

4 calls:

45.0ms	(* (/ (cbrt x) (sqrt (+ 1.0 (sqrt (+ x 1.0))))) (cbrt x))
21.0ms	(cbrt x)
21.0ms	(cbrt x)
21.0ms	(cbrt x)

simplify35.0ms (1%)

Algorithm

1×	egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 0 (22.0ms)

Iter	Nodes	Cost
0	5485	1933

prune386.0ms (11.3%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	123	0	123
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	123	4	127

Merged error: 0b

Counts

127 → 4

localize7.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ x 1.0))
0.0b	(+ 1.0 (sqrt (+ x 1.0)))
0.1b	(/ (+ 1.0 (sqrt (+ x 1.0))) (sqrt x))
0.1b	(/ (sqrt x) (/ (+ 1.0 (sqrt (+ x 1.0))) (sqrt x)))

rewrite47.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

360×	`times-frac`
287×	`*-un-lft-identity`
190×	`sqrt-prod`
186×	`add-sqr-sqrt`
185×	`add-cube-cbrt`
51×	`distribute-lft-out`
34×	`associate-/r*`
11×	`add-exp-log` `add-cbrt-cube`
10×	`associate-/l*`
9×	`div-inv`
6×	`add-log-exp`
5×	`pow1`
4×	`cbrt-undiv` `div-exp`
3×	`flip3-+` `flip-+`
2×	`frac-2neg` `sqrt-div` `clear-num` `associate-/l/`
1×	`+-commutative` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `sum-log` `associate-/r/`

Counts

4 → 293

Calls

4 calls:

15.0ms	(/ (sqrt x) (/ (+ 1.0 (sqrt (+ x 1.0))) (sqrt x)))
8.0ms	(/ (+ 1.0 (sqrt (+ x 1.0))) (sqrt x))
5.0ms	(+ 1.0 (sqrt (+ x 1.0)))
3.0ms	(sqrt (+ x 1.0))

series38.0ms (1.1%)

Counts

4 → 12

Calls

4 calls:

19.0ms	(/ (sqrt x) (/ (+ 1.0 (sqrt (+ x 1.0))) (sqrt x)))
12.0ms	(/ (+ 1.0 (sqrt (+ x 1.0))) (sqrt x))
4.0ms	(+ 1.0 (sqrt (+ x 1.0)))
3.0ms	(sqrt (+ x 1.0))

simplify70.0ms (2%)

Algorithm

1×	egg-herbie

Counts

305 → 305

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5064	6022

prune569.0ms (16.6%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	305	0	305
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	305	4	309

Merged error: 0b

Counts

309 → 4

regimes71.0ms (2.1%)

Accuracy

Total 0.2b remaining (93.8%)

Threshold costs 0.2b (93.8%)

bsearch0.0ms (0%)

simplify1.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	8
1	8	8

end0.0ms (0%)

sample314.0ms (9.2%)

Algorithm

1×

intervals

Results

223.0ms	7997×	body	80	valid
0.0ms	3×	body	1280	valid

Details

analyze3.0ms (0.1%)

sample12.0ms (0.4%)

simplify2.0ms (0.1%)

prune4.0ms (0.1%)

localize5.0ms (0.2%)

rewrite21.0ms (0.6%)

series25.0ms (0.7%)

simplify25.0ms (0.7%)

prune141.0ms (4.1%)

localize8.0ms (0.2%)

rewrite59.0ms (1.7%)

series69.0ms (2%)

simplify76.0ms (2.2%)

prune1.3s (37.6%)

localize11.0ms (0.3%)

rewrite29.0ms (0.8%)

series109.0ms (3.2%)

simplify35.0ms (1%)

prune386.0ms (11.3%)

localize7.0ms (0.2%)

rewrite47.0ms (1.4%)

series38.0ms (1.1%)

simplify70.0ms (2%)

prune569.0ms (16.6%)

regimes71.0ms (2.1%)

bsearch0.0ms (0%)

simplify1.0ms (0%)

end0.0ms (0%)

sample314.0ms (9.2%)

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