Details

analyze810.0ms (19.5%)

Algorithm

1×

Search

True	Other	False	Iter
0%	48.6%	51.4%	0
0%	48.6%	51.4%	1
24.3%	24.3%	51.4%	2
24.3%	24.3%	51.4%	3
30.4%	18.2%	51.4%	4
30.4%	18.2%	51.4%	5
33.4%	15.2%	51.4%	6
33.4%	15.2%	51.4%	7
34.6%	14.1%	51.4%	8
34.8%	13.9%	51.4%	9
35.4%	13.2%	51.4%	10
35.6%	13.1%	51.4%	11
35.9%	12.7%	51.4%	12
36%	12.6%	51.4%	13
36.2%	12.4%	51.4%	14

sample41.0ms (1%)

Algorithm

1×

intervals

Results

10.0ms	190×	body	80	valid
9.0ms	27×	body	2560	valid
5.0ms	18×	body	1280	valid
4.0ms	256×	pre	80	true
2.0ms	12×	body	640	valid
1.0ms	6×	body	320	valid
0.0ms	3×	body	160	valid

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	38	17
1	38	17

prune7.0ms (0.2%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 14.4b

Counts

2 → 1

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
0.0b	(+ (* (* 4.0 p) p) (* x x))
1.2b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
13.3b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite40.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`pow1` `add-log-exp`
7×	`*-un-lft-identity`
6×	`add-sqr-sqrt`
5×	`add-cube-cbrt`
4×	`add-exp-log` `flip3-+` `sqrt-div` `sqrt-prod` `add-cbrt-cube` `flip-+`
3×	`sqrt-pow1`
2×	`+-commutative` `pow1/2` `associate-*r/` `sum-log`
1×	`rem-sqrt-square` `pow-prod-down` `distribute-lft-out`

Counts

4 → 51

Calls

4 calls:

13.0ms	(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
12.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
9.0ms	(+ (* (* 4.0 p) p) (* x x))
5.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series58.0ms (1.4%)

Counts

4 → 12

Calls

4 calls:

31.0ms	(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
12.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
8.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
6.0ms	(+ (* (* 4.0 p) p) (* x x))

simplify47.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

63 → 63

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5214	875

prune162.0ms (3.9%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	53	10	63
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	54	10	64

Merged error: 14.1b

Counts

64 → 10

localize16.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.5b	(* (sqrt (sqrt (+ (* p (* 4.0 p)) (* x x)))) (sqrt (sqrt (+ (* p (* 4.0 p)) (* x x)))))
8.2b	(+ 1.0 (/ x (* (sqrt (sqrt (+ (* p (* 4.0 p)) (* x x)))) (sqrt (sqrt (+ (* p (* 4.0 p)) (* x x)))))))
13.3b	(sqrt (+ (* p (* 4.0 p)) (* x x)))
13.3b	(sqrt (+ (* p (* 4.0 p)) (* x x)))

rewrite43.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

72×	`sqrt-prod`
50×	`add-sqr-sqrt`
34×	`sqrt-pow1`
29×	`pow1`
28×	`sqrt-div`
20×	`*-un-lft-identity`
18×	`add-cube-cbrt` `pow1/2`
15×	`swap-sqr`
9×	`flip3-+` `associate-r` `associate-l` `pow-prod-up` `flip-+` `unswap-sqr`
6×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
5×	`pow-prod-down` `pow-sqr`
4×	`frac-times`
2×	`rem-sqrt-square` `associate-r/` `associate-l/`
1×	`+-commutative` `pow2` `pow-plus` `sqrt-unprod` `prod-exp` `sum-log` `rem-square-sqrt` `*-commutative` `cbrt-unprod` `distribute-lft-out`

Counts

4 → 125

Calls

4 calls:

18.0ms	(* (sqrt (sqrt (+ (* p (* 4.0 p)) (* x x)))) (sqrt (sqrt (+ (* p (* 4.0 p)) (* x x)))))
10.0ms	(+ 1.0 (/ x (* (sqrt (sqrt (+ (* p (* 4.0 p)) (* x x)))) (sqrt (sqrt (+ (* p (* 4.0 p)) (* x x)))))))
5.0ms	(sqrt (+ (* p (* 4.0 p)) (* x x)))
5.0ms	(sqrt (+ (* p (* 4.0 p)) (* x x)))

series40.0ms (1%)

Counts

4 → 12

Calls

4 calls:

12.0ms	(+ 1.0 (/ x (* (sqrt (sqrt (+ (* p (* 4.0 p)) (* x x)))) (sqrt (sqrt (+ (* p (* 4.0 p)) (* x x)))))))
12.0ms	(* (sqrt (sqrt (+ (* p (* 4.0 p)) (* x x)))) (sqrt (sqrt (+ (* p (* 4.0 p)) (* x x)))))
8.0ms	(sqrt (+ (* p (* 4.0 p)) (* x x)))
8.0ms	(sqrt (+ (* p (* 4.0 p)) (* x x)))

simplify38.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

137 → 137

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	5089	1899

prune393.0ms (9.4%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	131	6	137
Fresh	3	6	9
Picked	0	1	1
Done	0	0	0
Total	134	13	147

Merged error: 14.1b

Counts

147 → 13

localize25.0ms (0.6%)

Local error

Found 4 expressions with local error:

8.5b	(+ 1.0 (/ x (* (* (sqrt (sqrt (+ (* p (* p 4.0)) (* x x)))) (fabs (cbrt (sqrt (+ (* p (* p 4.0)) (* x x)))))) (sqrt (cbrt (sqrt (+ (* p (* 4.0 p)) (* x x))))))))
13.3b	(sqrt (+ (* p (* p 4.0)) (* x x)))
13.3b	(sqrt (+ (* p (* p 4.0)) (* x x)))
13.3b	(sqrt (+ (* p (* 4.0 p)) (* x x)))

rewrite28.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 57

Calls

4 calls:

11.0ms	(+ 1.0 (/ x (* (* (sqrt (sqrt (+ (* p (* p 4.0)) (* x x)))) (fabs (cbrt (sqrt (+ (* p (* p 4.0)) (* x x)))))) (sqrt (cbrt (sqrt (+ (* p (* 4.0 p)) (* x x))))))))
5.0ms	(sqrt (+ (* p (* 4.0 p)) (* x x)))
5.0ms	(sqrt (+ (* p (* p 4.0)) (* x x)))
5.0ms	(sqrt (+ (* p (* p 4.0)) (* x x)))

series81.0ms (2%)

Counts

4 → 12

Calls

4 calls:

56.0ms	(+ 1.0 (/ x (* (* (sqrt (sqrt (+ (* p (* p 4.0)) (* x x)))) (fabs (cbrt (sqrt (+ (* p (* p 4.0)) (* x x)))))) (sqrt (cbrt (sqrt (+ (* p (* 4.0 p)) (* x x))))))))
10.0ms	(sqrt (+ (* p (* 4.0 p)) (* x x)))
8.0ms	(sqrt (+ (* p (* p 4.0)) (* x x)))
8.0ms	(sqrt (+ (* p (* p 4.0)) (* x x)))

simplify63.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	5021	1360

prune337.0ms (8.1%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	64	5	69
Fresh	3	8	11
Picked	1	0	1
Done	0	1	1
Total	68	14	82

Merged error: 14.1b

Counts

82 → 14

localize23.0ms (0.6%)

Local error

Found 4 expressions with local error:

8.5b	(+ 1.0 (/ x (* (* (sqrt (sqrt (+ (* p (* p 4.0)) (* x x)))) (fabs (cbrt (sqrt (+ (* p (* p 4.0)) (* x x)))))) (sqrt (cbrt (sqrt (+ (* p (* p 4.0)) (* x x))))))))
13.3b	(sqrt (+ (* p (* p 4.0)) (* x x)))
13.3b	(sqrt (+ (* p (* p 4.0)) (* x x)))
13.3b	(sqrt (+ (* p (* p 4.0)) (* x x)))

rewrite29.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 57

Calls

4 calls:

11.0ms	(+ 1.0 (/ x (* (* (sqrt (sqrt (+ (* p (* p 4.0)) (* x x)))) (fabs (cbrt (sqrt (+ (* p (* p 4.0)) (* x x)))))) (sqrt (cbrt (sqrt (+ (* p (* p 4.0)) (* x x))))))))
6.0ms	(sqrt (+ (* p (* p 4.0)) (* x x)))
6.0ms	(sqrt (+ (* p (* p 4.0)) (* x x)))
6.0ms	(sqrt (+ (* p (* p 4.0)) (* x x)))

series81.0ms (2%)

Counts

4 → 12

Calls

4 calls:

58.0ms	(+ 1.0 (/ x (* (* (sqrt (sqrt (+ (* p (* p 4.0)) (* x x)))) (fabs (cbrt (sqrt (+ (* p (* p 4.0)) (* x x)))))) (sqrt (cbrt (sqrt (+ (* p (* p 4.0)) (* x x))))))))
8.0ms	(sqrt (+ (* p (* p 4.0)) (* x x)))
8.0ms	(sqrt (+ (* p (* p 4.0)) (* x x)))
8.0ms	(sqrt (+ (* p (* p 4.0)) (* x x)))

simplify60.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5021	1360

prune317.0ms (7.6%)

Pruning

17 alts after pruning (15 fresh and 2 done)

	Pruned	Kept	Total
New	61	8	69
Fresh	5	7	12
Picked	0	1	1
Done	0	1	1
Total	66	17	83

Merged error: 14.1b

Counts

83 → 17

regimes259.0ms (6.2%)

Accuracy

Total 1.2b remaining (8.6%)

Threshold costs 0b (0%)

bsearch0.0ms (0%)

simplify1.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	30
1	21	30

end0.0ms (0%)

sample1.1s (27.5%)

Algorithm

1×

intervals

Results

320.0ms	6030×	body	80	valid
255.0ms	795×	body	2560	valid
158.0ms	610×	body	1280	valid
145.0ms	8000×	pre	80	true
73.0ms	356×	body	640	valid
23.0ms	146×	body	320	valid
6.0ms	63×	body	160	valid

Details

analyze810.0ms (19.5%)

sample41.0ms (1%)

simplify3.0ms (0.1%)

prune7.0ms (0.2%)

localize11.0ms (0.3%)

rewrite40.0ms (1%)

series58.0ms (1.4%)

simplify47.0ms (1.1%)

prune162.0ms (3.9%)

localize16.0ms (0.4%)

rewrite43.0ms (1%)

series40.0ms (1%)

simplify38.0ms (0.9%)

prune393.0ms (9.4%)

localize25.0ms (0.6%)

rewrite28.0ms (0.7%)

series81.0ms (2%)

simplify63.0ms (1.5%)

prune337.0ms (8.1%)

localize23.0ms (0.6%)

rewrite29.0ms (0.7%)

series81.0ms (2%)

simplify60.0ms (1.4%)

prune317.0ms (7.6%)

regimes259.0ms (6.2%)

bsearch0.0ms (0%)

simplify1.0ms (0%)

end0.0ms (0%)

sample1.1s (27.5%)

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