Details

analyze138.0ms (3.7%)

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
25%	74.9%	0.1%	5
25%	68.7%	6.3%	6
25%	56.2%	18.8%	7
25%	48.4%	26.6%	8
25%	35.1%	39.9%	9
28.1%	18.3%	53.6%	10
31.6%	12.3%	56.1%	11
33.4%	5.9%	60.8%	12
35.2%	3.8%	61%	13
36.1%	2.9%	61%	14

sample26.0ms (0.7%)

Algorithm

1×

intervals

Results

17.0ms

256×

body

valid

simplify110.0ms (3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (108.0ms)

Iter	Nodes	Cost
0	4906	31
1	4906	31

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: 0.2b

Counts

2 → 1

localize21.0ms (0.6%)

Local error

Found 4 expressions with local error:

0.0b	(* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))
0.1b	(* (* a a) (+ 1.0 a))
0.3b	(pow (+ (* a a) (* b b)) 2.0)
0.6b	(* (* b b) (- 1.0 (* 3.0 a)))

rewrite35.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`associate-*r/`
17×	`pow1` `add-exp-log`
16×	`add-cbrt-cube`
14×	`add-sqr-sqrt`
12×	`*-un-lft-identity`
10×	`add-cube-cbrt` `associate-r`
7×	`pow-prod-down` `prod-exp` `cbrt-unprod`
5×	`associate-l`
4×	`flip3-+` `frac-add` `flip-+` `add-log-exp`
3×	`distribute-rgt-in` `unpow-prod-down` `pow-unpow` `flip3--` `distribute-lft-in` `*-commutative` `flip--` `unswap-sqr`
2×	`sub-neg`
1×	`pow-to-exp` `pow-pow` `pow-exp` `distribute-lft-out` `sqr-pow`

Counts

4 → 90

Calls

4 calls:

13.0ms	(* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))
8.0ms	(* (* a a) (+ 1.0 a))
7.0ms	(* (* b b) (- 1.0 (* 3.0 a)))
5.0ms	(pow (+ (* a a) (* b b)) 2.0)

series50.0ms (1.4%)

Counts

4 → 12

Calls

4 calls:

21.0ms	(pow (+ (* a a) (* b b)) 2.0)
17.0ms	(* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))
7.0ms	(* (* b b) (- 1.0 (* 3.0 a)))
5.0ms	(* (* a a) (+ 1.0 a))

simplify48.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	4997	1432
1	4997	1432

prune230.0ms (6.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	99	3	102
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	99	4	103

Merged error: 0.1b

Counts

103 → 4

localize21.0ms (0.6%)

Local error

Found 4 expressions with local error:

0.6b	(* (* b b) (- 1.0 (* 3.0 a)))
18.5b	(cbrt (pow (+ (* b b) (* a a)) 2.0))
18.5b	(cbrt (pow (+ (* b b) (* a a)) 2.0))
18.5b	(cbrt (pow (+ (* b b) (* a a)) 2.0))

rewrite23.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`cbrt-prod`
12×	`add-sqr-sqrt`
11×	`add-cube-cbrt` `*-un-lft-identity`
9×	`pow1` `add-exp-log` `unpow-prod-down` `add-cbrt-cube`
4×	`add-log-exp`
3×	`pow1/3` `associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod` `sqr-pow`
2×	`sub-neg` `associate-*r/`
1×	`distribute-rgt-in` `flip3--` `distribute-lft-in` `associate-l` `*-commutative` `flip--` `unswap-sqr`

Counts

4 → 68

Calls

4 calls:

7.0ms	(* (* b b) (- 1.0 (* 3.0 a)))
5.0ms	(cbrt (pow (+ (* b b) (* a a)) 2.0))
5.0ms	(cbrt (pow (+ (* b b) (* a a)) 2.0))
5.0ms	(cbrt (pow (+ (* b b) (* a a)) 2.0))

series110.0ms (3%)

Counts

4 → 12

Calls

4 calls:

35.0ms	(cbrt (pow (+ (* b b) (* a a)) 2.0))
34.0ms	(cbrt (pow (+ (* b b) (* a a)) 2.0))
34.0ms	(cbrt (pow (+ (* b b) (* a a)) 2.0))
7.0ms	(* (* b b) (- 1.0 (* 3.0 a)))

simplify43.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	4988	1098
1	4988	1098

prune316.0ms (8.5%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	76	4	80
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	76	8	84

Merged error: 0.1b

Counts

84 → 8

localize29.0ms (0.8%)

Local error

Found 4 expressions with local error:

8.4b	(cbrt (pow (sqrt (+ (* b b) (* a a))) 2.0))
8.4b	(cbrt (pow (sqrt (+ (* b b) (* a a))) 2.0))
18.5b	(cbrt (pow (+ (* b b) (* a a)) 2.0))
18.5b	(cbrt (pow (+ (* b b) (* a a)) 2.0))

rewrite23.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

34×	`cbrt-prod`
18×	`unpow-prod-down`
14×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`sqrt-prod`
4×	`pow1` `add-exp-log` `pow1/3` `add-cbrt-cube` `add-log-exp` `sqr-pow`

Counts

4 → 66

Calls

4 calls:

5.0ms	(cbrt (pow (sqrt (+ (* b b) (* a a))) 2.0))
5.0ms	(cbrt (pow (sqrt (+ (* b b) (* a a))) 2.0))
5.0ms	(cbrt (pow (+ (* b b) (* a a)) 2.0))
5.0ms	(cbrt (pow (+ (* b b) (* a a)) 2.0))

series139.0ms (3.7%)

Counts

4 → 12

Calls

4 calls:

36.0ms	(cbrt (pow (+ (* b b) (* a a)) 2.0))
35.0ms	(cbrt (pow (sqrt (+ (* b b) (* a a))) 2.0))
34.0ms	(cbrt (pow (+ (* b b) (* a a)) 2.0))
33.0ms	(cbrt (pow (sqrt (+ (* b b) (* a a))) 2.0))

simplify61.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4832	1262
1	4832	1262

prune371.0ms (10%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	75	3	78
Fresh	1	4	5
Picked	0	1	1
Done	0	2	2
Total	76	10	86

Merged error: 0.0b

Counts

86 → 10

localize38.0ms (1%)

Local error

Found 4 expressions with local error:

7.9b	(sqrt (+ (* b b) (* a a)))
8.4b	(cbrt (pow (sqrt (+ (* b b) (* a a))) 2.0))
18.5b	(cbrt (pow (+ (* b b) (* a a)) 2.0))
18.5b	(cbrt (pow (+ (* b b) (* a a)) 2.0))

rewrite20.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`cbrt-prod`
13×	`add-sqr-sqrt`
12×	`add-cube-cbrt` `unpow-prod-down` `*-un-lft-identity`
6×	`sqrt-prod`
5×	`pow1`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`pow1/3` `sqr-pow`
2×	`sqrt-div`
1×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`

Counts

4 → 63

Calls

4 calls:

5.0ms	(cbrt (pow (sqrt (+ (* b b) (* a a))) 2.0))
5.0ms	(cbrt (pow (+ (* b b) (* a a)) 2.0))
4.0ms	(cbrt (pow (+ (* b b) (* a a)) 2.0))
4.0ms	(sqrt (+ (* b b) (* a a)))

series107.0ms (2.9%)

Counts

4 → 12

Calls

4 calls:

36.0ms	(cbrt (pow (+ (* b b) (* a a)) 2.0))
33.0ms	(cbrt (pow (+ (* b b) (* a a)) 2.0))
33.0ms	(cbrt (pow (sqrt (+ (* b b) (* a a))) 2.0))
6.0ms	(sqrt (+ (* b b) (* a a)))

simplify52.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5677	1069

prune369.0ms (9.9%)

Pruning

14 alts after pruning (11 fresh and 3 done)

	Pruned	Kept	Total
New	69	6	75
Fresh	1	5	6
Picked	0	1	1
Done	1	2	3
Total	71	14	85

Merged error: 0.0b

Counts

85 → 14

regimes627.0ms (16.9%)

Accuracy

Total 0.1b remaining (62.5%)

Threshold costs 0.1b (62.5%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	61	31
1	61	31

end0.0ms (0%)

sample693.0ms (18.7%)

Algorithm

1×

intervals

Results

548.0ms	8000×	body	80	valid
0.0ms	5×	body	80	invalid

Details

analyze138.0ms (3.7%)

sample26.0ms (0.7%)

simplify110.0ms (3%)

prune7.0ms (0.2%)

localize21.0ms (0.6%)

rewrite35.0ms (1%)

series50.0ms (1.4%)

simplify48.0ms (1.3%)

prune230.0ms (6.2%)

localize21.0ms (0.6%)

rewrite23.0ms (0.6%)

series110.0ms (3%)

simplify43.0ms (1.1%)

prune316.0ms (8.5%)

localize29.0ms (0.8%)

rewrite23.0ms (0.6%)

series139.0ms (3.7%)

simplify61.0ms (1.7%)

prune371.0ms (10%)

localize38.0ms (1%)

rewrite20.0ms (0.5%)

series107.0ms (2.9%)

simplify52.0ms (1.4%)

prune369.0ms (9.9%)

regimes627.0ms (16.9%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample693.0ms (18.7%)

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