Details

analyze135.0ms (3.9%)

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%	53.1%	22%	7
25%	46.8%	28.2%	8
25%	33.6%	41.5%	9
28.1%	18%	54%	10
31.6%	12.1%	56.3%	11
33.4%	5.9%	60.8%	12
35.2%	3.8%	61%	13
36.1%	2.9%	61%	14

sample25.0ms (0.7%)

Algorithm

1×

intervals

Results

16.0ms

256×

body

valid

simplify72.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (70.0ms)

Iter	Nodes	Cost
0	5054	29

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

localize17.0ms (0.5%)

Local error

Found 4 expressions with local error:

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

rewrite38.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`associate-*r/`
17×	`pow1` `add-exp-log`
16×	`add-sqr-sqrt` `add-cbrt-cube`
14×	`*-un-lft-identity`
12×	`associate-r`
10×	`add-cube-cbrt`
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` `distribute-lft-out--` `difference-of-squares` `sqr-pow`

Counts

4 → 92

Calls

4 calls:

12.0ms	(* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))
10.0ms	(* (* b b) (+ 3.0 a))
8.0ms	(* (* a a) (- 1.0 a))
5.0ms	(pow (+ (* a a) (* b b)) 2.0)

series45.0ms (1.3%)

Counts

4 → 12

Calls

4 calls:

21.0ms	(pow (+ (* a a) (* b b)) 2.0)
12.0ms	(* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))
6.0ms	(* (* a a) (- 1.0 a))
6.0ms	(* (* b b) (+ 3.0 a))

simplify60.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4950	1310
1	4950	1310

prune237.0ms (6.9%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	99	5	104
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	99	6	105

Merged error: 0.1b

Counts

105 → 6

localize23.0ms (0.7%)

Local error

Found 4 expressions with local error:

0.6b	(* (* b b) (+ 3.0 a))
21.6b	(cbrt (pow (+ (* b b) (* a a)) 2.0))
21.6b	(cbrt (pow (+ (* b b) (* a a)) 2.0))
21.6b	(cbrt (pow (+ (* b b) (* a a)) 2.0))

rewrite23.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 69

Calls

4 calls:

7.0ms	(* (* b b) (+ 3.0 a))
4.0ms	(cbrt (pow (+ (* b b) (* a a)) 2.0))
4.0ms	(cbrt (pow (+ (* b b) (* a a)) 2.0))
4.0ms	(cbrt (pow (+ (* b b) (* a a)) 2.0))

series108.0ms (3.2%)

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 (+ (* b b) (* a a)) 2.0))
5.0ms	(* (* b b) (+ 3.0 a))

simplify57.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4918	1043
1	4918	1043

prune320.0ms (9.4%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	77	4	81
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	77	10	87

Merged error: 0.0b

Counts

87 → 10

localize35.0ms (1%)

Local error

Found 4 expressions with local error:

11.1b	(cbrt (+ (* b b) (* a a)))
16.2b	(cbrt (pow (* (cbrt (+ (* b b) (* a a))) (cbrt (+ (* b b) (* a a)))) 2.0))
21.6b	(cbrt (pow (+ (* b b) (* a a)) 2.0))
21.6b	(cbrt (pow (+ (* b b) (* a a)) 2.0))

rewrite20.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`cbrt-prod`
10×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
7×	`unpow-prod-down`
4×	`pow1` `add-exp-log` `pow1/3` `add-cbrt-cube` `add-log-exp`
3×	`sqr-pow`
2×	`cbrt-div`
1×	`flip3-+` `flip-+`

Counts

4 → 56

Calls

4 calls:

6.0ms	(cbrt (pow (+ (* b b) (* a a)) 2.0))
4.0ms	(cbrt (pow (+ (* b b) (* a a)) 2.0))
4.0ms	(cbrt (pow (* (cbrt (+ (* b b) (* a a))) (cbrt (+ (* b b) (* a a)))) 2.0))
4.0ms	(cbrt (+ (* b b) (* a a)))

series122.0ms (3.6%)

Counts

4 → 12

Calls

4 calls:

36.0ms	(cbrt (pow (* (cbrt (+ (* b b) (* a a))) (cbrt (+ (* b b) (* a a)))) 2.0))
33.0ms	(cbrt (pow (+ (* b b) (* a a)) 2.0))
33.0ms	(cbrt (pow (+ (* b b) (* a a)) 2.0))
20.0ms	(cbrt (+ (* b b) (* a a)))

simplify41.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	4990	1132
1	4990	1132

prune321.0ms (9.4%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	65	3	68
Fresh	1	6	7
Picked	1	0	1
Done	0	2	2
Total	67	11	78

Merged error: 0.0b

Counts

78 → 11

localize42.0ms (1.2%)

Local error

Found 4 expressions with local error:

11.1b	(cbrt (+ (* b b) (* a a)))
16.2b	(cbrt (pow (* (cbrt (+ (* b b) (* a a))) (cbrt (+ (* b b) (* a a)))) 2.0))
21.6b	(cbrt (pow (+ (* b b) (* a a)) 2.0))
21.6b	(cbrt (pow (+ (* b b) (* a a)) 2.0))

rewrite19.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`cbrt-prod`
10×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
7×	`unpow-prod-down`
4×	`pow1` `add-exp-log` `pow1/3` `add-cbrt-cube` `add-log-exp`
3×	`sqr-pow`
2×	`cbrt-div`
1×	`flip3-+` `flip-+`

Counts

4 → 56

Calls

4 calls:

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

series124.0ms (3.6%)

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))
33.0ms	(cbrt (pow (* (cbrt (+ (* b b) (* a a))) (cbrt (+ (* b b) (* a a)))) 2.0))
22.0ms	(cbrt (+ (* b b) (* a a)))

simplify41.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	4990	1132
1	4990	1132

prune278.0ms (8.1%)

Pruning

12 alts after pruning (9 fresh and 3 done)

	Pruned	Kept	Total
New	65	3	68
Fresh	2	6	8
Picked	0	1	1
Done	0	2	2
Total	67	12	79

Merged error: 0.0b

Counts

79 → 12

regimes552.0ms (16.2%)

Accuracy

Total 0.1b remaining (72.2%)

Threshold costs 0.1b (72.2%)

bsearch0.0ms (0%)

simplify1.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	43	29
1	43	29

end0.0ms (0%)

sample654.0ms (19.1%)

Algorithm

1×

intervals

Results

507.0ms	8000×	body	80	valid
0.0ms	6×	body	80	invalid

Details

analyze135.0ms (3.9%)

sample25.0ms (0.7%)

simplify72.0ms (2.1%)

prune7.0ms (0.2%)

localize17.0ms (0.5%)

rewrite38.0ms (1.1%)

series45.0ms (1.3%)

simplify60.0ms (1.8%)

prune237.0ms (6.9%)

localize23.0ms (0.7%)

rewrite23.0ms (0.7%)

series108.0ms (3.2%)

simplify57.0ms (1.7%)

prune320.0ms (9.4%)

localize35.0ms (1%)

rewrite20.0ms (0.6%)

series122.0ms (3.6%)

simplify41.0ms (1.2%)

prune321.0ms (9.4%)

localize42.0ms (1.2%)

rewrite19.0ms (0.5%)

series124.0ms (3.6%)

simplify41.0ms (1.2%)

prune278.0ms (8.1%)

regimes552.0ms (16.2%)

bsearch0.0ms (0%)

simplify1.0ms (0%)

end0.0ms (0%)

sample654.0ms (19.1%)

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