Details

analyze127.0ms

Algorithm

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

Algorithm

intervals

Results

16.0ms

256×

body

valid

simplify54.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4954	29
1	4954	29

prune11.0ms

Filtered

1 candidates to 1 candidates (0.0%)

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 → 2

localize15.0ms

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)
1.1b	(* (* b b) (+ 3.0 a))

rewrite39.0ms

Algorithm

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:

13.0ms	(* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))
8.0ms	(* (* a a) (- 1.0 a))
5.0ms	(pow (+ (* a a) (* b b)) 2.0)
10.0ms	(* (* b b) (+ 3.0 a))

series44.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))
5.0ms	(* (* a a) (- 1.0 a))
21.0ms	(pow (+ (* a a) (* b b)) 2.0)
5.0ms	(* (* b b) (+ 3.0 a))

simplify50.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	4951	1320
1	4951	1320

prune197.0ms

Filtered

74 candidates to 104 candidates (-40.5%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	99	5	104
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	100	6	106

Merged error: 0.1b

Counts

106 → 6

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(* b (+ a 3.0))
0.1b	(* a (* a (- 1.0 a)))
0.2b	(* b (* b (+ a 3.0)))
0.3b	(pow (+ (* a a) (* b b)) 2.0)

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 88

Calls

4 calls:

6.0ms	(* b (+ a 3.0))
7.0ms	(* a (* a (- 1.0 a)))
9.0ms	(* b (* b (+ a 3.0)))
5.0ms	(pow (+ (* a a) (* b b)) 2.0)

series36.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify28.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 0 (20.0ms)

Iter	Nodes	Cost
0	5263	852

prune142.0ms

Filtered

59 candidates to 100 candidates (-69.5%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	100	0	100
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	100	6	106

Merged error: 0.1b

Counts

106 → 6

localize20.0ms

Local error

Found 4 expressions with local error:

1.1b	(* (* b b) (+ 3.0 a))
20.9b	(cbrt (pow (+ (* b b) (* a a)) 2.0))
20.9b	(cbrt (pow (+ (* b b) (* a a)) 2.0))
20.9b	(cbrt (pow (+ (* b b) (* a a)) 2.0))

rewrite26.0ms

Algorithm

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:

10.0ms	(* (* b b) (+ 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))

series106.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(* (* b b) (+ 3.0 a))
34.0ms	(cbrt (pow (+ (* b b) (* a a)) 2.0))
34.0ms	(cbrt (pow (+ (* b b) (* a a)) 2.0))
33.0ms	(cbrt (pow (+ (* b b) (* a a)) 2.0))

simplify51.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5063	1043

prune235.0ms

Filtered

61 candidates to 81 candidates (-32.8%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	79	2	81
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	79	8	87

Merged error: 0.0b

Counts

87 → 8

localize35.0ms

Local error

Found 4 expressions with local error:

9.6b	(cbrt (+ (* b b) (* a a)))
15.4b	(cbrt (pow (* (cbrt (+ (* b b) (* a a))) (cbrt (+ (* b b) (* a a)))) 2.0))
20.9b	(cbrt (pow (+ (* b b) (* a a)) 2.0))
20.9b	(cbrt (pow (+ (* b b) (* a a)) 2.0))

rewrite19.0ms

Algorithm

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:

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

series123.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(cbrt (+ (* b b) (* a a)))
34.0ms	(cbrt (pow (* (cbrt (+ (* b b) (* a a))) (cbrt (+ (* 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))

simplify63.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	5694	1121

prune215.0ms

Filtered

54 candidates to 68 candidates (-25.9%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	65	3	68
Fresh	0	5	5
Picked	1	0	1
Done	0	2	2
Total	66	10	76

Merged error: 0.0b

Counts

76 → 10

regimes301.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	102	29
1	102	29

end0.0ms

sample680.0ms

Algorithm

intervals

Results

524.0ms	8000×	body	80	valid
0.0ms	5×	body	80	invalid

Details

analyze127.0ms

sample25.0ms

simplify54.0ms

prune11.0ms

localize15.0ms

rewrite39.0ms

series44.0ms

simplify50.0ms

prune197.0ms

localize17.0ms

rewrite30.0ms

series36.0ms

simplify28.0ms

prune142.0ms

localize20.0ms

rewrite26.0ms

series106.0ms

simplify51.0ms

prune235.0ms

localize35.0ms

rewrite19.0ms

series123.0ms

simplify63.0ms

prune215.0ms

regimes301.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample680.0ms

Profiling