Details

analyze129.0ms

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

sample26.0ms

Algorithm

intervals

Results

19.0ms

256×

body

valid

simplify67.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	5054	29

prune9.0ms

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	(+ (pow (+ (* a a) (* b b)) 2.0) (* 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)
0.3b	(* (* b b) (+ 3.0 a))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

15×	`pow1` `add-exp-log`
14×	`add-cbrt-cube`
12×	`add-sqr-sqrt` `*-un-lft-identity`
9×	`associate-r`
8×	`add-cube-cbrt`
6×	`pow-prod-down` `prod-exp` `cbrt-unprod` `add-log-exp`
4×	`associate-*r/`
3×	`distribute-rgt-in` `unpow-prod-down` `pow-unpow` `distribute-lft-in`
2×	`sub-neg` `associate-+r+` `flip3-+` `associate-l` `*-commutative` `flip-+` `unswap-sqr`
1×	`+-commutative` `pow-to-exp` `flip3--` `pow-pow` `pow-exp` `sum-log` `flip--` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares` `sqr-pow`

Counts

4 → 79

Calls

4 calls:

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

series57.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a)))))
5.0ms	(* (* a a) (- 1.0 a))
23.0ms	(pow (+ (* a a) (* b b)) 2.0)
5.0ms	(* (* b b) (+ 3.0 a))

simplify39.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	5666	1201

prune175.0ms

Filtered

64 candidates to 91 candidates (-42.2%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	86	5	91
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	87	6	93

Merged error: 0.0b

Counts

93 → 6

localize21.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (+ (* b b) (* a a))) (cbrt (+ (* b b) (* a a))))
11.4b	(cbrt (+ (* b b) (* a a)))
11.4b	(cbrt (+ (* b b) (* a a)))
11.4b	(cbrt (+ (* b b) (* a a)))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
18×	`cbrt-div`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`flip3-+` `pow1/3` `flip-+`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l`
4×	`frac-times` `add-cbrt-cube` `add-log-exp` `unswap-sqr`
2×	`associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 87

Calls

4 calls:

11.0ms	(* (cbrt (+ (* b b) (* a a))) (cbrt (+ (* b b) (* a a))))
4.0ms	(cbrt (+ (* b b) (* a a)))
4.0ms	(cbrt (+ (* b b) (* a a)))
4.0ms	(cbrt (+ (* b b) (* a a)))

series82.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(* (cbrt (+ (* b b) (* a a))) (cbrt (+ (* b b) (* a a))))
20.0ms	(cbrt (+ (* b b) (* a a)))
20.0ms	(cbrt (+ (* b b) (* a a)))
20.0ms	(cbrt (+ (* b b) (* a a)))

simplify60.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4872	1309
1	4872	1309

prune179.0ms

Filtered

71 candidates to 99 candidates (-39.4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	98	1	99
Fresh	0	4	4
Picked	1	0	1
Done	0	1	1
Total	99	6	105

Merged error: 0.0b

Counts

105 → 6

localize25.0ms

Local error

Found 4 expressions with local error:

10.8b	(sqrt (+ (* b b) (* a a)))
10.8b	(sqrt (+ (* b b) (* a a)))
11.4b	(cbrt (+ (* b b) (* a a)))
11.4b	(cbrt (+ (* b b) (* a a)))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
8×	`add-cube-cbrt` `*-un-lft-identity`
6×	`pow1` `cbrt-prod` `sqrt-prod`
4×	`add-exp-log` `cbrt-div` `flip3-+` `sqrt-div` `add-cbrt-cube` `flip-+` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow1/3`

Counts

4 → 56

Calls

4 calls:

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

series56.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(sqrt (+ (* b b) (* a a)))
6.0ms	(sqrt (+ (* b b) (* a a)))
20.0ms	(cbrt (+ (* b b) (* a a)))
25.0ms	(cbrt (+ (* b b) (* a a)))

simplify52.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5169	696

prune154.0ms

Filtered

56 candidates to 68 candidates (-21.4%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	68	0	68
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	68	6	74

Merged error: 0.0b

Counts

74 → 6

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* (* b b) (* (* a a) 2)) (pow a 4))
0.0b	(+ (pow b 4) (+ (* (* b b) (* (* a a) 2)) (pow a 4)))
0.0b	(* (* a a) 2)
1.7b	(* (* b b) (* (* a a) 2))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

30×	`pow1` `add-exp-log` `add-cbrt-cube`
18×	`pow-prod-down` `prod-exp` `cbrt-unprod`
11×	`add-log-exp`
7×	`*-un-lft-identity`
6×	`add-sqr-sqrt`
5×	`add-cube-cbrt`
4×	`associate-r` `sum-log`
2×	`+-commutative` `flip3-+` `associate-l` `*-commutative` `flip-+`
1×	`associate-+r+` `distribute-lft-out` `unswap-sqr`

Counts

4 → 72

Calls

4 calls:

11.0ms	(+ (* (* b b) (* (* a a) 2)) (pow a 4))
13.0ms	(+ (pow b 4) (+ (* (* b b) (* (* a a) 2)) (pow a 4)))
5.0ms	(* (* a a) 2)
9.0ms	(* (* b b) (* (* a a) 2))

series37.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(+ (* (* b b) (* (* a a) 2)) (pow a 4))
11.0ms	(+ (pow b 4) (+ (* (* b b) (* (* a a) 2)) (pow a 4)))
3.0ms	(* (* a a) 2)
7.0ms	(* (* b b) (* (* a a) 2))

simplify41.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5557	980

prune110.0ms

Filtered

47 candidates to 84 candidates (-78.7%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	84	0	84
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	84	6	90

Merged error: 0.0b

Counts

90 → 6

regimes254.0ms

Accuracy

0% (0.2b 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	43	29
1	43	29

end0.0ms

sample628.0ms

Algorithm

intervals

Results

501.0ms	8000×	body	80	valid
0.0ms	5×	body	80	invalid

Details

analyze129.0ms

sample26.0ms

simplify67.0ms

prune9.0ms

localize15.0ms

rewrite30.0ms

series57.0ms

simplify39.0ms

prune175.0ms

localize21.0ms

rewrite26.0ms

series82.0ms

simplify60.0ms

prune179.0ms

localize25.0ms

rewrite19.0ms

series56.0ms

simplify52.0ms

prune154.0ms

localize12.0ms

rewrite41.0ms

series37.0ms

simplify41.0ms

prune110.0ms

regimes254.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample628.0ms

Profiling