Details

analyze140.0ms

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%	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

sample25.0ms

Algorithm

intervals

Results

17.0ms

256×

body

valid

simplify83.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (81.0ms)

Iter	Nodes	Cost
0	4906	31
1	4906	31

prune6.0ms

Filtered

1 candidates to 1 candidates (0.0%)

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

localize20.0ms

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)
0.3b	(* (* b b) (- 1.0 (* 3.0 a)))

rewrite35.0ms

Algorithm

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:

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

series47.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))
5.0ms	(* (* a a) (+ 1.0 a))
21.0ms	(pow (+ (* a a) (* b b)) 2.0)
7.0ms	(* (* b b) (- 1.0 (* 3.0 a)))

simplify49.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	4997	1432
1	4997	1432

prune193.0ms

Filtered

73 candidates to 102 candidates (-39.7%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	98	4	102
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	98	5	103

Merged error: 0.1b

Counts

103 → 5

localize23.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (cbrt (pow (+ (* b b) (* a a)) 2.0)) (cbrt (pow (+ (* b b) (* a a)) 2.0)))
20.4b	(cbrt (pow (+ (* b b) (* a a)) 2.0))
20.4b	(cbrt (pow (+ (* b b) (* a a)) 2.0))
20.4b	(cbrt (pow (+ (* b b) (* a a)) 2.0))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

73×	`cbrt-prod`
46×	`add-sqr-sqrt`
29×	`unpow-prod-down`
22×	`add-cube-cbrt` `*-un-lft-identity`
16×	`unswap-sqr`
15×	`sqr-pow`
11×	`pow1`
10×	`swap-sqr` `associate-r` `associate-l`
9×	`pow1/3`
6×	`add-exp-log`
4×	`add-cbrt-cube` `add-log-exp`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 109

Calls

4 calls:

14.0ms	(* (cbrt (pow (+ (* b b) (* a a)) 2.0)) (cbrt (pow (+ (* b b) (* a a)) 2.0)))
5.0ms	(cbrt (pow (+ (* b b) (* a a)) 2.0))
7.0ms	(cbrt (pow (+ (* b b) (* a a)) 2.0))
5.0ms	(cbrt (pow (+ (* b b) (* a a)) 2.0))

series137.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify63.0ms

Algorithm

egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5048	2354

prune364.0ms

Filtered

89 candidates to 121 candidates (-36.0%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	115	6	121
Fresh	0	3	3
Picked	0	1	1
Done	1	0	1
Total	116	10	126

Merged error: 0.0b

Counts

126 → 10

localize30.0ms

Local error

Found 4 expressions with local error:

9.3b	(cbrt (pow (sqrt (+ (* b b) (* a a))) 2.0))
9.3b	(cbrt (pow (sqrt (+ (* b b) (* a a))) 2.0))
20.4b	(cbrt (pow (+ (* b b) (* a a)) 2.0))
20.4b	(cbrt (pow (+ (* b b) (* a a)) 2.0))

rewrite24.0ms

Algorithm

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))
7.0ms	(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))

series135.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify63.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4832	1262
1	4832	1262

prune294.0ms

Filtered

62 candidates to 78 candidates (-25.8%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	75	3	78
Fresh	1	7	8
Picked	0	1	1
Done	0	1	1
Total	76	12	88

Merged error: 0.0b

Counts

88 → 12

localize38.0ms

Local error

Found 4 expressions with local error:

8.7b	(sqrt (+ (* b b) (* a a)))
9.3b	(cbrt (pow (sqrt (+ (* b b) (* a a))) 2.0))
20.4b	(cbrt (pow (+ (* b b) (* a a)) 2.0))
20.4b	(cbrt (pow (+ (* b b) (* a a)) 2.0))

rewrite21.0ms

Algorithm

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:

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

series109.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(sqrt (+ (* b b) (* a a)))
33.0ms	(cbrt (pow (sqrt (+ (* b b) (* a a))) 2.0))
33.0ms	(cbrt (pow (+ (* b b) (* a a)) 2.0))
37.0ms	(cbrt (pow (+ (* b b) (* a a)) 2.0))

simplify56.0ms

Algorithm

egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5677	1069

prune264.0ms

Filtered

61 candidates to 75 candidates (-23.0%)

Pruning

12 alts after pruning (9 fresh and 3 done)

	Pruned	Kept	Total
New	75	0	75
Fresh	0	9	9
Picked	0	1	1
Done	0	2	2
Total	75	12	87

Merged error: 0.0b

Counts

87 → 12

regimes281.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 0.5b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	69	67
1	69	67

end0.0ms

sample680.0ms

Algorithm

intervals

Results

544.0ms	8000×	body	80	valid
0.0ms	5×	body	80	invalid

Details

analyze140.0ms

sample25.0ms

simplify83.0ms

prune6.0ms

localize20.0ms

rewrite35.0ms

series47.0ms

simplify49.0ms

prune193.0ms

localize23.0ms

rewrite35.0ms

series137.0ms

simplify63.0ms

prune364.0ms

localize30.0ms

rewrite24.0ms

series135.0ms

simplify63.0ms

prune294.0ms

localize38.0ms

rewrite21.0ms

series109.0ms

simplify56.0ms

prune264.0ms

regimes281.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample680.0ms

Profiling