Details

analyze2.0ms

Algorithm

Search

True	Other	False	Iter
0%	56.2%	43.8%	0
0%	56.2%	43.8%	1
28.1%	28.1%	43.8%	2
56.2%	0%	43.8%	3

sample30.0ms

Algorithm

intervals

Results

5.0ms	177×	body	80	valid
5.0ms	16×	body	320	valid
5.0ms	256×	pre	80	true
4.0ms	26×	body	1280	valid
4.0ms	32×	body	640	valid
0.0ms	5×	body	160	valid

simplify306.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (296.0ms)

Iter	Nodes	Cost
0	5019	19

prune3.0ms

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: 18.9b

Counts

2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2))
1.8b	(+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2)) 1)

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

58×	`*-un-lft-identity_binary64`
26×	`add-sqr-sqrt_binary64`
25×	`times-frac_binary64`
19×	`distribute-lft-out_binary64`
14×	`add-cube-cbrt_binary64`
6×	`difference-of-squares_binary64` `distribute-lft-out--_binary64`
5×	`associate-/r_binary64` `associate-/l_binary64`
4×	`add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
2×	`flip3-+_binary64` `associate-/l/_binary64` `pow1_binary64` `associate-/r/_binary64` `div-sub_binary64` `flip-+_binary64`
1×	`flip3--_binary64` `cbrt-undiv_binary64` `associate-+l-_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `+-commutative_binary64` `flip--_binary64` `sum-log_binary64`

Counts

2 → 65

Calls

2 calls:

10.0ms	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2))
18.0ms	(+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2)) 1)

series72.0ms

Counts

2 → 6

Calls

2 calls:

27.0ms	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2))
45.0ms	(+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2)) 1)

simplify83.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	6089	1488

prune77.0ms

Filtered

48 candidates to 71 candidates (-47.9%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	59	12	71
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	60	12	72

Merged error: 18.0b

Counts

72 → 12

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2)) (-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1))
0.0b	(/.f64 alpha (+.f64 (+.f64 beta alpha) 2))
0.0b	(/.f64 beta (+.f64 (+.f64 alpha beta) 2))
1.8b	(-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)

rewrite68.0ms

Algorithm

rewrite-expression-head

Rules

73×	`*-un-lft-identity_binary64`
40×	`add-sqr-sqrt_binary64`
34×	`times-frac_binary64`
24×	`distribute-lft-out_binary64` `add-cube-cbrt_binary64`
11×	`add-log-exp_binary64`
10×	`associate-/r*_binary64`
8×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
6×	`difference-of-squares_binary64` `associate-/l*_binary64`
4×	`pow1_binary64` `diff-log_binary64` `associate-/r/_binary64` `distribute-lft-out--_binary64`
3×	`sub-neg_binary64` `flip3--_binary64` `flip--_binary64`
2×	`flip3-+_binary64` `cbrt-undiv_binary64` `difference-of-sqr-1_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `flip-+_binary64` `frac-sub_binary64`
1×	`associate--r+_binary64` `associate--r-_binary64`

Counts

4 → 112

Calls

4 calls:

34.0ms	(-.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2)) (-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1))
8.0ms	(/.f64 alpha (+.f64 (+.f64 beta alpha) 2))
8.0ms	(/.f64 beta (+.f64 (+.f64 alpha beta) 2))
14.0ms	(-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)

series149.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(-.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2)) (-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1))
27.0ms	(/.f64 alpha (+.f64 (+.f64 beta alpha) 2))
26.0ms	(/.f64 beta (+.f64 (+.f64 alpha beta) 2))
52.0ms	(-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)

simplify104.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 0 (74.0ms)

Iter	Nodes	Cost
0	4942	2582
1	4942	2582

prune138.0ms

Filtered

86 candidates to 124 candidates (-44.2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	117	7	124
Fresh	10	1	11
Picked	1	0	1
Done	0	0	0
Total	128	8	136

Merged error: 3.8b

Counts

136 → 8

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (+.f64 (+.f64 alpha beta) 2) beta)
0.0b	(/.f64 alpha (+.f64 (+.f64 beta alpha) 2))
0.4b	(/.f64 1 (/.f64 (+.f64 (+.f64 alpha beta) 2) beta))
1.8b	(-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

184×	`*-un-lft-identity_binary64`
150×	`times-frac_binary64`
91×	`add-sqr-sqrt_binary64`
80×	`add-cube-cbrt_binary64`
60×	`distribute-lft-out_binary64`
27×	`associate-/r*_binary64`
19×	`add-exp-log_binary64`
13×	`add-cbrt-cube_binary64`
11×	`associate-/l*_binary64`
9×	`div-exp_binary64`
7×	`div-inv_binary64`
6×	`add-log-exp_binary64`
5×	`pow1_binary64` `cbrt-undiv_binary64`
4×	`difference-of-squares_binary64`
3×	`associate-/r/_binary64` `clear-num_binary64` `frac-2neg_binary64`
2×	`flip3-+_binary64` `associate-/l/_binary64` `1-exp_binary64` `difference-of-sqr-1_binary64` `rec-exp_binary64` `flip-+_binary64`
1×	`sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `inv-pow_binary64` `distribute-lft-out--_binary64` `flip--_binary64` `pow-flip_binary64`

Counts

4 → 192

Calls

4 calls:

9.0ms	(/.f64 (+.f64 (+.f64 alpha beta) 2) beta)
8.0ms	(/.f64 alpha (+.f64 (+.f64 beta alpha) 2))
11.0ms	(/.f64 1 (/.f64 (+.f64 (+.f64 alpha beta) 2) beta))
14.0ms	(-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)

series132.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(/.f64 (+.f64 (+.f64 alpha beta) 2) beta)
26.0ms	(/.f64 alpha (+.f64 (+.f64 beta alpha) 2))
35.0ms	(/.f64 1 (/.f64 (+.f64 (+.f64 alpha beta) 2) beta))
53.0ms	(-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)

simplify121.0ms

Algorithm

egg-herbie

Counts

204 → 204

Iterations

Useful iterations: 0 (76.0ms)

Iter	Nodes	Cost
0	4940	3825
1	4940	3825

prune172.0ms

Filtered

111 candidates to 204 candidates (-83.8%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	198	6	204
Fresh	2	5	7
Picked	1	0	1
Done	0	0	0
Total	201	11	212

Merged error: 3.8b

Counts

212 → 11

localize20.0ms

Local error

Found 4 expressions with local error:

0.7b	(cbrt.f64 (+.f64 (+.f64 alpha beta) 2))
0.7b	(cbrt.f64 (+.f64 (+.f64 alpha beta) 2))
0.7b	(cbrt.f64 (+.f64 (+.f64 alpha beta) 2))
1.8b	(-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

26×	`*-un-lft-identity_binary64`
18×	`add-sqr-sqrt_binary64`
15×	`cbrt-prod_binary64`
9×	`distribute-lft-out_binary64`
7×	`add-cube-cbrt_binary64`
6×	`cbrt-div_binary64` `add-log-exp_binary64`
4×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `difference-of-squares_binary64`
3×	`flip3-+_binary64` `pow1/3_binary64` `times-frac_binary64` `flip-+_binary64`
2×	`difference-of-sqr-1_binary64`
1×	`sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `distribute-lft-out--_binary64` `flip--_binary64`

Counts

4 → 63

Calls

4 calls:

6.0ms	(cbrt.f64 (+.f64 (+.f64 alpha beta) 2))
6.0ms	(cbrt.f64 (+.f64 (+.f64 alpha beta) 2))
6.0ms	(cbrt.f64 (+.f64 (+.f64 alpha beta) 2))
14.0ms	(-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)

series265.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(cbrt.f64 (+.f64 (+.f64 alpha beta) 2))
68.0ms	(cbrt.f64 (+.f64 (+.f64 alpha beta) 2))
75.0ms	(cbrt.f64 (+.f64 (+.f64 alpha beta) 2))
51.0ms	(-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)

simplify98.0ms

Algorithm

egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 0 (76.0ms)

Iter	Nodes	Cost
0	4905	1406
1	4905	1406

prune121.0ms

Filtered

60 candidates to 75 candidates (-25.0%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	71	4	75
Fresh	6	4	10
Picked	1	0	1
Done	0	0	0
Total	78	8	86

Merged error: 3.8b

Counts

86 → 8

regimes68.0ms

Accuracy

71.4% (3.9b remaining)

Error of 6.8b against oracle of 2.9b and baseline of 16.5b

bsearch27.0ms

Steps

Iters	Range		Point
9	131102036.62409312	1.8469906680894886e+17	104449142829.8675

simplify7.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	238	117
1	238	117

end0.0ms

sample717.0ms

Algorithm

intervals

Results

185.0ms	5866×	body	80	valid
129.0ms	8000×	pre	80	true
128.0ms	845×	body	1280	valid
87.0ms	714×	body	640	valid
36.0ms	380×	body	320	valid
12.0ms	195×	body	160	valid

Details

analyze2.0ms

sample30.0ms

simplify306.0ms

prune3.0ms

localize8.0ms

rewrite31.0ms

series72.0ms

simplify83.0ms

prune77.0ms

localize12.0ms

rewrite68.0ms

series149.0ms

simplify104.0ms

prune138.0ms

localize13.0ms

rewrite50.0ms

series132.0ms

simplify121.0ms

prune172.0ms

localize20.0ms

rewrite33.0ms

series265.0ms

simplify98.0ms

prune121.0ms

regimes68.0ms

bsearch27.0ms

simplify7.0ms

end0.0ms

sample717.0ms

Profiling