Details

analyze3.0ms

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

sample25.0ms

Algorithm

intervals

Results

6.0ms	188×	body	80	valid
4.0ms	256×	pre	80	true
4.0ms	24×	body	1280	valid
3.0ms	26×	body	640	valid
1.0ms	8×	body	320	valid
1.0ms	10×	body	160	valid

simplify221.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (218.0ms)

Iter	Nodes	Cost
0	5017	13

prune4.0ms

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: 15.7b

Counts

2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2))
2.2b	(+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2)) 1)

rewrite36.0ms

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:

15.0ms	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2))
18.0ms	(+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2)) 1)

series21.0ms

Counts

2 → 6

Calls

2 calls:

8.0ms	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2))
13.0ms	(+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2)) 1)

simplify57.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	6347	994

prune79.0ms

Filtered

48 candidates to 71 candidates (-47.9%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	57	14	71
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	58	14	72

Merged error: 15.2b

Counts

72 → 14

localize11.0ms

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))
2.2b	(-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)

rewrite67.0ms

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:

31.0ms	(-.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)

series38.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(-.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2)) (-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1))
7.0ms	(/.f64 alpha (+.f64 (+.f64 beta alpha) 2))
7.0ms	(/.f64 beta (+.f64 (+.f64 alpha beta) 2))
12.0ms	(-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)

simplify52.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	4921	1727
1	4921	1727

prune119.0ms

Filtered

87 candidates to 124 candidates (-42.5%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	116	8	124
Fresh	12	1	13
Picked	1	0	1
Done	0	0	0
Total	129	9	138

Merged error: 1.9b

Counts

138 → 9

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(/.f64 alpha (+.f64 (+.f64 beta alpha) 2))
0.0b	(/.f64 1 (+.f64 (+.f64 alpha beta) 2))
0.1b	(*.f64 beta (/.f64 1 (+.f64 (+.f64 alpha beta) 2)))
2.2b	(-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

94×	`*-un-lft-identity_binary64`
52×	`add-sqr-sqrt_binary64`
50×	`times-frac_binary64`
34×	`add-cube-cbrt_binary64`
33×	`distribute-lft-out_binary64`
21×	`associate-r_binary64`
19×	`add-exp-log_binary64`
13×	`add-cbrt-cube_binary64`
10×	`associate-/r*_binary64`
7×	`pow1_binary64`
6×	`add-log-exp_binary64` `associate-/r/_binary64` `associate-/l*_binary64`
5×	`div-exp_binary64`
4×	`prod-exp_binary64` `difference-of-squares_binary64`
3×	`flip3-+_binary64` `cbrt-undiv_binary64` `associate-l_binary64` `unswap-sqr_binary64` `div-inv_binary64` `flip-+_binary64`
2×	`cbrt-unprod_binary64` `1-exp_binary64` `difference-of-sqr-1_binary64` `clear-num_binary64` `frac-2neg_binary64` `rec-exp_binary64`
1×	`pow-prod-down_binary64` `sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `associate-r/_binary64` `inv-pow_binary64` `un-div-inv_binary64` `distribute-lft-out--_binary64` `flip--_binary64` `pow-flip_binary64` `-commutative_binary64`

Counts

4 → 140

Calls

4 calls:

8.0ms	(/.f64 alpha (+.f64 (+.f64 beta alpha) 2))
8.0ms	(/.f64 1 (+.f64 (+.f64 alpha beta) 2))
13.0ms	(*.f64 beta (/.f64 1 (+.f64 (+.f64 alpha beta) 2)))
14.0ms	(-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)

series34.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(/.f64 alpha (+.f64 (+.f64 beta alpha) 2))
5.0ms	(/.f64 1 (+.f64 (+.f64 alpha beta) 2))
7.0ms	(*.f64 beta (/.f64 1 (+.f64 (+.f64 alpha beta) 2)))
15.0ms	(-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)

simplify58.0ms

Algorithm

egg-herbie

Counts

152 → 152

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4912	1507
1	4912	1507

prune91.0ms

Filtered

89 candidates to 152 candidates (-70.8%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	151	1	152
Fresh	2	6	8
Picked	0	1	1
Done	0	0	0
Total	153	8	161

Merged error: 1.9b

Counts

161 → 8

localize19.0ms

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))
2.2b	(-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)

rewrite36.0ms

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

series64.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(cbrt.f64 (+.f64 (+.f64 alpha beta) 2))
17.0ms	(cbrt.f64 (+.f64 (+.f64 alpha beta) 2))
18.0ms	(cbrt.f64 (+.f64 (+.f64 alpha beta) 2))
12.0ms	(-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)

simplify63.0ms

Algorithm

egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4936	923
1	4936	923

prune76.0ms

Filtered

60 candidates to 75 candidates (-25.0%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	72	3	75
Fresh	2	4	6
Picked	1	0	1
Done	1	0	1
Total	76	7	83

Merged error: 1.9b

Counts

83 → 7

regimes93.0ms

Accuracy

76.4% (3.2b remaining)

Error of 6.4b against oracle of 3.2b and baseline of 16.8b

bsearch14.0ms

Steps

Iters	Range		Point
8	6882.889737396431	95459522.3875408	72043923.58267654

simplify7.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (6.0ms)

Iter	Nodes	Cost
0	236	44
1	236	44

end0.0ms

sample736.0ms

Algorithm

intervals

Results

185.0ms	5769×	body	80	valid
136.0ms	850×	body	1280	valid
130.0ms	8000×	pre	80	true
96.0ms	778×	body	640	valid
37.0ms	402×	body	320	valid
12.0ms	201×	body	160	valid

Details

analyze3.0ms

sample25.0ms

simplify221.0ms

prune4.0ms

localize8.0ms

rewrite36.0ms

series21.0ms

simplify57.0ms

prune79.0ms

localize11.0ms

rewrite67.0ms

series38.0ms

simplify52.0ms

prune119.0ms

localize13.0ms

rewrite49.0ms

series34.0ms

simplify58.0ms

prune91.0ms

localize19.0ms

rewrite36.0ms

series64.0ms

simplify63.0ms

prune76.0ms

regimes93.0ms

bsearch14.0ms

simplify7.0ms

end0.0ms

sample736.0ms

Profiling