Details

analyze1.7s

Algorithm

Search

True	Other	False	Iter
0%	49.9%	50.1%	0
0%	49.9%	50.1%	1
0%	49.9%	50.1%	2
0%	49.9%	50.1%	3
0%	49.9%	50.1%	4
0%	49.9%	50.1%	5
0%	49.9%	50.1%	6
0%	49.9%	50.1%	7
0%	49.9%	50.1%	8
0.4%	49.5%	50.1%	9
0.4%	49.3%	50.3%	10
0.6%	48.9%	50.5%	11
1.1%	48.1%	50.9%	12
1.5%	47.3%	51.2%	13
1.7%	46.9%	51.5%	14

sample218.0ms

Algorithm

intervals

Results

100.0ms	84×	body	2560	valid
68.0ms	118×	body	1280	valid
9.0ms	26×	body	640	valid
7.0ms	19×	body	1280	overflowed
6.0ms	297×	pre	80	true
2.0ms	8×	body	320	valid
2.0ms	1×	body	2560	invalid
2.0ms	6×	body	640	overflowed
1.0ms	2×	body	2560	overflowed
1.0ms	15×	body	80	valid
1.0ms	5×	body	320	overflowed
1.0ms	5×	body	160	valid
0.0ms	3×	body	160	overflowed
0.0ms	5×	body	80	overflowed

simplify31.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (22.0ms)

Iter	Nodes	Cost
0	5982	37

prune9.0ms

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: 60.1b

Counts

2 → 1

localize27.0ms

Local error

Found 4 expressions with local error:

0.5b	(.f64 (-.f64 (exp.f64 (.f64 a eps)) 1) (-.f64 (exp.f64 (*.f64 b eps)) 1))
2.3b	(-.f64 (exp.f64 (*.f64 a eps)) 1)
2.5b	(-.f64 (exp.f64 (*.f64 b eps)) 1)
3.1b	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt_binary64_559`
21×	`*-un-lft-identity_binary64_574`
10×	`difference-of-squares_binary64_603` `add-log-exp_binary64_539`
9×	`flip3--_binary64_573` `flip--_binary64_600`
7×	`associate-l_binary64_634` `associate-r_binary64_633`
6×	`add-cube-cbrt_binary64_545` `pow1_binary64_520` `add-cbrt-cube_binary64_546` `add-exp-log_binary64_538`
5×	`distribute-lft-out--_binary64_619` `sub-neg_binary64_578` `difference-of-sqr-1_binary64_604`
4×	`frac-times_binary64_566`
3×	`diff-log_binary64_490`
2×	`associate-l/_binary64_636` `associate-r/_binary64_635`
1×	`unswap-sqr_binary64_602` `cbrt-unprod_binary64_543` `distribute-lft-in_binary64_616` `distribute-rgt-in_binary64_617` `*-commutative_binary64_642` `pow-prod-down_binary64_501` `prod-exp_binary64_525`

Counts

4 → 81

Calls

4 calls:

11.0ms	(.f64 (-.f64 (exp.f64 (.f64 a eps)) 1) (-.f64 (exp.f64 (*.f64 b eps)) 1))
4.0ms	(-.f64 (exp.f64 (*.f64 a eps)) 1)
4.0ms	(-.f64 (exp.f64 (*.f64 b eps)) 1)
5.0ms	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)

series145.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(.f64 (-.f64 (exp.f64 (.f64 a eps)) 1) (-.f64 (exp.f64 (*.f64 b eps)) 1))
24.0ms	(-.f64 (exp.f64 (*.f64 a eps)) 1)
24.0ms	(-.f64 (exp.f64 (*.f64 b eps)) 1)
48.0ms	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)

simplify66.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	4986	1893
1	4986	1893

prune209.0ms

Filtered

70 candidates to 93 candidates (-32.9%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	86	7	93
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	87	7	94

Merged error: 49.7b

Counts

94 → 7

localize43.0ms

Local error

Found 4 expressions with local error:

2.5b	(+.f64 (.f64 1/6 (.f64 (pow.f64 eps 3) (pow.f64 a 3))) (.f64 eps (+.f64 a (.f64 eps (.f64 1/2 (.f64 a a))))))
3.1b	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)
6.0b	(.f64 eps (.f64 1/2 (*.f64 a a)))
13.2b	(*.f64 (pow.f64 eps 3) (pow.f64 a 3))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

39×	`add-sqr-sqrt_binary64_559`
25×	`add-exp-log_binary64_538`
16×	`unswap-sqr_binary64_602`
15×	`associate-l_binary64_634` `add-cbrt-cube_binary64_546` `prod-exp_binary64_525`
14×	`*-un-lft-identity_binary64_574` `unpow-prod-down_binary64_509` `cube-prod_binary64_547`
13×	`pow1_binary64_520` `associate-r_binary64_633`
11×	`add-cube-cbrt_binary64_545`
10×	`sqr-pow_binary64_606`
8×	`add-log-exp_binary64_539`
7×	`cbrt-unprod_binary64_543` `pow-prod-down_binary64_501`
6×	`pow-to-exp_binary64_499` `pow-exp_binary64_498`
2×	`associate-+r+_binary64_625` `unpow3_binary64_518` `difference-of-squares_binary64_603` `*-commutative_binary64_642` `cube-mult_binary64_549`
1×	`flip3--_binary64_573` `+-commutative_binary64_641` `flip3-+_binary64_572` `flip-+_binary64_599` `distribute-lft-out--_binary64_619` `diff-log_binary64_490` `sub-neg_binary64_578` `difference-of-sqr-1_binary64_604` `distribute-lft-in_binary64_616` `distribute-rgt-in_binary64_617` `flip--_binary64_600` `sum-log_binary64_489`

Counts

4 → 108

Calls

4 calls:

10.0ms	(+.f64 (.f64 1/6 (.f64 (pow.f64 eps 3) (pow.f64 a 3))) (.f64 eps (+.f64 a (.f64 eps (.f64 1/2 (.f64 a a))))))
5.0ms	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)
8.0ms	(.f64 eps (.f64 1/2 (*.f64 a a)))
10.0ms	(*.f64 (pow.f64 eps 3) (pow.f64 a 3))

series206.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(+.f64 (.f64 1/6 (.f64 (pow.f64 eps 3) (pow.f64 a 3))) (.f64 eps (+.f64 a (.f64 eps (.f64 1/2 (.f64 a a))))))
42.0ms	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)
28.0ms	(.f64 eps (.f64 1/2 (*.f64 a a)))
53.0ms	(*.f64 (pow.f64 eps 3) (pow.f64 a 3))

simplify62.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5781	2085

prune294.0ms

Filtered

77 candidates to 120 candidates (-55.8%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	117	3	120
Fresh	2	4	6
Picked	1	0	1
Done	0	0	0
Total	120	7	127

Merged error: 49.5b

Counts

127 → 7

localize31.0ms

Local error

Found 4 expressions with local error:

2.1b	(.f64 eps (+.f64 a (.f64 eps (.f64 (.f64 a a) 1/2))))
2.5b	(-.f64 (exp.f64 (*.f64 b eps)) 1)
3.1b	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)
6.0b	(.f64 eps (.f64 (*.f64 a a) 1/2))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt_binary64_559`
15×	`pow1_binary64_520` `add-cbrt-cube_binary64_546` `add-exp-log_binary64_538`
13×	`*-un-lft-identity_binary64_574`
8×	`add-log-exp_binary64_539`
7×	`add-cube-cbrt_binary64_545` `cbrt-unprod_binary64_543` `pow-prod-down_binary64_501` `prod-exp_binary64_525`
6×	`associate-l_binary64_634`
4×	`associate-r_binary64_633` `difference-of-squares_binary64_603`
2×	`flip3--_binary64_573` `distribute-lft-out--_binary64_619` `diff-log_binary64_490` `sub-neg_binary64_578` `difference-of-sqr-1_binary64_604` `flip--_binary64_600` `-commutative_binary64_642` `associate-r/_binary64_635`
1×	`unswap-sqr_binary64_602` `flip3-+_binary64_572` `flip-+_binary64_599` `distribute-lft-in_binary64_616` `distribute-rgt-in_binary64_617`

Counts

4 → 73

Calls

4 calls:

6.0ms	(.f64 eps (+.f64 a (.f64 eps (.f64 (.f64 a a) 1/2))))
4.0ms	(-.f64 (exp.f64 (*.f64 b eps)) 1)
5.0ms	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)
7.0ms	(.f64 eps (.f64 (*.f64 a a) 1/2))

series152.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(.f64 eps (+.f64 a (.f64 eps (.f64 (.f64 a a) 1/2))))
25.0ms	(-.f64 (exp.f64 (*.f64 b eps)) 1)
45.0ms	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)
33.0ms	(.f64 eps (.f64 (*.f64 a a) 1/2))

simplify64.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	6071	1351

prune206.0ms

Filtered

56 candidates to 85 candidates (-51.8%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	79	6	85
Fresh	2	4	6
Picked	1	0	1
Done	0	0	0
Total	82	10	92

Merged error: 49.0b

Counts

92 → 10

localize37.0ms

Local error

Found 4 expressions with local error:

2.1b	(.f64 eps (+.f64 a (.f64 eps (.f64 (.f64 a a) 1/2))))
2.5b	(-.f64 (exp.f64 (*.f64 b eps)) 1)
3.1b	(-.f64 (exp.f64 (*.f64 eps (+.f64 a b))) 1)
6.0b	(.f64 eps (.f64 (*.f64 a a) 1/2))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt_binary64_559`
15×	`pow1_binary64_520` `add-cbrt-cube_binary64_546` `add-exp-log_binary64_538`
13×	`*-un-lft-identity_binary64_574`
8×	`add-log-exp_binary64_539`
7×	`add-cube-cbrt_binary64_545` `cbrt-unprod_binary64_543` `pow-prod-down_binary64_501` `prod-exp_binary64_525`
6×	`associate-l_binary64_634`
4×	`associate-r_binary64_633` `difference-of-squares_binary64_603`
2×	`flip3--_binary64_573` `distribute-lft-out--_binary64_619` `diff-log_binary64_490` `sub-neg_binary64_578` `difference-of-sqr-1_binary64_604` `flip--_binary64_600` `-commutative_binary64_642` `associate-r/_binary64_635`
1×	`unswap-sqr_binary64_602` `flip3-+_binary64_572` `flip-+_binary64_599` `distribute-lft-in_binary64_616` `distribute-rgt-in_binary64_617`

Counts

4 → 73

Calls

4 calls:

6.0ms	(.f64 eps (+.f64 a (.f64 eps (.f64 (.f64 a a) 1/2))))
4.0ms	(-.f64 (exp.f64 (*.f64 b eps)) 1)
5.0ms	(-.f64 (exp.f64 (*.f64 eps (+.f64 a b))) 1)
7.0ms	(.f64 eps (.f64 (*.f64 a a) 1/2))

series139.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(.f64 eps (+.f64 a (.f64 eps (.f64 (.f64 a a) 1/2))))
24.0ms	(-.f64 (exp.f64 (*.f64 b eps)) 1)
29.0ms	(-.f64 (exp.f64 (*.f64 eps (+.f64 a b))) 1)
32.0ms	(.f64 eps (.f64 (*.f64 a a) 1/2))

simplify104.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 0 (84.0ms)

Iter	Nodes	Cost
0	5061	1339

prune159.0ms

Filtered

54 candidates to 85 candidates (-57.4%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	84	1	85
Fresh	1	8	9
Picked	1	0	1
Done	0	0	0
Total	86	9	95

Merged error: 49.0b

Counts

95 → 9

regimes333.0ms

Accuracy

33.8% (5.4b remaining)

Error of 54.4b against oracle of 49.0b and baseline of 57.1b

bsearch139.0ms

Steps

Iters	Range	Point
7	954242467040763717557442683826500819868093820358288773780819620459694305332937456546675509995823658172416	17718442551823355673840318411585669895339116514035531164831817475456912386232417011798211361624251533623296	1.0020287718930736e+105
6	-445587605514949206304143083312392647737017341550819869350880900960483777333192657948070470065721364179868298963335516282622331523826341626316308694129879910589356855004888878868198885152469785233960680074248192	-43459408188600635841782182542193647722892675665956379714915156215630584530845549828505969097781341462527171279534992176137700366856663501852626906524526760671187815880722123436766666910657749524659209892790272	-1.8812294181881513e+209

Iters

Range

Point

954242467040763717557442683826500819868093820358288773780819620459694305332937456546675509995823658172416

17718442551823355673840318411585669895339116514035531164831817475456912386232417011798211361624251533623296

1.0020287718930736e+105

-445587605514949206304143083312392647737017341550819869350880900960483777333192657948070470065721364179868298963335516282622331523826341626316308694129879910589356855004888878868198885152469785233960680074248192

-43459408188600635841782182542193647722892675665956379714915156215630584530845549828505969097781341462527171279534992176137700366856663501852626906524526760671187815880722123436766666910657749524659209892790272

-1.8812294181881513e+209

simplify4.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	79	127
1	79	127

end0.0ms

sample6.3s

Algorithm

intervals

Results

2.7s	2564×	body	2560	valid
2.0s	3495×	body	1280	valid
332.0ms	992×	body	640	valid
265.0ms	640×	body	1280	overflowed
199.0ms	9693×	pre	80	true
115.0ms	408×	body	640	overflowed
91.0ms	143×	body	2560	overflowed
80.0ms	351×	body	320	valid
36.0ms	180×	body	320	overflowed
33.0ms	452×	body	80	valid
22.0ms	146×	body	160	valid
16.0ms	224×	body	80	overflowed
12.0ms	93×	body	160	overflowed
5.0ms	5×	body	2560	invalid

Details

analyze1.7s

sample218.0ms

simplify31.0ms

prune9.0ms

localize27.0ms

rewrite26.0ms

series145.0ms

simplify66.0ms

prune209.0ms

localize43.0ms

rewrite36.0ms

series206.0ms

simplify62.0ms

prune294.0ms

localize31.0ms

rewrite24.0ms

series152.0ms

simplify64.0ms

prune206.0ms

localize37.0ms

rewrite24.0ms

series139.0ms

simplify104.0ms

prune159.0ms

regimes333.0ms

bsearch139.0ms

simplify4.0ms

end0.0ms

sample6.3s

Profiling