Details

analyze726.0ms

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
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
18.7%	81.1%	0.1%	7
21.8%	78%	0.1%	8
21.8%	78%	0.1%	9
49.1%	50.7%	0.1%	10
52.7%	47.2%	0.1%	11
52.7%	47.2%	0.1%	12
71.7%	28.2%	0.1%	13
74.1%	25.8%	0.1%	14

sample22.0ms

Algorithm

intervals

Results

13.0ms

256×

body

valid

simplify16.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (13.0ms)

Iter	Nodes	Cost
0	452	21
1	452	21

prune7.0ms

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: 21.9b

Counts

2 → 1

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)
0.0b	(.f64 (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992) z)
5.2b	(.f64 y (+.f64 (.f64 (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992) z) 5029535718965825/18014398509481984))
21.1b	(/.f64 (.f64 y (+.f64 (.f64 (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992) z) 5029535718965825/18014398509481984)) (+.f64 (.f64 (+.f64 z 1692356830115869/281474976710656) z) 7544303578448747/2251799813685248))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64`
13×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
10×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
8×	`pow1_binary64`
6×	`add-log-exp_binary64` `associate-r_binary64` `associate-l_binary64`
5×	`flip3-+_binary64` `flip-+_binary64`
4×	`associate-*r/_binary64`
3×	`associate-/r*_binary64` `cbrt-unprod_binary64` `prod-exp_binary64` `times-frac_binary64`
2×	`pow-prod-down_binary64` `associate-/l/_binary64` `cbrt-undiv_binary64` `associate-/r/_binary64` `unswap-sqr_binary64` `div-exp_binary64` `associate-l/_binary64` `-commutative_binary64`
1×	`distribute-lft-in_binary64` `distribute-rgt-in_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l*_binary64` `div-inv_binary64` `+-commutative_binary64` `sum-log_binary64`

Counts

4 → 78

Calls

4 calls:

8.0ms	(+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)
8.0ms	(.f64 (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992) z)
11.0ms	(.f64 y (+.f64 (.f64 (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992) z) 5029535718965825/18014398509481984))
17.0ms	(/.f64 (.f64 y (+.f64 (.f64 (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992) z) 5029535718965825/18014398509481984)) (+.f64 (.f64 (+.f64 z 1692356830115869/281474976710656) z) 7544303578448747/2251799813685248))

series49.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)
7.0ms	(.f64 (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992) z)
12.0ms	(.f64 y (+.f64 (.f64 (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992) z) 5029535718965825/18014398509481984))
26.0ms	(/.f64 (.f64 y (+.f64 (.f64 (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992) z) 5029535718965825/18014398509481984)) (+.f64 (.f64 (+.f64 z 1692356830115869/281474976710656) z) 7544303578448747/2251799813685248))

simplify47.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	4944	1212
1	4944	1212

prune133.0ms

Filtered

67 candidates to 90 candidates (-34.3%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	87	3	90
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	88	3	91

Merged error: 0b

Counts

91 → 3

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)
0.0b	(.f64 z (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992))
0.1b	(.f64 y (/.f64 (+.f64 (.f64 z (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984) (+.f64 (.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248)))
17.3b	(/.f64 (+.f64 (.f64 z (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984) (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt_binary64`
22×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
19×	`times-frac_binary64`
18×	`associate-r_binary64`
13×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
8×	`pow1_binary64`
6×	`add-log-exp_binary64` `associate-l_binary64`
5×	`flip3-+_binary64` `flip-+_binary64`
4×	`associate-/r/_binary64`
3×	`associate-/r_binary64` `cbrt-unprod_binary64` `associate-r/_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `associate-/l*_binary64`
2×	`pow-prod-down_binary64` `associate-/l/_binary64` `cbrt-undiv_binary64` `div-inv_binary64` `div-exp_binary64` `*-commutative_binary64`
1×	`distribute-lft-in_binary64` `distribute-rgt-in_binary64` `clear-num_binary64` `frac-2neg_binary64` `+-commutative_binary64` `sum-log_binary64`

Counts

4 → 98

Calls

4 calls:

5.0ms	(+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)
7.0ms	(.f64 z (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992))
22.0ms	(.f64 y (/.f64 (+.f64 (.f64 z (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984) (+.f64 (.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248)))
16.0ms	(/.f64 (+.f64 (.f64 z (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984) (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248))

series43.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)
7.0ms	(.f64 z (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992))
26.0ms	(.f64 y (/.f64 (+.f64 (.f64 z (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984) (+.f64 (.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248)))
6.0ms	(/.f64 (+.f64 (.f64 z (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984) (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248))

simplify57.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	4921	1886
1	4921	1886

prune144.0ms

Filtered

84 candidates to 110 candidates (-31.0%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	110	0	110
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	110	3	113

Merged error: 0b

Counts

113 → 3

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)
0.0b	(.f64 z (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992))
0.3b	(/.f64 y (/.f64 (+.f64 (.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248) (+.f64 (.f64 z (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984)))
17.4b	(/.f64 (+.f64 (.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248) (+.f64 (.f64 z (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

90×	`times-frac_binary64`
60×	`add-sqr-sqrt_binary64`
58×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
18×	`associate-/r*_binary64`
13×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
11×	`associate-/r/_binary64`
8×	`flip3-+_binary64` `flip-+_binary64`
6×	`add-log-exp_binary64` `pow1_binary64` `associate-/l*_binary64` `div-inv_binary64`
4×	`cbrt-undiv_binary64` `div-exp_binary64`
3×	`associate-r_binary64` `associate-l_binary64`
2×	`associate-/l/_binary64` `associate-*r/_binary64` `clear-num_binary64` `frac-2neg_binary64`
1×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `+-commutative_binary64` `sum-log_binary64` `*-commutative_binary64`

Counts

4 → 142

Calls

4 calls:

5.0ms	(+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)
8.0ms	(.f64 z (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992))
17.0ms	(/.f64 y (/.f64 (+.f64 (.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248) (+.f64 (.f64 z (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984)))
18.0ms	(/.f64 (+.f64 (.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248) (+.f64 (.f64 z (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984))

series43.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)
6.0ms	(.f64 z (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992))
26.0ms	(/.f64 y (/.f64 (+.f64 (.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248) (+.f64 (.f64 z (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984)))
6.0ms	(/.f64 (+.f64 (.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248) (+.f64 (.f64 z (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984))

simplify97.0ms

Algorithm

egg-herbie

Counts

154 → 154

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	5043	3676

prune236.0ms

Filtered

122 candidates to 154 candidates (-26.2%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	154	0	154
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	154	3	157

Merged error: 0b

Counts

157 → 3

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(.f64 2309983484609776662134346528109328893269301179/5708990770823839524233143877797980545530986496 (/.f64 y (.f64 z z)))
0.4b	(*.f64 1523656921787578761671131903927/20282409603651670423947251286016 (/.f64 y z))
4.7b	(-.f64 (+.f64 (.f64 1523656921787578761671131903927/20282409603651670423947251286016 (/.f64 y z)) (.f64 y 4992947066835229/72057594037927936)) (.f64 2309983484609776662134346528109328893269301179/5708990770823839524233143877797980545530986496 (/.f64 y (.f64 z z))))
7.7b	(/.f64 y (*.f64 z z))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt_binary64`
23×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
20×	`associate-r_binary64`
17×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `times-frac_binary64`
9×	`add-log-exp_binary64`
8×	`pow1_binary64`
7×	`cbrt-unprod_binary64` `prod-exp_binary64`
6×	`associate-l_binary64`
5×	`cbrt-undiv_binary64` `div-exp_binary64`
4×	`associate-*r/_binary64` `unswap-sqr_binary64`
3×	`associate-/l*_binary64` `div-inv_binary64`
2×	`pow-prod-down_binary64` `diff-log_binary64` `frac-sub_binary64` `*-commutative_binary64`
1×	`flip3-+_binary64` `associate-/r*_binary64` `sub-neg_binary64` `flip3--_binary64` `clear-num_binary64` `frac-2neg_binary64` `flip--_binary64` `flip-+_binary64` `associate--l+_binary64` `sum-log_binary64`

Counts

4 → 96

Calls

4 calls:

8.0ms	(.f64 2309983484609776662134346528109328893269301179/5708990770823839524233143877797980545530986496 (/.f64 y (.f64 z z)))
10.0ms	(*.f64 1523656921787578761671131903927/20282409603651670423947251286016 (/.f64 y z))
10.0ms	(-.f64 (+.f64 (.f64 1523656921787578761671131903927/20282409603651670423947251286016 (/.f64 y z)) (.f64 y 4992947066835229/72057594037927936)) (.f64 2309983484609776662134346528109328893269301179/5708990770823839524233143877797980545530986496 (/.f64 y (.f64 z z))))
6.0ms	(/.f64 y (*.f64 z z))

series26.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(.f64 2309983484609776662134346528109328893269301179/5708990770823839524233143877797980545530986496 (/.f64 y (.f64 z z)))
4.0ms	(*.f64 1523656921787578761671131903927/20282409603651670423947251286016 (/.f64 y z))
10.0ms	(-.f64 (+.f64 (.f64 1523656921787578761671131903927/20282409603651670423947251286016 (/.f64 y z)) (.f64 y 4992947066835229/72057594037927936)) (.f64 2309983484609776662134346528109328893269301179/5708990770823839524233143877797980545530986496 (/.f64 y (.f64 z z))))
6.0ms	(/.f64 y (*.f64 z z))

simplify53.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	4987	1027
1	4987	1027

prune98.0ms

Filtered

77 candidates to 108 candidates (-40.3%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	108	0	108
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	108	3	111

Merged error: 0b

Counts

111 → 3

regimes214.0ms

Accuracy

99.6% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 16.0b

bsearch30.0ms

Steps

Iters	Range		Point
7	377665.22669107385	37489223.38271465	507564.9114127195
7	-7663268.459521334	-34474.14597864379	-500484.1251851992

simplify4.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	85	49
1	85	49

end0.0ms

sample590.0ms

Algorithm

intervals

Results

410.0ms

8000×

body

valid

Details

analyze726.0ms

sample22.0ms

simplify16.0ms

prune7.0ms

localize14.0ms

rewrite46.0ms

series49.0ms

simplify47.0ms

prune133.0ms

localize14.0ms

rewrite53.0ms

series43.0ms

simplify57.0ms

prune144.0ms

localize14.0ms

rewrite53.0ms

series43.0ms

simplify97.0ms

prune236.0ms

localize13.0ms

rewrite36.0ms

series26.0ms

simplify53.0ms

prune98.0ms

regimes214.0ms

bsearch30.0ms

simplify4.0ms

end0.0ms

sample590.0ms

Profiling