Details

analyze497.0ms

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

sample21.0ms

Algorithm

intervals

Results

13.0ms

256×

body

128

valid

simplify20.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (13.0ms)

Iter	Nodes	Cost
0	453	31
1	453	31

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: 22.2b

Counts

2 → 1

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(*.f64 (+.f64 z 1692356830115869/281474976710656) z)
0.1b	(.f64 (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992) z)
4.5b	(.f64 y (+.f64 (.f64 (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992) z) 5029535718965825/18014398509481984))
21.4b	(/.f64 (.f64 y (+.f64 (.f64 (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992) z) 5029535718965825/18014398509481984)) (+.f64 (.f64 (+.f64 z 1692356830115869/281474976710656) z) 7544303578448747/2251799813685248))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt_binary64`
15×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
14×	`*-un-lft-identity_binary64`
12×	`add-cube-cbrt_binary64`
10×	`pow1_binary64` `associate-l_binary64`
9×	`associate-r_binary64`
5×	`flip3-+_binary64` `flip-+_binary64`
4×	`add-log-exp_binary64` `cbrt-unprod_binary64` `associate-r/_binary64` `prod-exp_binary64` `associate-l/_binary64`
3×	`pow-prod-down_binary64` `associate-/r_binary64` `unswap-sqr_binary64` `times-frac_binary64` `-commutative_binary64`
2×	`associate-/l/_binary64` `cbrt-undiv_binary64` `associate-/r/_binary64` `div-exp_binary64`
1×	`distribute-lft-out_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l*_binary64` `div-inv_binary64`

Counts

4 → 88

Calls

4 calls:

6.0ms	(*.f64 (+.f64 z 1692356830115869/281474976710656) z)
7.0ms	(.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))

series414.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(*.f64 (+.f64 z 1692356830115869/281474976710656) z)
88.0ms	(.f64 (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992) z)
76.0ms	(.f64 y (+.f64 (.f64 (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992) z) 5029535718965825/18014398509481984))
189.0ms	(/.f64 (.f64 y (+.f64 (.f64 (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992) z) 5029535718965825/18014398509481984)) (+.f64 (.f64 (+.f64 z 1692356830115869/281474976710656) z) 7544303578448747/2251799813685248))

simplify87.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4915	1847
1	4915	1847

prune121.0ms

Filtered

74 candidates to 100 candidates (-35.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	97	3	100
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	98	3	101

Merged error: 0.0b

Counts

101 → 3

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(+.f64 x (.f64 y (/.f64 (+.f64 (.f64 z (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984) (+.f64 (.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248))))
0.1b	(.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)))
17.0b	(/.f64 (+.f64 (.f64 z (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984) (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248))

rewrite55.0ms

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:

4.0ms	(+.f64 x (.f64 y (/.f64 (+.f64 (.f64 z (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984) (+.f64 (.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248))))
7.0ms	(.f64 z (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992))
18.0ms	(.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))

series778.0ms

Counts

4 → 12

Calls

4 calls:

450.0ms	(+.f64 x (.f64 y (/.f64 (+.f64 (.f64 z (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984) (+.f64 (.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248))))
88.0ms	(.f64 z (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992))
197.0ms	(.f64 y (/.f64 (+.f64 (.f64 z (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984) (+.f64 (.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248)))
43.0ms	(/.f64 (+.f64 (.f64 z (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984) (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248))

simplify68.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	5477	3185

prune141.0ms

Filtered

85 candidates to 110 candidates (-29.4%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	109	1	110
Fresh	1	1	2
Picked	0	1	1
Done	0	0	0
Total	110	3	113

Merged error: 0.0b

Counts

113 → 3

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(+.f64 x (/.f64 y (/.f64 (+.f64 (.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248) (+.f64 (.f64 z (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984))))
0.1b	(.f64 z (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992))
0.4b	(/.f64 y (/.f64 (+.f64 (.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248) (+.f64 (.f64 z (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984)))
17.1b	(/.f64 (+.f64 (.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248) (+.f64 (.f64 z (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984))

rewrite83.0ms

Algorithm

rewrite-expression-head

Rules

90×	`times-frac_binary64`
60×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64`
58×	`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-out_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `+-commutative_binary64` `sum-log_binary64` `*-commutative_binary64`

Counts

4 → 143

Calls

4 calls:

26.0ms	(+.f64 x (/.f64 y (/.f64 (+.f64 (.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248) (+.f64 (.f64 z (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984))))
7.0ms	(.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)))
16.0ms	(/.f64 (+.f64 (.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248) (+.f64 (.f64 z (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984))

series765.0ms

Counts

4 → 12

Calls

4 calls:

453.0ms	(+.f64 x (/.f64 y (/.f64 (+.f64 (.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248) (+.f64 (.f64 z (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984))))
83.0ms	(.f64 z (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992))
179.0ms	(/.f64 y (/.f64 (+.f64 (.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248) (+.f64 (.f64 z (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984)))
50.0ms	(/.f64 (+.f64 (.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248) (+.f64 (.f64 z (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984))

simplify128.0ms

Algorithm

egg-herbie

Counts

155 → 155

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	4946	5972
1	4946	5972

prune246.0ms

Filtered

125 candidates to 155 candidates (-24.0%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	154	1	155
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	154	4	158

Merged error: 0.0b

Counts

158 → 4

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(/.f64 390056171977620162987809767405312/24929520412218516726673835482441 z)
0.2b	(-.f64 (+.f64 (/.f64 12601190682500060247286489862352539773304146868320/124471775819795412045694910318123546404269713989 (*.f64 z z)) 72057594037927936/4992947066835229) (/.f64 390056171977620162987809767405312/24929520412218516726673835482441 z))
0.4b	(/.f64 12601190682500060247286489862352539773304146868320/124471775819795412045694910318123546404269713989 (*.f64 z z))
2.8b	(/.f64 y (-.f64 (+.f64 (/.f64 12601190682500060247286489862352539773304146868320/124471775819795412045694910318123546404269713989 (*.f64 z z)) 72057594037927936/4992947066835229) (/.f64 390056171977620162987809767405312/24929520412218516726673835482441 z)))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

51×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64`
38×	`times-frac_binary64`
26×	`add-cube-cbrt_binary64`
13×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
11×	`associate-/r*_binary64`
10×	`difference-of-squares_binary64` `distribute-lft-out--_binary64`
9×	`add-log-exp_binary64` `associate-/l*_binary64`
5×	`distribute-lft-out_binary64`
4×	`pow1_binary64` `cbrt-undiv_binary64` `associate-/r/_binary64` `div-exp_binary64` `frac-sub_binary64`
3×	`clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64`
2×	`flip3-+_binary64` `flip3--_binary64` `diff-log_binary64` `flip--_binary64` `flip-+_binary64`
1×	`sub-neg_binary64` `cbrt-unprod_binary64` `prod-exp_binary64` `associate--l+_binary64` `sum-log_binary64`

Counts

4 → 114

Calls

4 calls:

3.0ms	(/.f64 390056171977620162987809767405312/24929520412218516726673835482441 z)
15.0ms	(-.f64 (+.f64 (/.f64 12601190682500060247286489862352539773304146868320/124471775819795412045694910318123546404269713989 (*.f64 z z)) 72057594037927936/4992947066835229) (/.f64 390056171977620162987809767405312/24929520412218516726673835482441 z))
6.0ms	(/.f64 12601190682500060247286489862352539773304146868320/124471775819795412045694910318123546404269713989 (*.f64 z z))
17.0ms	(/.f64 y (-.f64 (+.f64 (/.f64 12601190682500060247286489862352539773304146868320/124471775819795412045694910318123546404269713989 (*.f64 z z)) 72057594037927936/4992947066835229) (/.f64 390056171977620162987809767405312/24929520412218516726673835482441 z)))

series177.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(/.f64 390056171977620162987809767405312/24929520412218516726673835482441 z)
20.0ms	(-.f64 (+.f64 (/.f64 12601190682500060247286489862352539773304146868320/124471775819795412045694910318123546404269713989 (*.f64 z z)) 72057594037927936/4992947066835229) (/.f64 390056171977620162987809767405312/24929520412218516726673835482441 z))
33.0ms	(/.f64 12601190682500060247286489862352539773304146868320/124471775819795412045694910318123546404269713989 (*.f64 z z))
103.0ms	(/.f64 y (-.f64 (+.f64 (/.f64 12601190682500060247286489862352539773304146868320/124471775819795412045694910318123546404269713989 (*.f64 z z)) 72057594037927936/4992947066835229) (/.f64 390056171977620162987809767405312/24929520412218516726673835482441 z)))

simplify121.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 0 (77.0ms)

Iter	Nodes	Cost
0	5082	2542

prune119.0ms

Filtered

89 candidates to 126 candidates (-41.6%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	124	2	126
Fresh	0	1	1
Picked	1	0	1
Done	0	2	2
Total	125	5	130

Merged error: 0.0b

Counts

130 → 5

regimes101.0ms

Accuracy

99.2% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 16.1b

bsearch47.0ms

Steps

Iters	Range		Point
10	3.3146825816483673e-18	0.2056783482404748	0.20227657563480705
8	-2677215645.3694563	-3657913.120212774	-656965632.3933399

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	48	61
1	48	61

end0.0ms

sample576.0ms

Algorithm

intervals

Results

403.0ms

8000×

body

128

valid

Details

analyze497.0ms

sample21.0ms

simplify20.0ms

prune3.0ms

localize17.0ms

rewrite50.0ms

series414.0ms

simplify87.0ms

prune121.0ms

localize17.0ms

rewrite55.0ms

series778.0ms

simplify68.0ms

prune141.0ms

localize17.0ms

rewrite83.0ms

series765.0ms

simplify128.0ms

prune246.0ms

localize14.0ms

rewrite51.0ms

series177.0ms

simplify121.0ms

prune119.0ms

regimes101.0ms

bsearch47.0ms

simplify3.0ms

end0.0ms

sample576.0ms

Profiling