Details

analyze4.0ms

Algorithm

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
75%	25%	0%	4
75%	12.5%	12.5%	5
75%	6.2%	18.8%	6
75%	3.1%	21.9%	7
75%	1.6%	23.5%	8
75%	0.8%	24.3%	9
75%	0.4%	24.6%	10
75%	0.2%	24.8%	11
75%	0.1%	24.9%	12
75%	0%	24.9%	13
75%	0%	25%	14

sample11.0ms

Algorithm

intervals

Results

6.0ms

256×

body

valid

simplify25.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (16.0ms)

Iter	Nodes	Cost
0	290	13
1	290	13

prune1.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 0.1b

Counts

2 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(+.f64 2278821411449471/9007199254740992 (*.f64 x 1080863910568919/9007199254740992))
0.1b	(.f64 x (+.f64 2278821411449471/9007199254740992 (.f64 x 1080863910568919/9007199254740992)))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-sqr-sqrt_binary64`
4×	`*-un-lft-identity_binary64` `add-log-exp_binary64` `pow1_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
3×	`associate-r_binary64` `associate-l_binary64`
2×	`flip3-+_binary64` `associate-*r/_binary64` `flip-+_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

2 → 33

Calls

2 calls:

3.0ms	(+.f64 2278821411449471/9007199254740992 (*.f64 x 1080863910568919/9007199254740992))
10.0ms	(.f64 x (+.f64 2278821411449471/9007199254740992 (.f64 x 1080863910568919/9007199254740992)))

series58.0ms

Counts

2 → 6

Calls

2 calls:

20.0ms	(+.f64 2278821411449471/9007199254740992 (*.f64 x 1080863910568919/9007199254740992))
38.0ms	(.f64 x (+.f64 2278821411449471/9007199254740992 (.f64 x 1080863910568919/9007199254740992)))

simplify101.0ms

Algorithm

egg-herbie

Counts

39 → 39

Iterations

Useful iterations: 0 (86.0ms)

Iter	Nodes	Cost
0	4947	455
1	4947	455

prune40.0ms

Filtered

26 candidates to 39 candidates (-50.0%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	33	6	39
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	33	7	40

Merged error: 0.0b

Counts

40 → 7

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(.f64 x (/.f64 (-.f64 5193027025280559198049186179841/81129638414606681695789005144064 (.f64 x (.f64 x 1168266793170336129950248828561/81129638414606681695789005144064))) (-.f64 2278821411449471/9007199254740992 (.f64 x 1080863910568919/9007199254740992))))
0.1b	(/.f64 (-.f64 5193027025280559198049186179841/81129638414606681695789005144064 (.f64 x (.f64 x 1168266793170336129950248828561/81129638414606681695789005144064))) (-.f64 2278821411449471/9007199254740992 (*.f64 x 1080863910568919/9007199254740992)))
0.1b	(.f64 x (.f64 x 1168266793170336129950248828561/81129638414606681695789005144064))
0.3b	(*.f64 x 1168266793170336129950248828561/81129638414606681695789005144064)

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 102

Calls

4 calls:

10.0ms	(.f64 x (/.f64 (-.f64 5193027025280559198049186179841/81129638414606681695789005144064 (.f64 x (.f64 x 1168266793170336129950248828561/81129638414606681695789005144064))) (-.f64 2278821411449471/9007199254740992 (.f64 x 1080863910568919/9007199254740992))))
6.0ms	(/.f64 (-.f64 5193027025280559198049186179841/81129638414606681695789005144064 (.f64 x (.f64 x 1168266793170336129950248828561/81129638414606681695789005144064))) (-.f64 2278821411449471/9007199254740992 (*.f64 x 1080863910568919/9007199254740992)))
5.0ms	(.f64 x (.f64 x 1168266793170336129950248828561/81129638414606681695789005144064))
4.0ms	(*.f64 x 1168266793170336129950248828561/81129638414606681695789005144064)

series174.0ms

Counts

4 → 12

Calls

4 calls:

84.0ms	(.f64 x (/.f64 (-.f64 5193027025280559198049186179841/81129638414606681695789005144064 (.f64 x (.f64 x 1168266793170336129950248828561/81129638414606681695789005144064))) (-.f64 2278821411449471/9007199254740992 (.f64 x 1080863910568919/9007199254740992))))
58.0ms	(/.f64 (-.f64 5193027025280559198049186179841/81129638414606681695789005144064 (.f64 x (.f64 x 1168266793170336129950248828561/81129638414606681695789005144064))) (-.f64 2278821411449471/9007199254740992 (*.f64 x 1080863910568919/9007199254740992)))
17.0ms	(.f64 x (.f64 x 1168266793170336129950248828561/81129638414606681695789005144064))
14.0ms	(*.f64 x 1168266793170336129950248828561/81129638414606681695789005144064)

simplify64.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	4971	2079
1	4971	2079

prune110.0ms

Filtered

76 candidates to 114 candidates (-50.0%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	113	1	114
Fresh	1	4	5
Picked	1	0	1
Done	0	1	1
Total	115	6	121

Merged error: 0.0b

Counts

121 → 6

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(-.f64 2278821411449471/9007199254740992 (*.f64 x 1080863910568919/9007199254740992))
0.1b	(.f64 x (/.f64 (-.f64 5193027025280559198049186179841/81129638414606681695789005144064 (.f64 (.f64 x x) 1168266793170336129950248828561/81129638414606681695789005144064)) (-.f64 2278821411449471/9007199254740992 (.f64 x 1080863910568919/9007199254740992))))
0.1b	(/.f64 (-.f64 5193027025280559198049186179841/81129638414606681695789005144064 (.f64 (.f64 x x) 1168266793170336129950248828561/81129638414606681695789005144064)) (-.f64 2278821411449471/9007199254740992 (*.f64 x 1080863910568919/9007199254740992)))
0.2b	(.f64 (.f64 x x) 1168266793170336129950248828561/81129638414606681695789005144064)

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt_binary64`
21×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
19×	`times-frac_binary64`
18×	`associate-r_binary64`
16×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
11×	`pow1_binary64`
6×	`add-log-exp_binary64`
5×	`cbrt-unprod_binary64` `prod-exp_binary64`
4×	`pow-prod-down_binary64` `flip3--_binary64` `associate-/r/_binary64` `associate-l_binary64` `flip--_binary64`
3×	`associate-/r_binary64` `unswap-sqr_binary64` `associate-/l_binary64`
2×	`associate-/l/_binary64` `cbrt-undiv_binary64` `div-inv_binary64` `div-exp_binary64` `*-commutative_binary64`
1×	`sub-neg_binary64` `diff-log_binary64` `associate-*r/_binary64` `div-sub_binary64` `clear-num_binary64` `frac-2neg_binary64`

Counts

4 → 96

Calls

4 calls:

3.0ms	(-.f64 2278821411449471/9007199254740992 (*.f64 x 1080863910568919/9007199254740992))
10.0ms	(.f64 x (/.f64 (-.f64 5193027025280559198049186179841/81129638414606681695789005144064 (.f64 (.f64 x x) 1168266793170336129950248828561/81129638414606681695789005144064)) (-.f64 2278821411449471/9007199254740992 (.f64 x 1080863910568919/9007199254740992))))
6.0ms	(/.f64 (-.f64 5193027025280559198049186179841/81129638414606681695789005144064 (.f64 (.f64 x x) 1168266793170336129950248828561/81129638414606681695789005144064)) (-.f64 2278821411449471/9007199254740992 (*.f64 x 1080863910568919/9007199254740992)))
6.0ms	(.f64 (.f64 x x) 1168266793170336129950248828561/81129638414606681695789005144064)

series194.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(-.f64 2278821411449471/9007199254740992 (*.f64 x 1080863910568919/9007199254740992))
89.0ms	(.f64 x (/.f64 (-.f64 5193027025280559198049186179841/81129638414606681695789005144064 (.f64 (.f64 x x) 1168266793170336129950248828561/81129638414606681695789005144064)) (-.f64 2278821411449471/9007199254740992 (.f64 x 1080863910568919/9007199254740992))))
64.0ms	(/.f64 (-.f64 5193027025280559198049186179841/81129638414606681695789005144064 (.f64 (.f64 x x) 1168266793170336129950248828561/81129638414606681695789005144064)) (-.f64 2278821411449471/9007199254740992 (*.f64 x 1080863910568919/9007199254740992)))
21.0ms	(.f64 (.f64 x x) 1168266793170336129950248828561/81129638414606681695789005144064)

simplify91.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4912	2109
1	4912	2109

prune104.0ms

Filtered

75 candidates to 108 candidates (-44.0%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	108	0	108
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	108	6	114

Merged error: 0.0b

Counts

114 → 6

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(.f64 x (.f64 x 1168266793170336129950248828561/81129638414606681695789005144064))
0.3b	(*.f64 x 1168266793170336129950248828561/81129638414606681695789005144064)
0.4b	(.f64 x (-.f64 5193027025280559198049186179841/81129638414606681695789005144064 (.f64 x (*.f64 x 1168266793170336129950248828561/81129638414606681695789005144064))))
7.4b	(/.f64 (.f64 x (-.f64 5193027025280559198049186179841/81129638414606681695789005144064 (.f64 x (.f64 x 1168266793170336129950248828561/81129638414606681695789005144064)))) (-.f64 2278821411449471/9007199254740992 (.f64 x 1080863910568919/9007199254740992)))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 83

Calls

4 calls:

5.0ms	(.f64 x (.f64 x 1168266793170336129950248828561/81129638414606681695789005144064))
4.0ms	(*.f64 x 1168266793170336129950248828561/81129638414606681695789005144064)
6.0ms	(.f64 x (-.f64 5193027025280559198049186179841/81129638414606681695789005144064 (.f64 x (*.f64 x 1168266793170336129950248828561/81129638414606681695789005144064))))
8.0ms	(/.f64 (.f64 x (-.f64 5193027025280559198049186179841/81129638414606681695789005144064 (.f64 x (.f64 x 1168266793170336129950248828561/81129638414606681695789005144064)))) (-.f64 2278821411449471/9007199254740992 (.f64 x 1080863910568919/9007199254740992)))

series168.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(.f64 x (.f64 x 1168266793170336129950248828561/81129638414606681695789005144064))
10.0ms	(*.f64 x 1168266793170336129950248828561/81129638414606681695789005144064)
58.0ms	(.f64 x (-.f64 5193027025280559198049186179841/81129638414606681695789005144064 (.f64 x (*.f64 x 1168266793170336129950248828561/81129638414606681695789005144064))))
83.0ms	(/.f64 (.f64 x (-.f64 5193027025280559198049186179841/81129638414606681695789005144064 (.f64 x (.f64 x 1168266793170336129950248828561/81129638414606681695789005144064)))) (-.f64 2278821411449471/9007199254740992 (.f64 x 1080863910568919/9007199254740992)))

simplify82.0ms

Algorithm

egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4871	1257
1	4871	1257

prune69.0ms

Filtered

60 candidates to 95 candidates (-58.3%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	93	2	95
Fresh	1	2	3
Picked	0	1	1
Done	0	2	2
Total	94	7	101

Merged error: 0b

Counts

101 → 7

regimes49.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify4.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	65	13
1	65	13

end0.0ms

sample279.0ms

Algorithm

intervals

Results

192.0ms	8000×	body	80	valid
0.0ms	2×	body	80	invalid

Details

analyze4.0ms

sample11.0ms

simplify25.0ms

prune1.0ms

localize6.0ms

rewrite14.0ms

series58.0ms

simplify101.0ms

prune40.0ms

localize11.0ms

rewrite27.0ms

series174.0ms

simplify64.0ms

prune110.0ms

localize11.0ms

rewrite28.0ms

series194.0ms

simplify91.0ms

prune104.0ms

localize13.0ms

rewrite25.0ms

series168.0ms

simplify82.0ms

prune69.0ms

regimes49.0ms

bsearch0.0ms

simplify4.0ms

end0.0ms

sample279.0ms

Profiling