Details

analyze3.0ms

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

sample10.0ms

Algorithm

intervals

Results

6.0ms

256×

body

128

valid

simplify20.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (13.0ms)

Iter	Nodes	Cost
0	289	13
1	289	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)))

rewrite11.0ms

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))
6.0ms	(.f64 x (+.f64 2278821411449471/9007199254740992 (.f64 x 1080863910568919/9007199254740992)))

series124.0ms

Counts

2 → 6

Calls

2 calls:

47.0ms	(+.f64 2278821411449471/9007199254740992 (*.f64 x 1080863910568919/9007199254740992))
77.0ms	(.f64 x (+.f64 2278821411449471/9007199254740992 (.f64 x 1080863910568919/9007199254740992)))

simplify83.0ms

Algorithm

egg-herbie

Counts

39 → 39

Iterations

Useful iterations: 0 (72.0ms)

Iter	Nodes	Cost
0	4946	455
1	4946	455

prune38.0ms

Filtered

26 candidates to 39 candidates (-50.0%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	36	3	39
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	36	4	40

Merged error: 0.0b

Counts

40 → 4

localize12.0ms

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 x (.f64 x 1168266793170336129950248828561/81129638414606681695789005144064))
0.2b	(/.f64 (-.f64 5193027025280559198049186179841/81129638414606681695789005144064 (.f64 x (.f64 x 1168266793170336129950248828561/81129638414606681695789005144064))) (-.f64 2278821411449471/9007199254740992 (*.f64 x 1080863910568919/9007199254740992)))
0.3b	(*.f64 x 1168266793170336129950248828561/81129638414606681695789005144064)

rewrite35.0ms

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))))
5.0ms	(.f64 x (.f64 x 1168266793170336129950248828561/81129638414606681695789005144064))
7.0ms	(/.f64 (-.f64 5193027025280559198049186179841/81129638414606681695789005144064 (.f64 x (.f64 x 1168266793170336129950248828561/81129638414606681695789005144064))) (-.f64 2278821411449471/9007199254740992 (*.f64 x 1080863910568919/9007199254740992)))
4.0ms	(*.f64 x 1168266793170336129950248828561/81129638414606681695789005144064)

series396.0ms

Counts

4 → 12

Calls

4 calls:

196.0ms	(.f64 x (/.f64 (-.f64 5193027025280559198049186179841/81129638414606681695789005144064 (.f64 x (.f64 x 1168266793170336129950248828561/81129638414606681695789005144064))) (-.f64 2278821411449471/9007199254740992 (.f64 x 1080863910568919/9007199254740992))))
34.0ms	(.f64 x (.f64 x 1168266793170336129950248828561/81129638414606681695789005144064))
147.0ms	(/.f64 (-.f64 5193027025280559198049186179841/81129638414606681695789005144064 (.f64 x (.f64 x 1168266793170336129950248828561/81129638414606681695789005144064))) (-.f64 2278821411449471/9007199254740992 (*.f64 x 1080863910568919/9007199254740992)))
20.0ms	(*.f64 x 1168266793170336129950248828561/81129638414606681695789005144064)

simplify61.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	4969	2079
1	4969	2079

prune115.0ms

Filtered

77 candidates to 114 candidates (-48.1%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	113	1	114
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	113	5	118

Merged error: 0b

Counts

118 → 5

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

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

80×	`add-sqr-sqrt_binary64`
66×	`times-frac_binary64`
48×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
36×	`sqrt-prod_binary64`
30×	`associate-l_binary64`
28×	`associate-r_binary64`
25×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
13×	`pow1_binary64`
10×	`unswap-sqr_binary64`
8×	`cbrt-unprod_binary64` `prod-exp_binary64`
6×	`associate-/r*_binary64` `associate-/r/_binary64` `sqrt-div_binary64`
5×	`pow-prod-down_binary64` `cbrt-undiv_binary64` `div-exp_binary64`
4×	`add-log-exp_binary64`
3×	`flip3--_binary64` `associate-/l_binary64` `div-inv_binary64` `flip--_binary64` `-commutative_binary64`
1×	`associate-r/_binary64` `clear-num_binary64` `frac-2neg_binary64` `frac-times_binary64` `associate-l/_binary64`

Counts

4 → 154

Calls

4 calls:

5.0ms	(.f64 x (.f64 x 1168266793170336129950248828561/81129638414606681695789005144064))
4.0ms	(*.f64 x 1168266793170336129950248828561/81129638414606681695789005144064)
6.0ms	(/.f64 x (sqrt.f64 (-.f64 2278821411449471/9007199254740992 (*.f64 x 1080863910568919/9007199254740992))))
30.0ms	(.f64 (/.f64 x (sqrt.f64 (-.f64 2278821411449471/9007199254740992 (.f64 x 1080863910568919/9007199254740992)))) (/.f64 (-.f64 5193027025280559198049186179841/81129638414606681695789005144064 (.f64 x (.f64 x 1168266793170336129950248828561/81129638414606681695789005144064))) (sqrt.f64 (-.f64 2278821411449471/9007199254740992 (*.f64 x 1080863910568919/9007199254740992)))))

series309.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(.f64 x (.f64 x 1168266793170336129950248828561/81129638414606681695789005144064))
22.0ms	(*.f64 x 1168266793170336129950248828561/81129638414606681695789005144064)
68.0ms	(/.f64 x (sqrt.f64 (-.f64 2278821411449471/9007199254740992 (*.f64 x 1080863910568919/9007199254740992))))
187.0ms	(.f64 (/.f64 x (sqrt.f64 (-.f64 2278821411449471/9007199254740992 (.f64 x 1080863910568919/9007199254740992)))) (/.f64 (-.f64 5193027025280559198049186179841/81129638414606681695789005144064 (.f64 x (.f64 x 1168266793170336129950248828561/81129638414606681695789005144064))) (sqrt.f64 (-.f64 2278821411449471/9007199254740992 (*.f64 x 1080863910568919/9007199254740992)))))

simplify131.0ms

Algorithm

egg-herbie

Counts

166 → 166

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	4915	4270
1	4915	4270

prune215.0ms

Filtered

107 candidates to 166 candidates (-55.1%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	166	0	166
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	166	5	171

Merged error: 0b

Counts

171 → 5

localize8.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt.f64 (.f64 x (+.f64 2278821411449471/9007199254740992 (.f64 x 1080863910568919/9007199254740992))))
0.1b	(.f64 x (+.f64 2278821411449471/9007199254740992 (.f64 x 1080863910568919/9007199254740992)))
0.1b	(.f64 x (+.f64 2278821411449471/9007199254740992 (.f64 x 1080863910568919/9007199254740992)))
0.3b	(.f64 (sqrt.f64 (.f64 x (+.f64 2278821411449471/9007199254740992 (.f64 x 1080863910568919/9007199254740992)))) (sqrt.f64 (.f64 x (+.f64 2278821411449471/9007199254740992 (*.f64 x 1080863910568919/9007199254740992)))))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

60×	`pow1_binary64`
30×	`sqrt-pow1_binary64`
23×	`pow-prod-down_binary64`
20×	`associate-*r/_binary64`
18×	`add-sqr-sqrt_binary64`
14×	`sqrt-div_binary64`
12×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
11×	`pow1/2_binary64`
10×	`associate-r_binary64` `pow-prod-up_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `associate-l_binary64`
9×	`flip3-+_binary64` `flip-+_binary64`
6×	`pow-sqr_binary64`
5×	`sqrt-prod_binary64`
4×	`add-log-exp_binary64` `swap-sqr_binary64` `frac-times_binary64`
3×	`cbrt-unprod_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `*-commutative_binary64`
2×	`distribute-lft-in_binary64` `distribute-rgt-in_binary64` `associate-*l/_binary64`
1×	`rem-square-sqrt_binary64` `pow-plus_binary64` `sqrt-unprod_binary64` `pow2_binary64`

Counts

4 → 114

Calls

4 calls:

4.0ms	(sqrt.f64 (.f64 x (+.f64 2278821411449471/9007199254740992 (.f64 x 1080863910568919/9007199254740992))))
8.0ms	(.f64 x (+.f64 2278821411449471/9007199254740992 (.f64 x 1080863910568919/9007199254740992)))
6.0ms	(.f64 x (+.f64 2278821411449471/9007199254740992 (.f64 x 1080863910568919/9007199254740992)))
14.0ms	(.f64 (sqrt.f64 (.f64 x (+.f64 2278821411449471/9007199254740992 (.f64 x 1080863910568919/9007199254740992)))) (sqrt.f64 (.f64 x (+.f64 2278821411449471/9007199254740992 (*.f64 x 1080863910568919/9007199254740992)))))

series360.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(sqrt.f64 (.f64 x (+.f64 2278821411449471/9007199254740992 (.f64 x 1080863910568919/9007199254740992))))
85.0ms	(.f64 x (+.f64 2278821411449471/9007199254740992 (.f64 x 1080863910568919/9007199254740992)))
80.0ms	(.f64 x (+.f64 2278821411449471/9007199254740992 (.f64 x 1080863910568919/9007199254740992)))
150.0ms	(.f64 (sqrt.f64 (.f64 x (+.f64 2278821411449471/9007199254740992 (.f64 x 1080863910568919/9007199254740992)))) (sqrt.f64 (.f64 x (+.f64 2278821411449471/9007199254740992 (*.f64 x 1080863910568919/9007199254740992)))))

simplify94.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	4899	1672
1	4899	1672

prune97.0ms

Filtered

70 candidates to 126 candidates (-80.0%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	126	0	126
Fresh	0	1	1
Picked	0	1	1
Done	0	3	3
Total	126	5	131

Merged error: 0b

Counts

131 → 5

regimes43.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	64	13
1	64	13

end0.0ms

sample283.0ms

Algorithm

intervals

Results

186.0ms	8000×	body	128	valid
0.0ms	5×	body	128	invalid

Details

analyze3.0ms

sample10.0ms

simplify20.0ms

prune1.0ms

localize6.0ms

rewrite11.0ms

series124.0ms

simplify83.0ms

prune38.0ms

localize12.0ms

rewrite35.0ms

series396.0ms

simplify61.0ms

prune115.0ms

localize13.0ms

rewrite64.0ms

series309.0ms

simplify131.0ms

prune215.0ms

localize8.0ms

rewrite44.0ms

series360.0ms

simplify94.0ms

prune97.0ms

regimes43.0ms

bsearch0.0ms

simplify3.0ms

end0.0ms

sample283.0ms

Profiling