Details

analyze321.0ms

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
6.2%	93.6%	0.1%	6
15.6%	84.3%	0.1%	7
25%	74.9%	0.1%	8
37.4%	62.4%	0.1%	9
46.8%	53%	0.1%	10
55%	44.9%	0.1%	11
64.2%	35.7%	0.1%	12
70.3%	29.5%	0.1%	13
75.4%	24.4%	0.1%	14

sample14.0ms

Algorithm

intervals

Results

6.0ms	241×	body	128	valid
0.0ms	4×	body	1024	valid
0.0ms	5×	body	512	valid
0.0ms	5×	body	256	valid
0.0ms	1×	body	2048	valid

simplify11.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	148	13
1	148	13

prune4.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 0.1b

Counts

2 → 1

localize6.0ms

Local error

Found 1 expressions with local error:

0.0b	(+.f64 x (+.f64 (*.f64 (+.f64 x y) 2) z))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-log-exp_binary64`
3×	`*-un-lft-identity_binary64` `sum-log_binary64`
1×	`flip3-+_binary64` `pow1_binary64` `distribute-lft-out_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `add-sqr-sqrt_binary64` `+-commutative_binary64` `flip-+_binary64` `associate-+r+_binary64`

Counts

1 → 14

Calls

1 calls:

9.0ms

(+.f64 x (+.f64 (*.f64 (+.f64 x y) 2) z))

series38.0ms

Counts

1 → 3

Calls

1 calls:

38.0ms

(+.f64 x (+.f64 (*.f64 (+.f64 x y) 2) z))

simplify54.0ms

Algorithm

egg-herbie

Counts

17 → 17

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5232	299

prune14.0ms

Filtered

11 candidates to 17 candidates (-54.5%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	16	1	17
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	16	2	18

Merged error: 0.0b

Counts

18 → 2

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(+.f64 x (+.f64 (*.f64 (+.f64 x y) 2) z))
0.0b	(sqrt.f64 (+.f64 x (+.f64 (*.f64 (+.f64 x y) 2) z)))
0.0b	(sqrt.f64 (+.f64 x (+.f64 (*.f64 (+.f64 x y) 2) z)))
0.2b	(.f64 (sqrt.f64 (+.f64 x (+.f64 (.f64 (+.f64 x y) 2) z))) (sqrt.f64 (+.f64 x (+.f64 (*.f64 (+.f64 x y) 2) z))))

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

34×	`*-un-lft-identity_binary64` `sqrt-prod_binary64`
28×	`add-sqr-sqrt_binary64`
21×	`pow1_binary64`
16×	`sqrt-div_binary64`
14×	`add-cube-cbrt_binary64`
11×	`swap-sqr_binary64`
10×	`pow1/2_binary64` `sqrt-pow1_binary64`
9×	`flip3-+_binary64` `add-log-exp_binary64` `distribute-lft-out_binary64` `flip-+_binary64`
7×	`associate-r_binary64` `associate-l_binary64`
6×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
5×	`pow-prod-up_binary64`
4×	`unswap-sqr_binary64` `frac-times_binary64`
3×	`pow-prod-down_binary64` `pow-sqr_binary64` `sum-log_binary64`
2×	`associate-r/_binary64` `rem-sqrt-square_binary64` `associate-l/_binary64`
1×	`cbrt-unprod_binary64` `rem-square-sqrt_binary64` `pow-plus_binary64` `sqrt-unprod_binary64` `prod-exp_binary64` `+-commutative_binary64` `associate-+r+_binary64` `pow2_binary64` `*-commutative_binary64`

Counts

4 → 108

Calls

4 calls:

9.0ms	(+.f64 x (+.f64 (*.f64 (+.f64 x y) 2) z))
8.0ms	(sqrt.f64 (+.f64 x (+.f64 (*.f64 (+.f64 x y) 2) z)))
8.0ms	(sqrt.f64 (+.f64 x (+.f64 (*.f64 (+.f64 x y) 2) z)))
21.0ms	(.f64 (sqrt.f64 (+.f64 x (+.f64 (.f64 (+.f64 x y) 2) z))) (sqrt.f64 (+.f64 x (+.f64 (*.f64 (+.f64 x y) 2) z))))

series284.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(+.f64 x (+.f64 (*.f64 (+.f64 x y) 2) z))
73.0ms	(sqrt.f64 (+.f64 x (+.f64 (*.f64 (+.f64 x y) 2) z)))
80.0ms	(sqrt.f64 (+.f64 x (+.f64 (*.f64 (+.f64 x y) 2) z)))
93.0ms	(.f64 (sqrt.f64 (+.f64 x (+.f64 (.f64 (+.f64 x y) 2) z))) (sqrt.f64 (+.f64 x (+.f64 (*.f64 (+.f64 x y) 2) z))))

simplify78.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4993	2442
1	4993	2442

prune80.0ms

Filtered

65 candidates to 120 candidates (-84.6%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	118	2	120
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	118	4	122

Merged error: 0.0b

Counts

122 → 4

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(.f64 (.f64 (sqrt.f64 (+.f64 x (+.f64 (.f64 (+.f64 x y) 2) z))) (fabs.f64 (cbrt.f64 (+.f64 x (+.f64 (.f64 (+.f64 x y) 2) z))))) (sqrt.f64 (cbrt.f64 (+.f64 x (+.f64 (*.f64 (+.f64 x y) 2) z)))))
0.2b	(.f64 (sqrt.f64 (+.f64 x (+.f64 (.f64 (+.f64 x y) 2) z))) (fabs.f64 (cbrt.f64 (+.f64 x (+.f64 (*.f64 (+.f64 x y) 2) z)))))
0.5b	(cbrt.f64 (+.f64 x (+.f64 (*.f64 (+.f64 x y) 2) z)))
0.5b	(cbrt.f64 (+.f64 x (+.f64 (*.f64 (+.f64 x y) 2) z)))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

20×	`*-un-lft-identity_binary64`
16×	`add-sqr-sqrt_binary64`
14×	`sqrt-div_binary64`
13×	`associate-r_binary64`
12×	`add-cube-cbrt_binary64` `sqrt-prod_binary64` `cbrt-prod_binary64`
11×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
10×	`cbrt-div_binary64` `associate-*l/_binary64`
9×	`flip3-+_binary64` `flip-+_binary64`
8×	`associate-l_binary64`
4×	`pow-prod-down_binary64` `add-log-exp_binary64` `cbrt-unprod_binary64` `distribute-lft-out_binary64` `prod-exp_binary64` `frac-times_binary64`
2×	`associate-r/_binary64` `pow1/3_binary64` `unswap-sqr_binary64` `-commutative_binary64`

Counts

4 → 86

Calls

4 calls:

24.0ms	(.f64 (.f64 (sqrt.f64 (+.f64 x (+.f64 (.f64 (+.f64 x y) 2) z))) (fabs.f64 (cbrt.f64 (+.f64 x (+.f64 (.f64 (+.f64 x y) 2) z))))) (sqrt.f64 (cbrt.f64 (+.f64 x (+.f64 (*.f64 (+.f64 x y) 2) z)))))
12.0ms	(.f64 (sqrt.f64 (+.f64 x (+.f64 (.f64 (+.f64 x y) 2) z))) (fabs.f64 (cbrt.f64 (+.f64 x (+.f64 (*.f64 (+.f64 x y) 2) z)))))
8.0ms	(cbrt.f64 (+.f64 x (+.f64 (*.f64 (+.f64 x y) 2) z)))
8.0ms	(cbrt.f64 (+.f64 x (+.f64 (*.f64 (+.f64 x y) 2) z)))

series2.2s

Counts

4 → 12

Calls

4 calls:

1.2s	(.f64 (.f64 (sqrt.f64 (+.f64 x (+.f64 (.f64 (+.f64 x y) 2) z))) (fabs.f64 (cbrt.f64 (+.f64 x (+.f64 (.f64 (+.f64 x y) 2) z))))) (sqrt.f64 (cbrt.f64 (+.f64 x (+.f64 (*.f64 (+.f64 x y) 2) z)))))
316.0ms	(.f64 (sqrt.f64 (+.f64 x (+.f64 (.f64 (+.f64 x y) 2) z))) (fabs.f64 (cbrt.f64 (+.f64 x (+.f64 (*.f64 (+.f64 x y) 2) z)))))
368.0ms	(cbrt.f64 (+.f64 x (+.f64 (*.f64 (+.f64 x y) 2) z)))
335.0ms	(cbrt.f64 (+.f64 x (+.f64 (*.f64 (+.f64 x y) 2) z)))

simplify76.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	4966	4300
1	4966	4300

prune165.0ms

Filtered

77 candidates to 98 candidates (-27.3%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	96	2	98
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	96	6	102

Merged error: 0.0b

Counts

102 → 6

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(.f64 (cbrt.f64 (sqrt.f64 (+.f64 x (+.f64 (.f64 (+.f64 x y) 2) z)))) (cbrt.f64 (sqrt.f64 (+.f64 x (+.f64 (*.f64 (+.f64 x y) 2) z)))))
0.3b	(cbrt.f64 (sqrt.f64 (+.f64 x (+.f64 (*.f64 (+.f64 x y) 2) z))))
0.3b	(cbrt.f64 (sqrt.f64 (+.f64 x (+.f64 (*.f64 (+.f64 x y) 2) z))))
0.5b	(cbrt.f64 (+.f64 x (+.f64 (*.f64 (+.f64 x y) 2) z)))

rewrite75.0ms

Algorithm

rewrite-expression-head

Rules

66×	`cbrt-prod_binary64`
43×	`add-sqr-sqrt_binary64`
41×	`*-un-lft-identity_binary64`
36×	`sqrt-prod_binary64`
21×	`add-cube-cbrt_binary64`
18×	`cbrt-div_binary64`
16×	`sqrt-div_binary64`
14×	`swap-sqr_binary64`
11×	`pow1_binary64`
10×	`associate-r_binary64` `associate-l_binary64`
9×	`flip3-+_binary64` `distribute-lft-out_binary64` `pow1/3_binary64` `unswap-sqr_binary64` `flip-+_binary64`
6×	`add-exp-log_binary64`
4×	`add-log-exp_binary64` `add-cbrt-cube_binary64` `frac-times_binary64`
2×	`pow-prod-down_binary64` `pow-prod-up_binary64` `associate-r/_binary64` `pow-sqr_binary64` `associate-l/_binary64`
1×	`cbrt-unprod_binary64` `pow-plus_binary64` `prod-exp_binary64` `pow2_binary64` `*-commutative_binary64`

Counts

4 → 117

Calls

4 calls:

24.0ms	(.f64 (cbrt.f64 (sqrt.f64 (+.f64 x (+.f64 (.f64 (+.f64 x y) 2) z)))) (cbrt.f64 (sqrt.f64 (+.f64 x (+.f64 (*.f64 (+.f64 x y) 2) z)))))
9.0ms	(cbrt.f64 (sqrt.f64 (+.f64 x (+.f64 (*.f64 (+.f64 x y) 2) z))))
9.0ms	(cbrt.f64 (sqrt.f64 (+.f64 x (+.f64 (*.f64 (+.f64 x y) 2) z))))
8.0ms	(cbrt.f64 (+.f64 x (+.f64 (*.f64 (+.f64 x y) 2) z)))

series1.2s

Counts

4 → 12

Calls

4 calls:

297.0ms	(.f64 (cbrt.f64 (sqrt.f64 (+.f64 x (+.f64 (.f64 (+.f64 x y) 2) z)))) (cbrt.f64 (sqrt.f64 (+.f64 x (+.f64 (*.f64 (+.f64 x y) 2) z)))))
272.0ms	(cbrt.f64 (sqrt.f64 (+.f64 x (+.f64 (*.f64 (+.f64 x y) 2) z))))
273.0ms	(cbrt.f64 (sqrt.f64 (+.f64 x (+.f64 (*.f64 (+.f64 x y) 2) z))))
325.0ms	(cbrt.f64 (+.f64 x (+.f64 (*.f64 (+.f64 x y) 2) z)))

simplify74.0ms

Algorithm

egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5570	4253

prune209.0ms

Filtered

85 candidates to 129 candidates (-51.8%)

Pruning

6 alts after pruning (2 fresh and 4 done)

	Pruned	Kept	Total
New	129	0	129
Fresh	0	2	2
Picked	0	1	1
Done	0	3	3
Total	129	6	135

Merged error: 0.0b

Counts

135 → 6

regimes55.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	13
1	13	13

end0.0ms

sample398.0ms

Algorithm

intervals

Results

194.0ms	7472×	body	128	valid
21.0ms	198×	body	1024	valid
13.0ms	156×	body	512	valid
9.0ms	77×	body	2048	valid
5.0ms	97×	body	256	valid
0.0ms	9×	body	128	invalid

Details

analyze321.0ms

sample14.0ms

simplify11.0ms

prune4.0ms

localize6.0ms

rewrite10.0ms

series38.0ms

simplify54.0ms

prune14.0ms

localize9.0ms

rewrite59.0ms

series284.0ms

simplify78.0ms

prune80.0ms

localize16.0ms

rewrite65.0ms

series2.2s

simplify76.0ms

prune165.0ms

localize16.0ms

rewrite75.0ms

series1.2s

simplify74.0ms

prune209.0ms

regimes55.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample398.0ms

Profiling