Details

analyze86.0ms

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
25%	74.9%	0.1%	5
37.5%	62.4%	0.1%	6
56.2%	43.7%	0.1%	7
65.6%	34.3%	0.1%	8
76.5%	23.4%	0.1%	9
82%	18%	0.1%	10
87.8%	12.1%	0.1%	11
90.7%	9.2%	0.1%	12
93.8%	6.1%	0.1%	13
95.3%	4.6%	0.1%	14

sample14.0ms

Algorithm

intervals

Results

7.0ms

256×

body

valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	7	8
1	7	8

prune2.0ms

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: 32.1b

Counts

2 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(+.f64 (.f64 x x) (.f64 y y))
30.1b	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-log-exp_binary64` `add-sqr-sqrt_binary64`
3×	`*-un-lft-identity_binary64` `pow1_binary64` `add-cube-cbrt_binary64` `sqrt-prod_binary64`
2×	`flip3-+_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `flip-+_binary64` `sqrt-div_binary64`
1×	`pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `+-commutative_binary64` `sum-log_binary64`

Counts

2 → 26

Calls

2 calls:

4.0ms	(+.f64 (.f64 x x) (.f64 y y))
4.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))

series13.0ms

Counts

2 → 6

Calls

2 calls:

6.0ms	(+.f64 (.f64 x x) (.f64 y y))
7.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))

simplify62.0ms

Algorithm

egg-herbie

Counts

32 → 32

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4909	295
1	4909	295

prune39.0ms

Filtered

25 candidates to 32 candidates (-28.0%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	27	5	32
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	27	6	33

Merged error: 5.2b

Counts

33 → 6

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))))
0.5b	(.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))) (sqrt.f64 (sqrt.f64 (+.f64 (.f64 x x) (*.f64 y y)))))
30.1b	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))
30.1b	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

82×	`sqrt-prod_binary64`
54×	`add-sqr-sqrt_binary64`
38×	`sqrt-pow1_binary64`
32×	`sqrt-div_binary64`
31×	`pow1_binary64`
20×	`*-un-lft-identity_binary64` `pow1/2_binary64` `add-cube-cbrt_binary64`
15×	`swap-sqr_binary64`
9×	`flip3-+_binary64` `associate-r_binary64` `pow-prod-up_binary64` `associate-l_binary64` `unswap-sqr_binary64` `flip-+_binary64`
6×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
5×	`pow-prod-down_binary64` `pow-sqr_binary64`
4×	`add-log-exp_binary64` `rem-sqrt-square_binary64` `frac-times_binary64`
2×	`associate-r/_binary64` `associate-l/_binary64`
1×	`cbrt-unprod_binary64` `rem-square-sqrt_binary64` `pow-plus_binary64` `sqrt-unprod_binary64` `prod-exp_binary64` `pow2_binary64` `*-commutative_binary64`

Counts

4 → 134

Calls

4 calls:

5.0ms	(sqrt.f64 (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))))
15.0ms	(.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))) (sqrt.f64 (sqrt.f64 (+.f64 (.f64 x x) (*.f64 y y)))))
4.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))
5.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))

series40.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(sqrt.f64 (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))))
7.0ms	(.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))) (sqrt.f64 (sqrt.f64 (+.f64 (.f64 x x) (*.f64 y y)))))
7.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))
7.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))

simplify50.0ms

Algorithm

egg-herbie

Counts

146 → 146

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5084	1565

prune83.0ms

Filtered

77 candidates to 146 candidates (-89.6%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	145	1	146
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	145	7	152

Merged error: 5.2b

Counts

152 → 7

localize11.0ms

Local error

Found 4 expressions with local error:

0.5b	(.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))) (cbrt.f64 (pow.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 x x) (*.f64 y y)))) 3)))
20.7b	(cbrt.f64 (pow.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))) 3))
30.1b	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))
30.1b	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

96×	`sqrt-prod_binary64`
77×	`add-sqr-sqrt_binary64`
72×	`cbrt-prod_binary64`
32×	`sqrt-div_binary64`
27×	`associate-r_binary64` `unswap-sqr_binary64` `unpow-prod-down_binary64` `cube-prod_binary64`
24×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
9×	`flip3-+_binary64` `associate-l_binary64` `flip-+_binary64`
8×	`cbrt-div_binary64` `pow1_binary64` `cube-div_binary64`
6×	`add-exp-log_binary64`
5×	`sqr-pow_binary64` `add-cbrt-cube_binary64`
4×	`add-log-exp_binary64` `frac-times_binary64`
2×	`pow1/2_binary64` `associate-r/_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `unpow3_binary64` `associate-l/_binary64` `cube-mult_binary64`
1×	`pow-prod-down_binary64` `rem-cbrt-cube_binary64` `cbrt-unprod_binary64` `pow1/3_binary64` `prod-exp_binary64` `*-commutative_binary64`

Counts

4 → 147

Calls

4 calls:

20.0ms	(.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))) (cbrt.f64 (pow.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 x x) (*.f64 y y)))) 3)))
7.0ms	(cbrt.f64 (pow.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))) 3))
4.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))
4.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))

series50.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))) (cbrt.f64 (pow.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 x x) (*.f64 y y)))) 3)))
26.0ms	(cbrt.f64 (pow.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))) 3))
7.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))
7.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))

simplify53.0ms

Algorithm

egg-herbie

Counts

159 → 159

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	4983	2306
1	4983	2306

prune103.0ms

Filtered

83 candidates to 159 candidates (-91.6%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	157	2	159
Fresh	0	4	4
Picked	1	0	1
Done	0	2	2
Total	158	8	166

Merged error: 5.2b

Counts

166 → 8

localize17.0ms

Local error

Found 4 expressions with local error:

20.7b	(cbrt.f64 (pow.f64 (sqrt.f64 (.f64 (cbrt.f64 (+.f64 (.f64 x x) (.f64 y y))) (cbrt.f64 (sqrt.f64 (+.f64 (.f64 x x) (*.f64 y y)))))) 3))
30.1b	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))
30.1b	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))
31.1b	(cbrt.f64 (+.f64 (.f64 x x) (.f64 y y)))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

22×	`cbrt-div_binary64`
18×	`sqrt-div_binary64`
17×	`cbrt-prod_binary64`
12×	`add-sqr-sqrt_binary64`
10×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
9×	`flip3-+_binary64` `flip-+_binary64`
8×	`cube-div_binary64` `sqrt-prod_binary64`
6×	`pow1_binary64`
4×	`add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `unpow-prod-down_binary64` `cube-prod_binary64` `frac-times_binary64`
2×	`pow1/2_binary64` `associate-r/_binary64` `pow1/3_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `associate-l/_binary64`
1×	`rem-cbrt-cube_binary64` `sqr-pow_binary64` `unpow3_binary64` `cube-mult_binary64`

Counts

4 → 74

Calls

4 calls:

6.0ms	(cbrt.f64 (pow.f64 (sqrt.f64 (.f64 (cbrt.f64 (+.f64 (.f64 x x) (.f64 y y))) (cbrt.f64 (sqrt.f64 (+.f64 (.f64 x x) (*.f64 y y)))))) 3))
4.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))
4.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))
4.0ms	(cbrt.f64 (+.f64 (.f64 x x) (.f64 y y)))

series58.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(cbrt.f64 (pow.f64 (sqrt.f64 (.f64 (cbrt.f64 (+.f64 (.f64 x x) (.f64 y y))) (cbrt.f64 (sqrt.f64 (+.f64 (.f64 x x) (*.f64 y y)))))) 3))
7.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))
10.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))
22.0ms	(cbrt.f64 (+.f64 (.f64 x x) (.f64 y y)))

simplify84.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (71.0ms)

Iter	Nodes	Cost
0	4924	1448
1	4924	1448

prune79.0ms

Filtered

69 candidates to 86 candidates (-24.6%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	85	1	86
Fresh	1	4	5
Picked	0	1	1
Done	0	2	2
Total	86	8	94

Merged error: 5.2b

Counts

94 → 8

regimes487.0ms

Accuracy

54.2% (10.7b remaining)

Error of 18.9b against oracle of 8.2b and baseline of 31.6b

bsearch41.0ms

Steps

Iters	Range		Point
7	6.395471245595238e+116	6.569570556200689e+118	5.63142386051803e+118
9	-5.1104012668249873e-113	-2.112445118291879e-120	-5.047961066574088e-113
7	-7.472276120275499e-54	-4.459269101237006e-56	-4.576170092116779e-56
9	-1.838124499293251e+119	-1.1182452024942966e+113	-2.7569446232380357e+114

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	27	36
1	27	36

end0.0ms

sample362.0ms

Algorithm

intervals

Results

236.0ms

8000×

body

valid

Details

analyze86.0ms

sample14.0ms

simplify5.0ms

prune2.0ms

localize6.0ms

rewrite9.0ms

series13.0ms

simplify62.0ms

prune39.0ms

localize8.0ms

rewrite35.0ms

series40.0ms

simplify50.0ms

prune83.0ms

localize11.0ms

rewrite41.0ms

series50.0ms

simplify53.0ms

prune103.0ms

localize17.0ms

rewrite21.0ms

series58.0ms

simplify84.0ms

prune79.0ms

regimes487.0ms

bsearch41.0ms

simplify2.0ms

end0.0ms

sample362.0ms

Profiling