Details

analyze757.0ms

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
25%	74.9%	0.1%	6
25%	74.9%	0.1%	7
25%	74.9%	0.1%	8
25%	74.9%	0.1%	9
25%	64%	11.1%	10
31.2%	54.6%	14.2%	11
39%	44.1%	16.9%	12
39%	41.5%	19.5%	13
42.9%	37%	20.1%	14

sample88.0ms

Algorithm

intervals

Results

19.0ms	38×	body	1280	invalid
16.0ms	36×	body	1280	valid
12.0ms	39×	body	640	valid
11.0ms	158×	body	80	valid
9.0ms	30×	body	640	invalid
3.0ms	13×	body	320	invalid
3.0ms	13×	body	320	valid
1.0ms	10×	body	160	valid
1.0ms	14×	body	80	invalid
1.0ms	7×	body	160	invalid

simplify14.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (6.0ms)

Iter	Nodes	Cost
0	106	20
1	106	20

prune5.0ms

Filtered

1 candidates to 1 candidates (0.0%)

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: 0.3b

Counts

2 → 2

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b	(+.f64 (.f64 a1 a1) (.f64 a2 a2))
0.2b	(.f64 (cos.f64 th) (/.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (sqrt.f64 2)))
0.4b	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 2))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

40×	`add-sqr-sqrt_binary64`
38×	`times-frac_binary64`
32×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
22×	`associate-r_binary64` `sqrt-prod_binary64`
10×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
6×	`associate-/r*_binary64`
5×	`add-log-exp_binary64` `pow1_binary64`
3×	`associate-l_binary64` `unswap-sqr_binary64` `associate-/l*_binary64`
2×	`flip3-+_binary64` `associate-/l/_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `prod-exp_binary64` `div-inv_binary64` `div-exp_binary64` `flip-+_binary64`
1×	`pow-prod-down_binary64` `associate-r/_binary64` `clear-num_binary64` `frac-2neg_binary64` `+-commutative_binary64` `sum-log_binary64` `-commutative_binary64`

Counts

3 → 94

Calls

3 calls:

4.0ms	(+.f64 (.f64 a1 a1) (.f64 a2 a2))
12.0ms	(.f64 (cos.f64 th) (/.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (sqrt.f64 2)))
8.0ms	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 2))

series242.0ms

Counts

3 → 9

Calls

3 calls:

24.0ms	(+.f64 (.f64 a1 a1) (.f64 a2 a2))
168.0ms	(.f64 (cos.f64 th) (/.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (sqrt.f64 2)))
50.0ms	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 2))

simplify70.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5332	2380

prune108.0ms

Filtered

69 candidates to 103 candidates (-49.3%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	93	10	103
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	95	10	105

Merged error: 0b

Counts

105 → 10

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (cbrt.f64 (sqrt.f64 2)))
0.3b	(.f64 (/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (cbrt.f64 (sqrt.f64 2))))
5.2b	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
5.2b	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

149×	`add-sqr-sqrt_binary64`
146×	`times-frac_binary64`
127×	`sqrt-prod_binary64`
90×	`cbrt-prod_binary64`
87×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
58×	`associate-r_binary64`
27×	`add-exp-log_binary64`
21×	`unswap-sqr_binary64`
19×	`add-cbrt-cube_binary64`
10×	`associate-l_binary64`
9×	`associate-/r*_binary64`
8×	`pow1_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `prod-exp_binary64` `div-exp_binary64`
6×	`associate-/l*_binary64` `sqrt-div_binary64`
4×	`add-log-exp_binary64`
3×	`flip3-+_binary64` `div-inv_binary64` `flip-+_binary64`
2×	`associate-/l/_binary64` `pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64`
1×	`pow-prod-down_binary64` `associate-r/_binary64` `clear-num_binary64` `frac-2neg_binary64` `frac-times_binary64` `associate-l/_binary64` `*-commutative_binary64`

Counts

4 → 226

Calls

4 calls:

9.0ms	(/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (cbrt.f64 (sqrt.f64 2)))
34.0ms	(.f64 (/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (cbrt.f64 (sqrt.f64 2))))
4.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
4.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))

series235.0ms

Counts

4 → 12

Calls

4 calls:

118.0ms	(/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (cbrt.f64 (sqrt.f64 2)))
63.0ms	(.f64 (/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (cbrt.f64 (sqrt.f64 2))))
27.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
27.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))

simplify186.0ms

Algorithm

egg-herbie

Counts

238 → 238

Iterations

Useful iterations: 0 (113.0ms)

Iter	Nodes	Cost
0	4904	8058
1	4904	8058

prune244.0ms

Filtered

140 candidates to 238 candidates (-70.0%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	236	2	238
Fresh	2	7	9
Picked	0	1	1
Done	0	0	0
Total	238	10	248

Merged error: 0b

Counts

248 → 10

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (cbrt.f64 (sqrt.f64 2)))
0.3b	(.f64 (.f64 (/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (cos.f64 th)) (/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2))) (cbrt.f64 (sqrt.f64 2))))
5.2b	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
5.2b	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

108×	`times-frac_binary64`
102×	`sqrt-prod_binary64`
86×	`add-sqr-sqrt_binary64`
84×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
78×	`cbrt-prod_binary64`
58×	`associate-r_binary64`
38×	`add-exp-log_binary64`
29×	`add-cbrt-cube_binary64`
16×	`cbrt-unprod_binary64` `prod-exp_binary64`
11×	`pow1_binary64`
9×	`associate-/r*_binary64` `cbrt-undiv_binary64` `div-exp_binary64`
6×	`associate-/l*_binary64` `sqrt-div_binary64`
4×	`add-log-exp_binary64`
3×	`pow-prod-down_binary64` `flip3-+_binary64` `flip-+_binary64` `associate-*l/_binary64`
2×	`associate-/l/_binary64` `pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `div-inv_binary64`
1×	`associate-r/_binary64` `associate-l_binary64` `clear-num_binary64` `frac-2neg_binary64` `frac-times_binary64` `-commutative_binary64`

Counts

4 → 201

Calls

4 calls:

9.0ms	(/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (cbrt.f64 (sqrt.f64 2)))
29.0ms	(.f64 (.f64 (/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (cos.f64 th)) (/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2))) (cbrt.f64 (sqrt.f64 2))))
4.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
5.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))

series287.0ms

Counts

4 → 12

Calls

4 calls:

113.0ms	(/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (cbrt.f64 (sqrt.f64 2)))
121.0ms	(.f64 (.f64 (/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (cos.f64 th)) (/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2))) (cbrt.f64 (sqrt.f64 2))))
26.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
27.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))

simplify168.0ms

Algorithm

egg-herbie

Counts

213 → 213

Iterations

Useful iterations: 0 (102.0ms)

Iter	Nodes	Cost
0	4962	6998
1	4962	6998

prune222.0ms

Filtered

128 candidates to 213 candidates (-66.4%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	213	0	213
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	213	10	223

Merged error: 0b

Counts

223 → 10

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 a1 a1) (.f64 a2 a2))
0.2b	(.f64 (cos.f64 th) (/.f64 (/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (cbrt.f64 (sqrt.f64 2))) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))))
0.2b	(/.f64 (/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (cbrt.f64 (sqrt.f64 2))) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))))
0.3b	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (cbrt.f64 (sqrt.f64 2)))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

177×	`times-frac_binary64`
98×	`add-sqr-sqrt_binary64`
85×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
80×	`cbrt-prod_binary64`
40×	`sqrt-prod_binary64`
36×	`add-exp-log_binary64`
35×	`associate-r_binary64`
34×	`associate-/l*_binary64`
23×	`add-cbrt-cube_binary64`
13×	`cbrt-undiv_binary64` `div-exp_binary64`
10×	`associate-/r*_binary64`
9×	`cbrt-unprod_binary64` `prod-exp_binary64`
6×	`add-log-exp_binary64` `pow1_binary64` `div-inv_binary64`
5×	`unswap-sqr_binary64`
3×	`associate-/l/_binary64` `associate-l_binary64`
2×	`flip3-+_binary64` `clear-num_binary64` `frac-2neg_binary64` `flip-+_binary64`
1×	`pow-prod-down_binary64` `associate-r/_binary64` `+-commutative_binary64` `sum-log_binary64` `-commutative_binary64`

Counts

4 → 209

Calls

4 calls:

4.0ms	(+.f64 (.f64 a1 a1) (.f64 a2 a2))
23.0ms	(.f64 (cos.f64 th) (/.f64 (/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (cbrt.f64 (sqrt.f64 2))) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))))
16.0ms	(/.f64 (/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (cbrt.f64 (sqrt.f64 2))) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))))
9.0ms	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (cbrt.f64 (sqrt.f64 2)))

series362.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(+.f64 (.f64 a1 a1) (.f64 a2 a2))
161.0ms	(.f64 (cos.f64 th) (/.f64 (/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (cbrt.f64 (sqrt.f64 2))) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))))
53.0ms	(/.f64 (/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (cbrt.f64 (sqrt.f64 2))) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))))
124.0ms	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (cbrt.f64 (sqrt.f64 2)))

simplify137.0ms

Algorithm

egg-herbie

Counts

221 → 221

Iterations

Useful iterations: 0 (77.0ms)

Iter	Nodes	Cost
0	4938	6676
1	4938	6676

prune240.0ms

Filtered

156 candidates to 221 candidates (-41.7%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	221	0	221
Fresh	0	7	7
Picked	0	1	1
Done	0	2	2
Total	221	10	231

Merged error: 0b

Counts

231 → 10

regimes139.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 0.5b

bsearch0.0ms

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	20	52
1	20	52

end0.0ms

sample2.8s

Algorithm

intervals

Results

595.0ms	1359×	body	1280	valid
517.0ms	1190×	body	1280	invalid
349.0ms	1103×	body	640	valid
344.0ms	4714×	body	80	valid
289.0ms	956×	body	640	invalid
126.0ms	566×	body	320	valid
107.0ms	482×	body	320	invalid
40.0ms	518×	body	80	invalid
39.0ms	258×	body	160	valid
35.0ms	234×	body	160	invalid

Details

analyze757.0ms

sample88.0ms

simplify14.0ms

prune5.0ms

localize13.0ms

rewrite27.0ms

series242.0ms

simplify70.0ms

prune108.0ms

localize16.0ms

rewrite66.0ms

series235.0ms

simplify186.0ms

prune244.0ms

localize18.0ms

rewrite57.0ms

series287.0ms

simplify168.0ms

prune222.0ms

localize14.0ms

rewrite65.0ms

series362.0ms

simplify137.0ms

prune240.0ms

regimes139.0ms

bsearch0.0ms

simplify3.0ms

end0.0ms

sample2.8s

Profiling