Details

analyze775.0ms

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

sample98.0ms

Algorithm

intervals

Results

23.0ms	50×	body	1280	valid
21.0ms	38×	body	1280	invalid
12.0ms	155×	body	80	valid
10.0ms	33×	body	640	invalid
8.0ms	25×	body	640	valid
5.0ms	20×	body	320	valid
3.0ms	15×	body	320	invalid
2.0ms	21×	body	80	invalid
1.0ms	6×	body	160	valid
0.0ms	3×	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

prune4.0ms

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

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(+.f64 (.f64 a1 a1) (.f64 a2 a2))
0.1b	(.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))

rewrite26.0ms

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))
11.0ms	(.f64 (cos.f64 th) (/.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (sqrt.f64 2)))
7.0ms	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 2))

series235.0ms

Counts

3 → 9

Calls

3 calls:

22.0ms	(+.f64 (.f64 a1 a1) (.f64 a2 a2))
155.0ms	(.f64 (cos.f64 th) (/.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (sqrt.f64 2)))
57.0ms	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 2))

simplify67.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5332	2380

prune97.0ms

Filtered

69 candidates to 103 candidates (-49.3%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	96	7	103
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	97	8	105

Merged error: 0.0b

Counts

105 → 8

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (/.f64 (sqrt.f64 2) (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))))
0.4b	(/.f64 (sqrt.f64 2) (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))))
6.8b	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
6.8b	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

540×	`times-frac_binary64`
429×	`sqrt-prod_binary64`
297×	`add-sqr-sqrt_binary64`
295×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
48×	`associate-/r*_binary64`
22×	`sqrt-div_binary64`
17×	`associate-/r/_binary64`
12×	`associate-/l*_binary64`
11×	`flip3-+_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `flip-+_binary64`
9×	`div-inv_binary64`
6×	`pow1_binary64`
4×	`add-log-exp_binary64` `cbrt-undiv_binary64` `div-exp_binary64`
3×	`sqrt-undiv_binary64`
2×	`associate-/l/_binary64` `pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64`

Counts

4 → 411

Calls

4 calls:

20.0ms	(/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (/.f64 (sqrt.f64 2) (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))))
8.0ms	(/.f64 (sqrt.f64 2) (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))))
4.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
4.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))

series148.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (/.f64 (sqrt.f64 2) (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))))
42.0ms	(/.f64 (sqrt.f64 2) (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))))
22.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
26.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))

simplify217.0ms

Algorithm

egg-herbie

Counts

423 → 423

Iterations

Useful iterations: 0 (71.0ms)

Iter	Nodes	Cost
0	5058	17836

prune214.0ms

Filtered

163 candidates to 423 candidates (-159.5%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	423	0	423
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	423	8	431

Merged error: 0.0b

Counts

431 → 8

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 a1 a1) (.f64 a2 a2))
0.1b	(.f64 (cos.f64 th) (/.f64 (/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (cbrt.f64 (sqrt.f64 2))))
0.2b	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))))
0.3b	(/.f64 (/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (cbrt.f64 (sqrt.f64 2)))

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

195×	`times-frac_binary64`
111×	`add-sqr-sqrt_binary64`
94×	`cbrt-prod_binary64`
91×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
67×	`associate-r_binary64`
47×	`sqrt-prod_binary64`
32×	`add-exp-log_binary64`
22×	`div-inv_binary64`
20×	`add-cbrt-cube_binary64`
12×	`cbrt-undiv_binary64` `div-exp_binary64`
10×	`associate-/r_binary64` `associate-/l_binary64`
7×	`cbrt-unprod_binary64` `unswap-sqr_binary64` `prod-exp_binary64`
6×	`add-log-exp_binary64` `pow1_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 → 225

Calls

4 calls:

4.0ms	(+.f64 (.f64 a1 a1) (.f64 a2 a2))
27.0ms	(.f64 (cos.f64 th) (/.f64 (/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (cbrt.f64 (sqrt.f64 2))))
11.0ms	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))))
14.0ms	(/.f64 (/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (cbrt.f64 (sqrt.f64 2)))

series413.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(+.f64 (.f64 a1 a1) (.f64 a2 a2))
156.0ms	(.f64 (cos.f64 th) (/.f64 (/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (cbrt.f64 (sqrt.f64 2))))
175.0ms	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))))
57.0ms	(/.f64 (/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (cbrt.f64 (sqrt.f64 2)))

simplify146.0ms

Algorithm

egg-herbie

Counts

237 → 237

Iterations

Useful iterations: 0 (75.0ms)

Iter	Nodes	Cost
0	4959	8081
1	4959	8081

prune297.0ms

Filtered

172 candidates to 237 candidates (-37.8%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	236	1	237
Fresh	2	4	6
Picked	0	1	1
Done	0	1	1
Total	238	7	245

Merged error: 0b

Counts

245 → 7

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(+.f64 (.f64 a1 a1) (.f64 a2 a2))
0.1b	(.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (cos.f64 th))
0.4b	(/.f64 (.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (cos.f64 th)) (sqrt.f64 2))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 60

Calls

3 calls:

7.0ms	(+.f64 (.f64 a1 a1) (.f64 a2 a2))
7.0ms	(.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (cos.f64 th))
9.0ms	(/.f64 (.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (cos.f64 th)) (sqrt.f64 2))

series206.0ms

Counts

3 → 9

Calls

3 calls:

20.0ms	(+.f64 (.f64 a1 a1) (.f64 a2 a2))
71.0ms	(.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (cos.f64 th))
115.0ms	(/.f64 (.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (cos.f64 th)) (sqrt.f64 2))

simplify83.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	4957	1303
1	4957	1303

prune45.0ms

Filtered

48 candidates to 69 candidates (-43.8%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	69	0	69
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	69	7	76

Merged error: 0b

Counts

76 → 7

regimes104.0ms

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	16	36
1	16	36

end0.0ms

sample2.8s

Algorithm

intervals

Results

604.0ms	1313×	body	1280	valid
524.0ms	1141×	body	1280	invalid
369.0ms	4776×	body	80	valid
352.0ms	1093×	body	640	valid
326.0ms	1003×	body	640	invalid
123.0ms	541×	body	320	valid
123.0ms	519×	body	320	invalid
43.0ms	277×	body	160	valid
41.0ms	499×	body	80	invalid
32.0ms	206×	body	160	invalid

Details

analyze775.0ms

sample98.0ms

simplify14.0ms

prune4.0ms

localize10.0ms

rewrite26.0ms

series235.0ms

simplify67.0ms

prune97.0ms

localize13.0ms

rewrite67.0ms

series148.0ms

simplify217.0ms

prune214.0ms

localize13.0ms

rewrite69.0ms

series413.0ms

simplify146.0ms

prune297.0ms

localize10.0ms

rewrite24.0ms

series206.0ms

simplify83.0ms

prune45.0ms

regimes104.0ms

bsearch0.0ms

simplify3.0ms

end0.0ms

sample2.8s

Profiling