Details

analyze2.1s

Algorithm

sampling

Space saved by range analysis: 0.146413%

Space saved by search: 21.379927%

Guaranteed chance to sample good point: 60.031008%

sample96.0ms

Algorithm

intervals

Results

19.0ms	43×	body	1280	valid
16.0ms	36×	body	1280	invalid
16.0ms	149×	body	80	valid
10.0ms	33×	body	640	valid
10.0ms	32×	body	640	invalid
4.0ms	18×	body	320	valid
3.0ms	14×	body	320	invalid
2.0ms	13×	body	160	valid
2.0ms	10×	body	160	invalid
1.0ms	11×	body	80	invalid

simplify14.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	25	7
1	50	7
2	77	7
3	96	7
4	112	7
5	127	7
6	141	7
7	141	7

prune8.0ms

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: 0.5b

Counts

2 → 1

localize10.0ms

Local error

Found 2 expressions with local error:

0.4b	(* (/ (cos th) (sqrt 2.0)) (+ (* a1 a1) (* a2 a2)))
0.7b	(/ (cos th) (sqrt 2.0))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

39×	`add-sqr-sqrt`
38×	`times-frac`
31×	`add-cube-cbrt` `*-un-lft-identity`
22×	`associate-l` `sqrt-prod`
9×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/r*`
4×	`pow1`
3×	`associate-r` `associate-/l*` `unswap-sqr`
2×	`cbrt-undiv` `frac-times` `flip3-+` `associate-*r/` `div-exp` `prod-exp` `cbrt-unprod` `flip-+` `div-inv` `add-log-exp`
1×	`distribute-rgt-in` `frac-2neg` `distribute-lft-in` `pow-prod-down` `associate-l/` `clear-num` `-commutative`

Counts

2 → 87

Calls

2 calls:

10.0ms	(* (/ (cos th) (sqrt 2.0)) (+ (* a1 a1) (* a2 a2)))
4.0ms	(/ (cos th) (sqrt 2.0))

series43.0ms

Counts

2 → 6

Calls

2 calls:

37.0ms	(* (/ (cos th) (sqrt 2.0)) (+ (* a1 a1) (* a2 a2)))
6.0ms	(/ (cos th) (sqrt 2.0))

simplify51.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	479	795
1	2384	738
2	5003	725

prune169.0ms

Filtered

64 candidates to 93 candidates (-45.3%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	85	8	93
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	86	8	94

Merged error: 0.0b

Counts

94 → 8

localize12.0ms

Local error

Found 3 expressions with local error:

0.4b	(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (+ (* a1 a1) (* a2 a2)))
0.6b	(/ (cos th) (sqrt (sqrt 2.0)))
0.6b	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))

rewrite134.0ms

Algorithm

rewrite-expression-head

Rules

1137×	`sqrt-prod`
1119×	`times-frac`
624×	`add-sqr-sqrt`
577×	`add-cube-cbrt` `*-un-lft-identity`
283×	`associate-l`
34×	`associate-/l*`
22×	`div-inv`
19×	`add-exp-log` `add-cbrt-cube`
18×	`associate-/r*`
13×	`unswap-sqr`
7×	`cbrt-undiv` `div-exp`
5×	`pow1`
3×	`associate-r` `prod-exp` `cbrt-unprod` `add-log-exp`
2×	`frac-times` `frac-2neg` `flip3-+` `associate-*r/` `clear-num` `flip-+`
1×	`distribute-rgt-in` `distribute-lft-in` `pow-prod-down` `associate-l/` `-commutative` `associate-/l/`

Counts

3 → 706

Calls

3 calls:

50.0ms	(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (+ (* a1 a1) (* a2 a2)))
5.0ms	(/ (cos th) (sqrt (sqrt 2.0)))
19.0ms	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))

series56.0ms

Counts

3 → 9

Calls

3 calls:

35.0ms	(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (+ (* a1 a1) (* a2 a2)))
15.0ms	(/ (cos th) (sqrt (sqrt 2.0)))
6.0ms	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))

simplify120.0ms

Algorithm

egg-herbie

Counts

715 → 715

Iterations

Useful iterations: 1 (39.0ms)

Iter	Nodes	Cost
0	1950	10359
1	5001	9505

prune1.4s

Filtered

363 candidates to 715 candidates (-97.0%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	713	2	715
Fresh	1	6	7
Picked	1	0	1
Done	0	0	0
Total	715	8	723

Merged error: 0b

Counts

723 → 8

localize16.0ms

Local error

Found 3 expressions with local error:

0.3b

(* (/ (/ 1 (sqrt (sqrt (sqrt 2.0)))) (sqrt (sqrt (sqrt 2.0)))) (* (/ (cos th) (sqrt (sqrt 2.0))) (+ (* a1 a1) (* a2 a2))))

0.4b

(* (/ (cos th) (sqrt (sqrt 2.0))) (+ (* a1 a1) (* a2 a2)))

0.6b

(/ (cos th) (sqrt (sqrt 2.0)))

rewrite167.0ms

Algorithm

rewrite-expression-head

Rules

1434×	`sqrt-prod`
969×	`times-frac`
517×	`add-sqr-sqrt`
515×	`associate-l`
506×	`add-cube-cbrt` `*-un-lft-identity`
70×	`add-exp-log`
46×	`add-cbrt-cube`
27×	`prod-exp`
25×	`div-exp`
17×	`cbrt-unprod`
15×	`div-inv`
14×	`cbrt-undiv`
11×	`frac-times` `associate-*r/`
10×	`pow1`
9×	`associate-/r*`
6×	`flip3-+` `flip-+`
5×	`distribute-rgt-in` `distribute-lft-in`
4×	`associate-r` `pow-prod-down` `associate-*l/` `unswap-sqr`
3×	`rec-exp` `1-exp` `associate-/l*` `add-log-exp`
2×	`*-commutative`
1×	`frac-2neg` `clear-num`

Counts

3 → 643

Calls

3 calls:

85.0ms

(* (/ (/ 1 (sqrt (sqrt (sqrt 2.0)))) (sqrt (sqrt (sqrt 2.0)))) (* (/ (cos th) (sqrt (sqrt 2.0))) (+ (* a1 a1) (* a2 a2))))

13.0ms

(* (/ (cos th) (sqrt (sqrt 2.0))) (+ (* a1 a1) (* a2 a2)))

5.0ms

(/ (cos th) (sqrt (sqrt 2.0)))

series90.0ms

Counts

3 → 9

Calls

3 calls:

35.0ms

(* (/ (/ 1 (sqrt (sqrt (sqrt 2.0)))) (sqrt (sqrt (sqrt 2.0)))) (* (/ (cos th) (sqrt (sqrt 2.0))) (+ (* a1 a1) (* a2 a2))))

47.0ms

(* (/ (cos th) (sqrt (sqrt 2.0))) (+ (* a1 a1) (* a2 a2)))

8.0ms

(/ (cos th) (sqrt (sqrt 2.0)))

simplify117.0ms

Algorithm

egg-herbie

Counts

652 → 652

Iterations

Useful iterations: 1 (36.0ms)

Iter	Nodes	Cost
0	1777	11278
1	5002	10388

prune2.4s

Filtered

377 candidates to 652 candidates (-72.9%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	652	0	652
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	652	8	660

Merged error: 0b

Counts

660 → 8

localize12.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (/ (cos th) (sqrt 2.0)) (sqrt (+ (* a1 a1) (* a2 a2))))
0.7b	(/ (cos th) (sqrt 2.0))
5.1b	(sqrt (+ (* a1 a1) (* a2 a2)))
5.1b	(sqrt (+ (* a1 a1) (* a2 a2)))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

54×	`add-sqr-sqrt`
40×	`times-frac`
36×	`add-cube-cbrt` `*-un-lft-identity`
35×	`sqrt-prod`
22×	`associate-l`
11×	`add-exp-log` `add-cbrt-cube`
8×	`pow1` `sqrt-div`
6×	`associate-r` `associate-/r*` `unswap-sqr`
4×	`flip3-+` `flip-+` `add-log-exp`
3×	`associate-/l*`
2×	`cbrt-undiv` `frac-times` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-*r/` `div-exp` `prod-exp` `cbrt-unprod` `div-inv`
1×	`frac-2neg` `pow-prod-down` `associate-l/` `clear-num` `-commutative`

Counts

4 → 121

Calls

4 calls:

12.0ms	(* (/ (cos th) (sqrt 2.0)) (sqrt (+ (* a1 a1) (* a2 a2))))
4.0ms	(/ (cos th) (sqrt 2.0))
3.0ms	(sqrt (+ (* a1 a1) (* a2 a2)))
5.0ms	(sqrt (+ (* a1 a1) (* a2 a2)))

series47.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(* (/ (cos th) (sqrt 2.0)) (sqrt (+ (* a1 a1) (* a2 a2))))
5.0ms	(/ (cos th) (sqrt 2.0))
6.0ms	(sqrt (+ (* a1 a1) (* a2 a2)))
6.0ms	(sqrt (+ (* a1 a1) (* a2 a2)))

simplify43.0ms

Algorithm

egg-herbie

Counts

133 → 133

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	352	1093
1	1256	1042
2	5001	1028

prune152.0ms

Filtered

96 candidates to 133 candidates (-38.5%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	133	0	133
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	133	8	141

Merged error: 0b

Counts

141 → 8

regimes538.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	17
1	22	17

end0.0ms

analyze2.1s

Algorithm

sampling

Space saved by range analysis: 0.146413%

Space saved by search: 21.379927%

Guaranteed chance to sample good point: 60.031008%

sample3.0s

Algorithm

intervals

Results

842.0ms	1401×	body	1280	valid
503.0ms	1114×	body	1280	invalid
367.0ms	1149×	body	640	valid
347.0ms	4644×	body	80	valid
303.0ms	979×	body	640	invalid
119.0ms	525×	body	320	valid
105.0ms	460×	body	320	invalid
43.0ms	281×	body	160	valid
41.0ms	269×	body	160	invalid
27.0ms	326×	body	80	invalid

Details

analyze2.1s

sample96.0ms

simplify14.0ms

prune8.0ms

localize10.0ms

rewrite18.0ms

series43.0ms

simplify51.0ms

prune169.0ms

localize12.0ms

rewrite134.0ms

series56.0ms

simplify120.0ms

prune1.4s

localize16.0ms

rewrite167.0ms

series90.0ms

simplify117.0ms

prune2.4s

localize12.0ms

rewrite29.0ms

series47.0ms

simplify43.0ms

prune152.0ms

regimes538.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

analyze2.1s

sample3.0s

Profiling