Details

sample84.0ms

Algorithm

intervals

Results

29.0ms	88×	body	1280	valid
19.0ms	89×	body	640	valid
12.0ms	245×	body	80	valid
5.0ms	35×	body	320	valid
2.0ms	21×	body	160	valid

simplify17.0ms

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 (100.0%)

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: 0.7b

Counts

2 → 2

localize16.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* a1 a1) (* a2 a2))
0.6b	(* (/ (cos th) (sqrt 2.0)) (+ (* a1 a1) (* a2 a2)))
0.7b	(/ (cos th) (sqrt 2.0))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 98

Calls

3 calls:

4.0ms	(+ (* a1 a1) (* a2 a2))
11.0ms	(* (/ (cos th) (sqrt 2.0)) (+ (* a1 a1) (* a2 a2)))
5.0ms	(/ (cos th) (sqrt 2.0))

series310.0ms

Counts

3 → 9

Calls

3 calls:

26.0ms	(+ (* a1 a1) (* a2 a2))
218.0ms	(* (/ (cos th) (sqrt 2.0)) (+ (* a1 a1) (* a2 a2)))
65.0ms	(/ (cos th) (sqrt 2.0))

simplify57.0ms

Algorithm

egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	490	872
1	2426	805
2	5003	791

prune279.0ms

Filtered

107 candidates to 74 candidates (69.2%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	101	6	107
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	102	7	109

Merged error: 0.3b

Counts

109 → 7

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (pow a2 2) (pow a1 2))
0.2b	(* (cos th) (/ (+ (pow a2 2) (pow a1 2)) (sqrt 2.0)))
0.6b	(/ (+ (pow a2 2) (pow a1 2)) (sqrt 2.0))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

96×	`*-un-lft-identity`
62×	`times-frac`
48×	`add-sqr-sqrt`
40×	`add-cube-cbrt`
34×	`associate-r` `sqrt-prod`
28×	`unpow-prod-down` `distribute-lft-out`
10×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/r*`
5×	`pow1` `associate-/l*` `add-log-exp`
3×	`associate-l` `unswap-sqr`
2×	`cbrt-undiv` `flip3-+` `div-exp` `prod-exp` `cbrt-unprod` `flip-+` `div-inv` `associate-/l/`
1×	`+-commutative` `frac-2neg` `associate-r/` `pow-prod-down` `clear-num` `sum-log` `-commutative`

Counts

3 → 122

Calls

3 calls:

7.0ms	(+ (pow a2 2) (pow a1 2))
18.0ms	(* (cos th) (/ (+ (pow a2 2) (pow a1 2)) (sqrt 2.0)))
12.0ms	(/ (+ (pow a2 2) (pow a1 2)) (sqrt 2.0))

series338.0ms

Counts

3 → 9

Calls

3 calls:

27.0ms	(+ (pow a2 2) (pow a1 2))
217.0ms	(* (cos th) (/ (+ (pow a2 2) (pow a1 2)) (sqrt 2.0)))
93.0ms	(/ (+ (pow a2 2) (pow a1 2)) (sqrt 2.0))

simplify51.0ms

Algorithm

egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	344	1118
1	1557	1023
2	5001	1018

prune256.0ms

Filtered

131 candidates to 70 candidates (53.4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	129	2	131
Fresh	2	3	5
Picked	0	1	1
Done	1	0	1
Total	132	6	138

Merged error: 0.3b

Counts

138 → 6

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* a1 a1) (* a2 a2))
0.6b	(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (+ (* a1 a1) (* a2 a2)))
0.6b	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
0.6b	(/ (cos th) (sqrt (sqrt 2.0)))

rewrite151.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 717

Calls

4 calls:

4.0ms	(+ (* a1 a1) (* a2 a2))
55.0ms	(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (+ (* a1 a1) (* a2 a2)))
22.0ms	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
6.0ms	(/ (cos th) (sqrt (sqrt 2.0)))

series611.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(+ (* a1 a1) (* a2 a2))
417.0ms	(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (+ (* a1 a1) (* a2 a2)))
58.0ms	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
108.0ms	(/ (cos th) (sqrt (sqrt 2.0)))

simplify132.0ms

Algorithm

egg-herbie

Counts

729 → 729

Iterations

Useful iterations: 1 (44.0ms)

Iter	Nodes	Cost
0	1961	10436
1	5001	9573

prune1.5s

Filtered

729 candidates to 374 candidates (51.3%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	729	0	729
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	729	6	735

Merged error: 0.3b

Counts

735 → 6

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (pow a2 2) (pow a1 2))
0.2b	(* (cos th) (/ (/ (+ (pow a2 2) (pow a1 2)) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))))
0.2b	(/ (/ (+ (pow a2 2) (pow a1 2)) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
0.5b	(/ (+ (pow a2 2) (pow a1 2)) (sqrt (sqrt 2.0)))

rewrite291.0ms

Algorithm

rewrite-expression-head

Rules

1821×	`sqrt-prod`
1803×	`times-frac`
1534×	`*-un-lft-identity`
853×	`add-sqr-sqrt`
806×	`add-cube-cbrt`
445×	`associate-r`
364×	`unpow-prod-down` `distribute-lft-out`
54×	`associate-/l*`
22×	`div-inv`
20×	`add-exp-log` `add-cbrt-cube`
18×	`associate-/r*`
13×	`unswap-sqr`
7×	`cbrt-undiv` `div-exp`
6×	`pow1` `add-log-exp`
3×	`associate-l` `prod-exp` `cbrt-unprod` `associate-/l/`
2×	`frac-2neg` `flip3-+` `clear-num` `flip-+`
1×	`+-commutative` `associate-r/` `pow-prod-down` `sum-log` `-commutative`

Counts

4 → 1077

Calls

4 calls:

8.0ms	(+ (pow a2 2) (pow a1 2))
118.0ms	(* (cos th) (/ (/ (+ (pow a2 2) (pow a1 2)) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))))
29.0ms	(/ (/ (+ (pow a2 2) (pow a1 2)) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
13.0ms	(/ (+ (pow a2 2) (pow a1 2)) (sqrt (sqrt 2.0)))

series499.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(+ (pow a2 2) (pow a1 2))
216.0ms	(* (cos th) (/ (/ (+ (pow a2 2) (pow a1 2)) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))))
96.0ms	(/ (/ (+ (pow a2 2) (pow a1 2)) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
159.0ms	(/ (+ (pow a2 2) (pow a1 2)) (sqrt (sqrt 2.0)))

simplify195.0ms

Algorithm

egg-herbie

Counts

1089 → 1089

Iterations

Useful iterations: 1 (41.0ms)

Iter	Nodes	Cost
0	1824	16929
1	5001	14723

prune1.2s

Filtered

1089 candidates to 289 candidates (26.5%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	1089	0	1089
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	1089	6	1095

Merged error: 0.3b

Counts

1095 → 6

regimes230.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 0.5b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	7
1	14	7

end0.0ms

sample2.2s

Algorithm

intervals

Results

804.0ms	2509×	body	1280	valid
448.0ms	2065×	body	640	valid
390.0ms	7918×	body	80	valid
163.0ms	1063×	body	320	valid
58.0ms	500×	body	160	valid