Details

sample105.0ms

Algorithm

intervals

Results

37.0ms	85×	body	1280	valid
17.0ms	246×	body	80	valid
17.0ms	57×	body	640	valid
9.0ms	39×	body	320	valid
3.0ms	15×	body	160	valid

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

prune12.0ms

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

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* a1 a1) (* a2 a2))
0.4b	(* (/ (cos th) (sqrt 2.0)) (+ (* a1 a1) (* a2 a2)))
0.7b	(/ (cos th) (sqrt 2.0))

rewrite22.0ms

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))
10.0ms	(* (/ (cos th) (sqrt 2.0)) (+ (* a1 a1) (* a2 a2)))
5.0ms	(/ (cos th) (sqrt 2.0))

series54.0ms

Counts

3 → 9

Calls

3 calls:

8.0ms	(+ (* a1 a1) (* a2 a2))
40.0ms	(* (/ (cos th) (sqrt 2.0)) (+ (* a1 a1) (* a2 a2)))
6.0ms	(/ (cos th) (sqrt 2.0))

simplify53.0ms

Algorithm

egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	490	872
1	2426	805
2	5001	791

prune201.0ms

Filtered

107 candidates to 75 candidates (29.9%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	99	8	107
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	100	8	108

Merged error: 0b

Counts

108 → 8

localize13.0ms

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)))
0.4b	(/ (+ (pow a2 2) (pow a1 2)) (sqrt 2.0))

rewrite44.0ms

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))
19.0ms	(* (cos th) (/ (+ (pow a2 2) (pow a1 2)) (sqrt 2.0)))
11.0ms	(/ (+ (pow a2 2) (pow a1 2)) (sqrt 2.0))

series57.0ms

Counts

3 → 9

Calls

3 calls:

6.0ms	(+ (pow a2 2) (pow a1 2))
39.0ms	(* (cos th) (/ (+ (pow a2 2) (pow a1 2)) (sqrt 2.0)))
12.0ms	(/ (+ (pow a2 2) (pow a1 2)) (sqrt 2.0))

simplify51.0ms

Algorithm

egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 2 (36.0ms)

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

prune243.0ms

Filtered

131 candidates to 70 candidates (46.6%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	130	1	131
Fresh	1	6	7
Picked	0	1	1
Done	0	0	0
Total	131	8	139

Merged error: 0b

Counts

139 → 8

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* a1 a1) (* a2 a2))
0.4b	(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (+ (* a1 a1) (* a2 a2)))
0.6b	(/ (cos th) (sqrt (sqrt 2.0)))
0.7b	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))

rewrite145.0ms

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))
57.0ms	(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (+ (* a1 a1) (* a2 a2)))
6.0ms	(/ (cos th) (sqrt (sqrt 2.0)))
16.0ms	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))

series65.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(+ (* a1 a1) (* a2 a2))
43.0ms	(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (+ (* a1 a1) (* a2 a2)))
9.0ms	(/ (cos th) (sqrt (sqrt 2.0)))
6.0ms	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))

simplify122.0ms

Algorithm

egg-herbie

Counts

729 → 729

Iterations

Useful iterations: 1 (38.0ms)

Iter	Nodes	Cost
0	1961	10436
1	5001	9573

prune1.6s

Filtered

729 candidates to 374 candidates (48.7%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	728	1	729
Fresh	1	5	6
Picked	0	1	1
Done	0	1	1
Total	729	8	737

Merged error: 0b

Counts

737 → 8

localize16.0ms

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))
4.3b	(sqrt (+ (* a1 a1) (* a2 a2)))
4.3b	(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:

13.0ms	(* (/ (cos th) (sqrt 2.0)) (sqrt (+ (* a1 a1) (* a2 a2))))
5.0ms	(/ (cos th) (sqrt 2.0))
3.0ms	(sqrt (+ (* a1 a1) (* a2 a2)))
4.0ms	(sqrt (+ (* a1 a1) (* a2 a2)))

series53.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(* (/ (cos th) (sqrt 2.0)) (sqrt (+ (* a1 a1) (* a2 a2))))
6.0ms	(/ (cos th) (sqrt 2.0))
6.0ms	(sqrt (+ (* a1 a1) (* a2 a2)))
6.0ms	(sqrt (+ (* a1 a1) (* a2 a2)))

simplify45.0ms

Algorithm

egg-herbie

Counts

133 → 133

Iterations

Useful iterations: 2 (31.0ms)

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

prune163.0ms

Filtered

133 candidates to 96 candidates (27.8%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	133	0	133
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	133	8	141

Merged error: 0b

Counts

141 → 8

regimes654.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.1b 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

sample3.3s

Algorithm

intervals

Results

1.1s	2598×	body	1280	valid
641.0ms	2079×	body	640	valid
589.0ms	8122×	body	80	valid
242.0ms	1076×	body	320	valid
77.0ms	484×	body	160	valid

Details

sample105.0ms

simplify14.0ms

prune12.0ms

localize11.0ms

rewrite22.0ms

series54.0ms

simplify53.0ms

prune201.0ms

localize13.0ms

rewrite44.0ms

series57.0ms

simplify51.0ms

prune243.0ms

localize13.0ms

rewrite145.0ms

series65.0ms

simplify122.0ms

prune1.6s

localize16.0ms

rewrite29.0ms

series53.0ms

simplify45.0ms

prune163.0ms

regimes654.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample3.3s

Profiling