Details

sample83.0ms

Algorithm

intervals

Results

32.0ms	88×	body	1280	valid
15.0ms	70×	body	640	valid
14.0ms	280×	body	80	valid
5.0ms	31×	body	320	valid
2.0ms	14×	body	160	valid

simplify18.0ms

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

prune6.0ms

Filtered

1 candidates to 1 candidates (100.0%)

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))
0.3b	(* (/ (cos th) (sqrt 2.0)) (+ (* a1 a1) (* a2 a2)))
0.7b	(/ (cos th) (sqrt 2.0))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

6×	`frac-times`
5×	`flip3-+` `flip-+`
4×	`frac-2neg` `clear-num`
3×	`+-commutative` `associate-*l/`
2×	`distribute-rgt-in` `distribute-lft-in` `associate-*r/` `div-inv`
1×	`associate-l` `*-commutative`

Counts

3 → 23

Calls

3 calls:

4.0ms	(+ (* a1 a1) (* a2 a2))
7.0ms	(* (/ (cos th) (sqrt 2.0)) (+ (* a1 a1) (* a2 a2)))
3.0ms	(/ (cos th) (sqrt 2.0))

series293.0ms

Counts

3 → 9

Calls

3 calls:

26.0ms	(+ (* a1 a1) (* a2 a2))
206.0ms	(* (/ (cos th) (sqrt 2.0)) (+ (* a1 a1) (* a2 a2)))
61.0ms	(/ (cos th) (sqrt 2.0))

simplify34.0ms

Algorithm

egg-herbie

Counts

32 → 32

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	250	268
1	1126	250
2	5002	243

prune116.0ms

Filtered

32 candidates to 23 candidates (71.9%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	22	10	32
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	22	11	33

Merged error: 0.2b

Counts

33 → 11

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* a1 a1) (* a2 a2))
0.2b	(/ (sqrt 2.0) (cos th))
0.4b	(/ (+ (* a1 a1) (* a2 a2)) (/ (sqrt 2.0) (cos th)))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

3×	`frac-2neg` `clear-num` `associate-/r/` `div-inv`
2×	`flip3-+` `flip-+` `associate-/l/`
1×	`+-commutative` `associate-/r*`

Counts

3 → 15

Calls

3 calls:

4.0ms	(+ (* a1 a1) (* a2 a2))
2.0ms	(/ (sqrt 2.0) (cos th))
9.0ms	(/ (+ (* a1 a1) (* a2 a2)) (/ (sqrt 2.0) (cos th)))

series228.0ms

Counts

3 → 9

Calls

3 calls:

26.0ms	(+ (* a1 a1) (* a2 a2))
44.0ms	(/ (sqrt 2.0) (cos th))
158.0ms	(/ (+ (* a1 a1) (* a2 a2)) (/ (sqrt 2.0) (cos th)))

simplify59.0ms

Algorithm

egg-herbie

Counts

24 → 24

Iterations

Useful iterations: 2 (15.0ms)

Iter	Nodes	Cost
0	151	146
1	570	139
2	1758	136
3	5002	136

prune91.0ms

Filtered

24 candidates to 17 candidates (70.8%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	19	5	24
Fresh	4	5	9
Picked	1	0	1
Done	0	1	1
Total	24	11	35

Merged error: 0.1b

Counts

35 → 11

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* a1 a1) (* a2 a2))
0.4b	(/ (+ (* a1 a1) (* a2 a2)) (/ 1 (/ (cos th) (sqrt 2.0))))
0.7b	(/ 1 (/ (cos th) (sqrt 2.0)))
0.7b	(/ (cos th) (sqrt 2.0))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

10×	`associate-/r/`
7×	`clear-num`
6×	`frac-2neg` `associate-/r*` `div-inv`
2×	`flip3-+` `flip-+` `associate-/l/`
1×	`+-commutative` `remove-double-div` `inv-pow`

Counts

4 → 28

Calls

4 calls:

4.0ms	(+ (* a1 a1) (* a2 a2))
7.0ms	(/ (+ (* a1 a1) (* a2 a2)) (/ 1 (/ (cos th) (sqrt 2.0))))
3.0ms	(/ 1 (/ (cos th) (sqrt 2.0)))
3.0ms	(/ (cos th) (sqrt 2.0))

series287.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(+ (* a1 a1) (* a2 a2))
160.0ms	(/ (+ (* a1 a1) (* a2 a2)) (/ 1 (/ (cos th) (sqrt 2.0))))
41.0ms	(/ 1 (/ (cos th) (sqrt 2.0)))
59.0ms	(/ (cos th) (sqrt 2.0))

simplify150.0ms

Algorithm

egg-herbie

Counts

40 → 40

Iterations

Useful iterations: 3 (143.0ms)

Iter	Nodes	Cost
0	183	200
1	771	189
2	4097	178
3	5001	177

prune113.0ms

Filtered

40 candidates to 25 candidates (62.5%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	37	3	40
Fresh	3	6	9
Picked	0	1	1
Done	0	1	1
Total	40	11	51

Merged error: 0.1b

Counts

51 → 11

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* a1 a1) (* a2 a2))
0.1b	(/ 1 (cos th))
0.3b	(* (/ 1 (cos th)) (sqrt 2.0))
0.4b	(/ (+ (* a1 a1) (* a2 a2)) (* (/ 1 (cos th)) (sqrt 2.0)))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

6×	`associate-*l/`
4×	`frac-2neg` `clear-num` `div-inv`
3×	`associate-/r*` `associate-/r/`
2×	`flip3-+` `associate-l` `*-commutative` `flip-+` `associate-/l/`
1×	`+-commutative` `inv-pow`

Counts

4 → 23

Calls

4 calls:

4.0ms	(+ (* a1 a1) (* a2 a2))
2.0ms	(/ 1 (cos th))
4.0ms	(* (/ 1 (cos th)) (sqrt 2.0))
8.0ms	(/ (+ (* a1 a1) (* a2 a2)) (* (/ 1 (cos th)) (sqrt 2.0)))

series253.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(+ (* a1 a1) (* a2 a2))
11.0ms	(/ 1 (cos th))
50.0ms	(* (/ 1 (cos th)) (sqrt 2.0))
163.0ms	(/ (+ (* a1 a1) (* a2 a2)) (* (/ 1 (cos th)) (sqrt 2.0)))

simplify139.0ms

Algorithm

egg-herbie

Counts

35 → 35

Iterations

Useful iterations: 2 (24.0ms)

Iter	Nodes	Cost
0	175	174
1	827	162
2	3952	152
3	5001	152

prune78.0ms

Filtered

35 candidates to 24 candidates (68.6%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	33	2	35
Fresh	1	7	8
Picked	0	1	1
Done	1	1	2
Total	35	11	46

Merged error: 0.1b

Counts

46 → 11

regimes360.0ms

Accuracy

0% (0.3b remaining)

Error of 0.5b against oracle of 0.2b and baseline of 0.5b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	8
1	17	8

end0.0ms

sample2.3s

Algorithm

intervals

Results

847.0ms	2566×	body	1280	valid
462.0ms	2102×	body	640	valid
409.0ms	8126×	body	80	valid
162.0ms	1026×	body	320	valid
53.0ms	506×	body	160	valid