Details

sample87.0ms

Algorithm

intervals

Results

30.0ms	88×	body	1280	valid
18.0ms	280×	body	80	valid
16.0ms	70×	body	640	valid
5.0ms	31×	body	320	valid
2.0ms	14×	body	160	valid

simplify19.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	26	7
1	57	6
2	87	6
3	114	6
4	132	6
5	151	6
6	171	6
7	173	6
8	173	6

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: 0.4b

Counts

2 → 2

localize10.0ms

Local error

Found 3 expressions with local error:

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

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

3×	`fma-udef`
2×	`-commutative` `associate-/l`
1×	`distribute-rgt-in` `frac-2neg` `distribute-lft-in` `clear-num` `div-inv`

Counts

3 → 9

Calls

3 calls:

1.0ms	(fma a1 a1 (* a2 a2))
2.0ms	(* (cos th) (fma a1 a1 (* a2 a2)))
4.0ms	(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt 2.0))

series349.0ms

Counts

3 → 9

Calls

3 calls:

33.0ms	(fma a1 a1 (* a2 a2))
108.0ms	(* (cos th) (fma a1 a1 (* a2 a2)))
208.0ms	(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt 2.0))

simplify111.0ms

Algorithm

egg-herbie

Counts

18 → 18

Iterations

Useful iterations: 3 (11.0ms)

Iter	Nodes	Cost
0	66	84
1	157	80
2	324	78
3	847	69
4	3374	69
5	5002	69

prune44.0ms

Filtered

18 candidates to 11 candidates (61.1%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	13	5	18
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	14	6	20

Merged error: 0.3b

Counts

20 → 6

localize10.0ms

Local error

Found 3 expressions with local error:

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

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

3×	`frac-2neg` `clear-num` `associate-/r/` `div-inv`
1×	`associate-/r*` `fma-udef`

Counts

3 → 11

Calls

3 calls:

1.0ms	(fma a1 a1 (* a2 a2))
2.0ms	(/ (sqrt 2.0) (cos th))
3.0ms	(/ (fma a1 a1 (* a2 a2)) (/ (sqrt 2.0) (cos th)))

series245.0ms

Counts

3 → 9

Calls

3 calls:

37.0ms	(fma a1 a1 (* a2 a2))
40.0ms	(/ (sqrt 2.0) (cos th))
168.0ms	(/ (fma a1 a1 (* a2 a2)) (/ (sqrt 2.0) (cos th)))

simplify32.0ms

Algorithm

egg-herbie

Counts

20 → 20

Iterations

Useful iterations: 3 (29.0ms)

Iter	Nodes	Cost
0	85	93
1	241	92
2	757	87
3	5002	77

prune51.0ms

Filtered

20 candidates to 11 candidates (55.0%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	16	4	20
Fresh	1	3	4
Picked	0	1	1
Done	1	0	1
Total	18	8	26

Merged error: 0.2b

Counts

26 → 8

localize11.0ms

Local error

Found 4 expressions with local error:

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

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

6×	`associate-*r/` `clear-num`
5×	`associate-/r/`
4×	`frac-2neg` `un-div-inv` `div-inv`
3×	`associate-/r*`
2×	`associate-r` `*-commutative`
1×	`fma-udef` `inv-pow`

Counts

4 → 23

Calls

4 calls:

1.0ms	(fma a1 a1 (* a2 a2))
2.0ms	(/ 1 (cos th))
4.0ms	(* (sqrt 2.0) (/ 1 (cos th)))
4.0ms	(/ (fma a1 a1 (* a2 a2)) (* (sqrt 2.0) (/ 1 (cos th))))

series256.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(fma a1 a1 (* a2 a2))
14.0ms	(/ 1 (cos th))
40.0ms	(* (sqrt 2.0) (/ 1 (cos th)))
168.0ms	(/ (fma a1 a1 (* a2 a2)) (* (sqrt 2.0) (/ 1 (cos th))))

simplify70.0ms

Algorithm

egg-herbie

Counts

35 → 35

Iterations

Useful iterations: 2 (14.0ms)

Iter	Nodes	Cost
0	110	126
1	473	120
2	2292	106
3	5002	106

prune61.0ms

Filtered

35 candidates to 15 candidates (42.9%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	33	2	35
Fresh	2	4	6
Picked	0	1	1
Done	0	1	1
Total	35	8	43

Merged error: 0.2b

Counts

43 → 8

localize10.0ms

Local error

Found 3 expressions with local error:

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

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

3×	`associate-*l/`
2×	`frac-2neg` `clear-num` `div-inv`
1×	`associate-l` `*-commutative` `fma-udef`

Counts

3 → 9

Calls

3 calls:

1.0ms	(fma a1 a1 (* a2 a2))
3.0ms	(* (/ (fma a1 a1 (* a2 a2)) (sqrt 2.0)) (cos th))
2.0ms	(/ (fma a1 a1 (* a2 a2)) (sqrt 2.0))

series300.0ms

Counts

3 → 9

Calls

3 calls:

34.0ms	(fma a1 a1 (* a2 a2))
167.0ms	(* (/ (fma a1 a1 (* a2 a2)) (sqrt 2.0)) (cos th))
99.0ms	(/ (fma a1 a1 (* a2 a2)) (sqrt 2.0))

simplify120.0ms

Algorithm

egg-herbie

Counts

18 → 18

Iterations

Useful iterations: 3 (22.0ms)

Iter	Nodes	Cost
0	53	81
1	187	81
2	757	79
3	3844	67
4	5001	67

prune30.0ms

Filtered

18 candidates to 9 candidates (50.0%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	17	1	18
Fresh	1	4	5
Picked	0	1	1
Done	0	2	2
Total	18	8	26

Merged error: 0.2b

Counts

26 → 8

regimes186.0ms

Accuracy

0% (0.2b 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	10	6

end0.0ms

sample2.4s

Algorithm

intervals

Results

865.0ms	2566×	body	1280	valid
497.0ms	2102×	body	640	valid
433.0ms	8126×	body	80	valid
172.0ms	1026×	body	320	valid
57.0ms	506×	body	160	valid