Details

sample77.0ms

Algorithm

intervals

Results

28.0ms	91×	body	1280	valid
17.0ms	74×	body	640	valid
12.0ms	253×	body	80	valid
3.0ms	20×	body	320	valid
1.0ms	13×	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: 0.3b

Counts

2 → 2

localize15.0ms

Local error

Found 2 expressions with local error:

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

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

Counts

2 → 8

Calls

2 calls:

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

series314.0ms

Counts

2 → 6

Calls

2 calls:

105.0ms	(* (cos th) (fma a1 a1 (* a2 a2)))
209.0ms	(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt 2.0))

simplify115.0ms

Algorithm

egg-herbie

Counts

14 → 14

Iterations

Useful iterations: 3 (11.0ms)

Iter	Nodes	Cost
0	66	77
1	157	73
2	324	71
3	847	62
4	3374	62
5	5002	62

prune43.0ms

Filtered

14 candidates to 10 candidates (71.4%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	9	5	14
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	11	5	16

Merged error: 0.2b

Counts

16 → 5

localize10.0ms

Local error

Found 2 expressions with local error:

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

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 10

Calls

2 calls:

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

series215.0ms

Counts

2 → 6

Calls

2 calls:

44.0ms	(/ (sqrt 2.0) (cos th))
170.0ms	(/ (fma a1 a1 (* a2 a2)) (/ (sqrt 2.0) (cos th)))

simplify33.0ms

Algorithm

egg-herbie

Counts

16 → 16

Iterations

Useful iterations: 3 (30.0ms)

Iter	Nodes	Cost
0	83	86
1	238	85
2	755	80
3	5002	70

prune44.0ms

Filtered

16 candidates to 10 candidates (62.5%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	14	2	16
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	14	7	21

Merged error: 0.2b

Counts

21 → 7

localize15.0ms

Local error

Found 3 expressions with local error:

0.4b	(/ (fma a1 a1 (* a2 a2)) (/ 1 (/ (cos th) (sqrt 2.0))))
0.6b	(/ 1 (/ (cos th) (sqrt 2.0)))
0.7b	(/ (cos th) (sqrt 2.0))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 23

Calls

3 calls:

4.0ms	(/ (fma 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))

series276.0ms

Counts

3 → 9

Calls

3 calls:

174.0ms	(/ (fma a1 a1 (* a2 a2)) (/ 1 (/ (cos th) (sqrt 2.0))))
45.0ms	(/ 1 (/ (cos th) (sqrt 2.0)))
57.0ms	(/ (cos th) (sqrt 2.0))

simplify74.0ms

Algorithm

egg-herbie

Counts

32 → 32

Iterations

Useful iterations: 3 (71.0ms)

Iter	Nodes	Cost
0	115	134
1	401	132
2	2177	117
3	5002	116

prune77.0ms

Filtered

32 candidates to 19 candidates (59.4%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	31	1	32
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	32	7	39

Merged error: 0.2b

Counts

39 → 7

localize11.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ 1 (cos th))
0.2b	(/ (/ (fma a1 a1 (* a2 a2)) (sqrt 2.0)) (/ 1 (cos th)))
0.4b	(/ (fma a1 a1 (* a2 a2)) (sqrt 2.0))

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

7×	`div-inv`
5×	`frac-2neg` `clear-num`
3×	`associate-/r/` `associate-/l/`
1×	`times-frac` `associate-/r` `associate-/l` `inv-pow`

Counts

3 → 19

Calls

3 calls:

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

series289.0ms

Counts

3 → 9

Calls

3 calls:

11.0ms	(/ 1 (cos th))
173.0ms	(/ (/ (fma a1 a1 (* a2 a2)) (sqrt 2.0)) (/ 1 (cos th)))
105.0ms	(/ (fma a1 a1 (* a2 a2)) (sqrt 2.0))

simplify86.0ms

Algorithm

egg-herbie

Counts

28 → 28

Iterations

Useful iterations: 3 (83.0ms)

Iter	Nodes	Cost
0	110	137
1	416	128
2	2238	126
3	5001	122

prune57.0ms

Filtered

28 candidates to 16 candidates (57.1%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	26	2	28
Fresh	1	3	4
Picked	1	0	1
Done	0	2	2
Total	28	7	35

Merged error: 0.2b

Counts

35 → 7

regimes198.0ms

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	10	6

end0.0ms

sample2.2s

Algorithm

intervals

Results

822.0ms	2560×	body	1280	valid
449.0ms	2073×	body	640	valid
408.0ms	8000×	body	80	valid
164.0ms	1043×	body	320	valid
53.0ms	509×	body	160	valid