Details

sample77.0ms

Algorithm

intervals

Results

29.0ms	91×	body	1280	valid
16.0ms	74×	body	640	valid
12.0ms	253×	body	80	valid
3.0ms	20×	body	320	valid
1.0ms	13×	body	160	valid

simplify16.0ms

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

localize10.0ms

Local error

Found 2 expressions with local error:

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

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 20

Calls

2 calls:

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

series274.0ms

Counts

2 → 6

Calls

2 calls:

211.0ms	(* (/ (cos th) (sqrt 2.0)) (+ (* a1 a1) (* a2 a2)))
63.0ms	(/ (cos th) (sqrt 2.0))

simplify32.0ms

Algorithm

egg-herbie

Counts

26 → 26

Iterations

Useful iterations: 2 (28.0ms)

Iter	Nodes	Cost
0	248	235
1	1137	221
2	5001	214

prune96.0ms

Filtered

26 candidates to 21 candidates (80.8%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	18	8	26
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	19	8	27

Merged error: 0.2b

Counts

27 → 8

localize11.0ms

Local error

Found 2 expressions with local error:

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

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 12

Calls

2 calls:

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

series208.0ms

Counts

2 → 6

Calls

2 calls:

45.0ms	(/ (sqrt 2.0) (cos th))
163.0ms	(/ (+ (* a1 a1) (* a2 a2)) (/ (sqrt 2.0) (cos th)))

simplify47.0ms

Algorithm

egg-herbie

Counts

18 → 18

Iterations

Useful iterations: 3 (45.0ms)

Iter	Nodes	Cost
0	133	113
1	499	110
2	1481	107
3	5002	99

prune68.0ms

Filtered

18 candidates to 14 candidates (77.8%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	15	3	18
Fresh	2	5	7
Picked	0	1	1
Done	0	0	0
Total	17	9	26

Merged error: 0.1b

Counts

26 → 9

localize12.0ms

Local error

Found 2 expressions with local error:

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

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 22

Calls

2 calls:

5.0ms	(* (- (cos th)) (+ (* a1 a1) (* a2 a2)))
8.0ms	(/ (* (- (cos th)) (+ (* a1 a1) (* a2 a2))) (- (sqrt 2.0)))

series337.0ms

Counts

2 → 6

Calls

2 calls:

124.0ms	(* (- (cos th)) (+ (* a1 a1) (* a2 a2)))
213.0ms	(/ (* (- (cos th)) (+ (* a1 a1) (* a2 a2))) (- (sqrt 2.0)))

simplify56.0ms

Algorithm

egg-herbie

Counts

28 → 28

Iterations

Useful iterations: 3 (52.0ms)

Iter	Nodes	Cost
0	198	200
1	691	198
2	2149	186
3	5001	185

prune98.0ms

Filtered

28 candidates to 22 candidates (78.6%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	26	2	28
Fresh	2	5	7
Picked	1	0	1
Done	0	1	1
Total	29	8	37

Merged error: 0.1b

Counts

37 → 8

localize11.0ms

Local error

Found 3 expressions with local error:

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

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

9×	`associate-/l/`
7×	`div-inv`
5×	`frac-2neg` `clear-num`
3×	`associate-/r/`
2×	`flip3-+` `flip-+`
1×	`times-frac` `associate-/r` `associate-/l` `inv-pow`

Counts

3 → 23

Calls

3 calls:

2.0ms	(/ 1 (cos th))
7.0ms	(/ (/ (+ (* a1 a1) (* a2 a2)) (sqrt 2.0)) (/ 1 (cos th)))
6.0ms	(/ (+ (* a1 a1) (* a2 a2)) (sqrt 2.0))

series275.0ms

Counts

3 → 9

Calls

3 calls:

11.0ms	(/ 1 (cos th))
171.0ms	(/ (/ (+ (* a1 a1) (* a2 a2)) (sqrt 2.0)) (/ 1 (cos th)))
92.0ms	(/ (+ (* a1 a1) (* a2 a2)) (sqrt 2.0))

simplify155.0ms

Algorithm

egg-herbie

Counts

32 → 32

Iterations

Useful iterations: 1 (6.0ms)

Iter	Nodes	Cost
0	165	187
1	753	172
2	4037	172
3	5001	172

prune73.0ms

Filtered

32 candidates to 21 candidates (65.6%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	30	2	32
Fresh	1	5	6
Picked	1	0	1
Done	0	1	1
Total	32	8	40

Merged error: 0.1b

Counts

40 → 8

regimes226.0ms

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	12	7
1	12	7

end0.0ms

sample2.2s

Algorithm

intervals

Results

809.0ms	2560×	body	1280	valid
453.0ms	2073×	body	640	valid
399.0ms	8000×	body	80	valid
162.0ms	1043×	body	320	valid
57.0ms	509×	body	160	valid