Details

analyze2.3s

Algorithm

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
12.5%	87.3%	0.2%	9
12.5%	87.3%	0.2%	10
18.7%	81.1%	0.2%	11
18.7%	81.1%	0.2%	12
18.7%	81.1%	0.2%	13
20.5%	79.3%	0.2%	14

sample48.0ms

Algorithm

intervals

Results

26.0ms	249×	body	80	valid
2.0ms	4×	body	640	invalid
2.0ms	4×	body	640	valid
1.0ms	9×	body	80	invalid
1.0ms	2×	body	320	valid
1.0ms	2×	body	320	invalid
1.0ms	1×	body	1280	invalid
0.0ms	1×	body	160	valid
0.0ms	1×	body	160	invalid

simplify44.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4986	28
1	4986	28

prune16.0ms

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: 13.7b

Counts

2 → 1

localize19.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (pow (- (/ (+ m n) 2.0) M) 2.0) l)
0.0b	(pow (- (/ (+ m n) 2.0) M) 2.0)
33.8b	(cos (- (* K (/ (+ m n) 2.0)) M))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
9×	`*-un-lft-identity`
6×	`unpow-prod-down`
5×	`add-cube-cbrt` `add-log-exp`
4×	`pow1` `add-exp-log`
3×	`pow-unpow` `add-cbrt-cube`
2×	`difference-of-squares`
1×	`+-commutative` `cos-diff` `pow-to-exp` `sub-neg` `cos-sum` `pow-pow` `flip3-+` `times-frac` `pow-exp` `sum-log` `flip-+` `distribute-lft-out` `distribute-lft-out--` `sqr-pow`

Counts

3 → 41

Calls

3 calls:

13.0ms	(+ (pow (- (/ (+ m n) 2.0) M) 2.0) l)
10.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
7.0ms	(cos (- (* K (/ (+ m n) 2.0)) M))

series93.0ms

Counts

3 → 9

Calls

3 calls:

34.0ms	(+ (pow (- (/ (+ m n) 2.0) M) 2.0) l)
40.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
19.0ms	(cos (- (* K (/ (+ m n) 2.0)) M))

simplify52.0ms

Algorithm

egg-herbie

Counts

50 → 50

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4960	668
1	4960	668

prune128.0ms

Filtered

39 candidates to 50 candidates (-28.2%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	46	4	50
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	47	4	51

Merged error: 1.6b

Counts

51 → 4

localize13.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (pow (- (/ (+ m n) 2.0) M) 2.0) l)
0.0b	(pow (- (/ (+ m n) 2.0) M) 2.0)

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-sqr-sqrt`
8×	`*-un-lft-identity`
6×	`unpow-prod-down`
4×	`add-cube-cbrt` `add-log-exp`
3×	`pow1` `add-exp-log` `pow-unpow`
2×	`add-cbrt-cube` `difference-of-squares`
1×	`+-commutative` `pow-to-exp` `pow-pow` `flip3-+` `times-frac` `pow-exp` `sum-log` `flip-+` `distribute-lft-out` `distribute-lft-out--` `sqr-pow`

Counts

2 → 32

Calls

2 calls:

13.0ms	(+ (pow (- (/ (+ m n) 2.0) M) 2.0) l)
10.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

series74.0ms

Counts

2 → 6

Calls

2 calls:

34.0ms	(+ (pow (- (/ (+ m n) 2.0) M) 2.0) l)
39.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

simplify73.0ms

Algorithm

egg-herbie

Counts

38 → 38

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	4878	512
1	4878	512

prune80.0ms

Filtered

28 candidates to 38 candidates (-35.7%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	38	0	38
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	38	4	42

Merged error: 1.6b

Counts

42 → 4

localize23.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (cos (- (* K (/ (+ m n) 2.0)) M)))
33.8b	(cos (- (* K (/ (+ m n) 2.0)) M))
33.8b	(cos (- (* K (/ (+ m n) 2.0)) M))
33.8b	(cos (- (* K (/ (+ m n) 2.0)) M))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

5×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`cbrt-prod` `cos-diff` `sub-neg` `cos-sum`
1×	`pow1/3`

Counts

4 → 38

Calls

4 calls:

2.0ms	(cbrt (cos (- (* K (/ (+ m n) 2.0)) M)))
8.0ms	(cos (- (* K (/ (+ m n) 2.0)) M))
8.0ms	(cos (- (* K (/ (+ m n) 2.0)) M))
8.0ms	(cos (- (* K (/ (+ m n) 2.0)) M))

series116.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(cbrt (cos (- (* K (/ (+ m n) 2.0)) M)))
19.0ms	(cos (- (* K (/ (+ m n) 2.0)) M))
21.0ms	(cos (- (* K (/ (+ m n) 2.0)) M))
20.0ms	(cos (- (* K (/ (+ m n) 2.0)) M))

simplify57.0ms

Algorithm

egg-herbie

Counts

50 → 50

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4967	618
1	4967	618

prune196.0ms

Filtered

43 candidates to 50 candidates (-16.3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	47	3	50
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	48	6	54

Merged error: 1.6b

Counts

54 → 6

localize31.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (* (cos (* K (/ (+ m n) 2.0))) (cos M)) (* (sin (* K (/ (+ m n) 2.0))) (sin M)))
0.3b	(* (sin (* K (/ (+ m n) 2.0))) (sin M))
38.9b	(cos (* K (/ (+ m n) 2.0)))
39.1b	(sin (* K (/ (+ m n) 2.0)))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
6×	`pow1` `add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `add-log-exp`
3×	`associate-r` `associate-l`
2×	`sin-mult`
1×	`+-commutative` `flip3-+` `pow-prod-down` `frac-add` `prod-exp` `sum-log` `cos-mult` `*-commutative` `cbrt-unprod` `flip-+` `unswap-sqr`

Counts

4 → 45

Calls

4 calls:

6.0ms	(+ (* (cos (* K (/ (+ m n) 2.0))) (cos M)) (* (sin (* K (/ (+ m n) 2.0))) (sin M)))
5.0ms	(* (sin (* K (/ (+ m n) 2.0))) (sin M))
2.0ms	(cos (* K (/ (+ m n) 2.0)))
2.0ms	(sin (* K (/ (+ m n) 2.0)))

series76.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(+ (* (cos (* K (/ (+ m n) 2.0))) (cos M)) (* (sin (* K (/ (+ m n) 2.0))) (sin M)))
18.0ms	(* (sin (* K (/ (+ m n) 2.0))) (sin M))
7.0ms	(cos (* K (/ (+ m n) 2.0)))
9.0ms	(sin (* K (/ (+ m n) 2.0)))

simplify57.0ms

Algorithm

egg-herbie

Counts

57 → 57

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5029	897

prune126.0ms

Filtered

46 candidates to 57 candidates (-23.9%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	56	1	57
Fresh	0	4	4
Picked	1	0	1
Done	0	1	1
Total	57	6	63

Merged error: 1.6b

Counts

63 → 6

regimes431.0ms

Accuracy

0% (0.2b remaining)

Error of 1.5b against oracle of 1.3b and baseline of 1.5b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	61	17
1	61	17

end0.0ms

sample1.4s

Algorithm

intervals

Results

855.0ms	7802×	body	80	valid
53.0ms	88×	body	1280	invalid
41.0ms	84×	body	640	valid
32.0ms	52×	body	1280	valid
31.0ms	293×	body	80	invalid
30.0ms	71×	body	640	invalid
21.0ms	67×	body	320	invalid
13.0ms	42×	body	320	valid
8.0ms	39×	body	160	invalid
5.0ms	20×	body	160	valid
1.0ms	1×	body	2560	invalid

Details

analyze2.3s

sample48.0ms

simplify44.0ms

prune16.0ms

localize19.0ms

rewrite31.0ms

series93.0ms

simplify52.0ms

prune128.0ms

localize13.0ms

rewrite24.0ms

series74.0ms

simplify73.0ms

prune80.0ms

localize23.0ms

rewrite26.0ms

series116.0ms

simplify57.0ms

prune196.0ms

localize31.0ms

rewrite16.0ms

series76.0ms

simplify57.0ms

prune126.0ms

regimes431.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample1.4s

Profiling