Details

analyze2.4s

Algorithm: search

sample57.0ms

Algorithm

intervals

Results

33.0ms	253×	body	80	valid
1.0ms	2×	body	1280	invalid
1.0ms	3×	body	640	invalid
1.0ms	2×	body	640	valid
1.0ms	8×	body	80	invalid
1.0ms	1×	body	1280	valid
0.0ms	2×	body	160	invalid
0.0ms	1×	body	320	invalid

simplify50.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 3 (8.0ms)

Iter	Nodes	Cost
0	50	16
1	93	16
2	200	16
3	517	15
4	1893	15
5	5001	15

prune13.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 14.0b

Counts

2 → 1

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b	(- l (fabs (- m n)))
0.0b	(pow (- (/ (+ m n) 2.0) M) 2.0)
0.0b	(* K (+ m n))
33.2b	(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt`
14×	`*-un-lft-identity`
8×	`add-cube-cbrt`
7×	`pow1` `add-exp-log`
6×	`unpow-prod-down` `add-cbrt-cube` `add-log-exp`
4×	`associate-r`
3×	`pow-unpow` `associate-l` `difference-of-squares`
2×	`sub-neg` `cos-sum` `associate-*r/` `distribute-lft-out--`
1×	`distribute-rgt-in` `cos-diff` `pow-to-exp` `flip3--` `pow-pow` `distribute-lft-in` `flip3-+` `times-frac` `diff-log` `pow-prod-down` `pow-exp` `prod-exp` `*-commutative` `flip--` `cbrt-unprod` `flip-+` `distribute-lft-out` `unswap-sqr` `sqr-pow`

Counts

4 → 67

Calls

4 calls:

3.0ms	(- l (fabs (- m n)))
11.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
10.0ms	(* K (+ m n))
8.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

series73.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(- l (fabs (- m n)))
41.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
6.0ms	(* K (+ m n))
21.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

simplify115.0ms

Algorithm

egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	387	467
1	1218	434
2	4673	430
3	5003	430

prune181.0ms

Filtered

55 candidates to 79 candidates (-43.6%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	75	4	79
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	76	4	80

Merged error: 0.6b

Counts

80 → 4

localize18.0ms

Local error

Found 2 expressions with local error:

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

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

11×	`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` `difference-of-squares`
2×	`add-cbrt-cube` `distribute-lft-out--`
1×	`pow-to-exp` `sub-neg` `flip3--` `pow-pow` `times-frac` `diff-log` `pow-exp` `flip--` `sqr-pow`

Counts

2 → 34

Calls

2 calls:

3.0ms	(- l (fabs (- m n)))
11.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

series45.0ms

Counts

2 → 6

Calls

2 calls:

4.0ms	(- l (fabs (- m n)))
40.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

simplify53.0ms

Algorithm

egg-herbie

Counts

40 → 40

Iterations

Useful iterations: 3 (48.0ms)

Iter	Nodes	Cost
0	228	270
1	578	258
2	1858	253
3	5001	245

prune91.0ms

Filtered

28 candidates to 40 candidates (-42.9%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	40	0	40
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	40	4	44

Merged error: 0.6b

Counts

44 → 4

localize26.0ms

Local error

Found 4 expressions with local error:

0.0b	(* K (+ m n))
0.6b	(cbrt (pow (cos (- (/ (* K (+ m n)) 2.0) M)) 3))
0.6b	(pow (cos (- (/ (* K (+ m n)) 2.0) M)) 3)
33.2b	(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt` `*-un-lft-identity`
12×	`cbrt-prod` `add-cube-cbrt`
7×	`pow1` `add-exp-log` `add-cbrt-cube`
6×	`unpow-prod-down` `cube-prod`
4×	`associate-r` `add-log-exp`
3×	`pow-unpow` `associate-l`
2×	`cube-mult` `cos-sum` `unpow3` `associate-*r/` `sqr-pow`
1×	`distribute-rgt-in` `cos-diff` `pow-to-exp` `sub-neg` `pow-pow` `distribute-lft-in` `flip3-+` `pow1/3` `pow-prod-down` `pow-exp` `prod-exp` `*-commutative` `rem-cbrt-cube` `cbrt-unprod` `flip-+` `distribute-lft-out` `rem-cube-cbrt` `unswap-sqr`

Counts

4 → 77

Calls

4 calls:

6.0ms	(* K (+ m n))
3.0ms	(cbrt (pow (cos (- (/ (* K (+ m n)) 2.0) M)) 3))
3.0ms	(pow (cos (- (/ (* K (+ m n)) 2.0) M)) 3)
8.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

series102.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(* K (+ m n))
21.0ms	(cbrt (pow (cos (- (/ (* K (+ m n)) 2.0) M)) 3))
53.0ms	(pow (cos (- (/ (* K (+ m n)) 2.0) M)) 3)
21.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

simplify40.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	256	621
1	995	580
2	5001	574

prune185.0ms

Filtered

52 candidates to 89 candidates (-71.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	88	1	89
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	89	4	93

Merged error: 0.6b

Counts

93 → 4

localize36.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (cos (- (/ (* K (+ m n)) 2.0) M)))
33.2b	(cos (- (/ (* K (+ m n)) 2.0) M))
33.2b	(cos (- (/ (* K (+ m n)) 2.0) M))
33.2b	(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

6×	`cos-sum`
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`
1×	`pow1/3`

Counts

4 → 41

Calls

4 calls:

2.0ms	(cbrt (cos (- (/ (* K (+ m n)) 2.0) M)))
9.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))
9.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))
9.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

series121.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(cbrt (cos (- (/ (* K (+ m n)) 2.0) M)))
23.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))
20.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))
21.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

simplify63.0ms

Algorithm

egg-herbie

Counts

53 → 53

Iterations

Useful iterations: 2 (6.0ms)

Iter	Nodes	Cost
0	86	463
1	132	417
2	213	415
3	406	415
4	1373	415
5	5001	415

prune214.0ms

Filtered

44 candidates to 53 candidates (-20.5%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	51	2	53
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	52	5	57

Merged error: 0.6b

Counts

57 → 5

regimes440.0ms

Accuracy

0% (0.2b remaining)

Error of 1.3b against oracle of 1.1b and baseline of 1.3b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	10
1	23	10
2	23	10

end0.0ms

analyze2.6s

Algorithm: search

sample1.4s

Algorithm

intervals

Results

880.0ms	7830×	body	80	valid
58.0ms	87×	body	1280	invalid
46.0ms	89×	body	640	invalid
30.0ms	64×	body	640	valid
28.0ms	262×	body	80	invalid
27.0ms	41×	body	1280	valid
26.0ms	69×	body	320	invalid
14.0ms	41×	body	320	valid
9.0ms	42×	body	160	invalid
6.0ms	24×	body	160	valid
4.0ms	4×	body	2560	invalid

Details

analyze2.4s

sample57.0ms

simplify50.0ms

prune13.0ms

localize23.0ms

rewrite34.0ms

series73.0ms

simplify115.0ms

prune181.0ms

localize18.0ms

rewrite15.0ms

series45.0ms

simplify53.0ms

prune91.0ms

localize26.0ms

rewrite22.0ms

series102.0ms

simplify40.0ms

prune185.0ms

localize36.0ms

rewrite28.0ms

series121.0ms

simplify63.0ms

prune214.0ms

regimes440.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

analyze2.6s

sample1.4s

Profiling