Details

sample47.0ms

Algorithm

intervals

Results

25.0ms	260×	body	80	valid
2.0ms	4×	body	640	valid
1.0ms	4×	body	320	valid
0.0ms	2×	body	160	valid

simplify51.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 3 (9.0ms)

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 (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: 16.6b

Counts

2 → 2

localize27.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (- (/ (+ m n) 2.0) M) 2.0)
0.0b	(exp (- (neg (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n)))))
0.0b	(* K (+ m n))
32.9b	(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 77

Calls

4 calls:

10.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
21.0ms	(exp (- (neg (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n)))))
6.0ms	(* K (+ m n))
8.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

series486.0ms

Counts

4 → 12

Calls

4 calls:

276.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
124.0ms	(exp (- (neg (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n)))))
26.0ms	(* K (+ m n))
60.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

simplify51.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	437	613
1	1474	567
2	5001	562

prune326.0ms

Filtered

89 candidates to 62 candidates (69.7%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	85	4	89
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	87	4	91

Merged error: 0.9b

Counts

91 → 4

localize15.0ms

Local error

Found 3 expressions with local error:

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

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

28×	`*-un-lft-identity`
24×	`add-log-exp`
15×	`add-sqr-sqrt`
13×	`distribute-lft-out--`
12×	`diff-log`
8×	`exp-prod`
6×	`add-cube-cbrt` `unpow-prod-down`
5×	`rem-exp-log`
4×	`pow1` `add-exp-log` `distribute-rgt-neg-in` `neg-log` `difference-of-squares`
3×	`sub-neg` `pow-unpow` `exp-sum` `add-cbrt-cube`
2×	`associate--r+` `associate--r-`
1×	`associate--l-` `neg-sub0` `pow-to-exp` `flip3--` `pow-pow` `times-frac` `exp-diff` `pow-exp` `flip--` `sqr-pow`

Counts

3 → 68

Calls

3 calls:

22.0ms	(- (neg (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
10.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
21.0ms	(exp (- (neg (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n)))))

series569.0ms

Counts

3 → 9

Calls

3 calls:

184.0ms	(- (neg (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
267.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
118.0ms	(exp (- (neg (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n)))))

simplify36.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 2 (28.0ms)

Iter	Nodes	Cost
0	356	720
1	1112	675
2	5002	670

prune201.0ms

Filtered

77 candidates to 51 candidates (66.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	77	0	77
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	77	4	81

Merged error: 0.9b

Counts

81 → 4

localize30.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (+ m n))
0.6b	(cbrt (+ m n))
0.6b	(cbrt (+ m n))
33.5b	(cos (- (/ (* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (cbrt (+ m n))) 2.0) M))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

13×	`*-un-lft-identity`
12×	`cbrt-prod`
7×	`add-sqr-sqrt` `add-cube-cbrt`
6×	`cbrt-div`
4×	`pow1` `add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`flip3-+` `pow1/3` `flip-+` `distribute-lft-out`
2×	`cos-sum`
1×	`cos-diff` `sub-neg`

Counts

4 → 52

Calls

4 calls:

3.0ms	(cbrt (+ m n))
3.0ms	(cbrt (+ m n))
3.0ms	(cbrt (+ m n))
15.0ms	(cos (- (/ (* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (cbrt (+ m n))) 2.0) M))

series528.0ms

Counts

4 → 12

Calls

4 calls:

170.0ms	(cbrt (+ m n))
128.0ms	(cbrt (+ m n))
130.0ms	(cbrt (+ m n))
100.0ms	(cos (- (/ (* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (cbrt (+ m n))) 2.0) M))

simplify153.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 4 (146.0ms)

Iter	Nodes	Cost
0	186	485
1	416	445
2	1213	439
3	4532	439
4	5003	433

prune326.0ms

Filtered

64 candidates to 52 candidates (81.3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	61	3	64
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	62	6	68

Merged error: 0.9b

Counts

68 → 6

localize33.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (+ m n))
33.5b	(cos (- (/ (* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (cbrt (+ m n))) 2.0) M))
33.5b	(cos (- (/ (* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (cbrt (+ m n))) 2.0) M))
33.5b	(cos (- (/ (* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (cbrt (+ m n))) 2.0) M))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

7×	`*-un-lft-identity`
6×	`cos-sum`
5×	`add-sqr-sqrt` `add-cube-cbrt`
4×	`pow1` `add-exp-log` `cbrt-prod` `add-cbrt-cube` `add-log-exp`
3×	`cos-diff` `sub-neg`
2×	`cbrt-div`
1×	`flip3-+` `pow1/3` `flip-+` `distribute-lft-out`

Counts

4 → 44

Calls

4 calls:

3.0ms	(cbrt (+ m n))
19.0ms	(cos (- (/ (* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (cbrt (+ m n))) 2.0) M))
16.0ms	(cos (- (/ (* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (cbrt (+ m n))) 2.0) M))
16.0ms	(cos (- (/ (* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (cbrt (+ m n))) 2.0) M))

series430.0ms

Counts

4 → 12

Calls

4 calls:

127.0ms	(cbrt (+ m n))
100.0ms	(cos (- (/ (* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (cbrt (+ m n))) 2.0) M))
100.0ms	(cos (- (/ (* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (cbrt (+ m n))) 2.0) M))
101.0ms	(cos (- (/ (* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (cbrt (+ m n))) 2.0) M))

simplify165.0ms

Algorithm

egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 4 (157.0ms)

Iter	Nodes	Cost
0	186	759
1	416	679
2	1213	677
3	4532	677
4	5003	675

prune337.0ms

Filtered

56 candidates to 47 candidates (83.9%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	55	1	56
Fresh	1	3	4
Picked	1	0	1
Done	0	1	1
Total	57	5	62

Merged error: 0.9b

Counts

62 → 5

regimes199.0ms

Accuracy

0% (0.2b remaining)

Error of 1.2b against oracle of 1.0b and baseline of 1.2b

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

sample1.3s

Algorithm

intervals

Results

822.0ms	8082×	body	80	valid
68.0ms	113×	body	1280	valid
67.0ms	159×	body	640	valid
25.0ms	83×	body	320	valid
13.0ms	62×	body	160	valid
4.0ms	4×	body	2560	valid

Details

sample47.0ms

simplify51.0ms

prune13.0ms

localize27.0ms

rewrite47.0ms

series486.0ms

simplify51.0ms

prune326.0ms

localize15.0ms

rewrite55.0ms

series569.0ms

simplify36.0ms

prune201.0ms

localize30.0ms

rewrite25.0ms

series528.0ms

simplify153.0ms

prune326.0ms

localize33.0ms

rewrite55.0ms

series430.0ms

simplify165.0ms

prune337.0ms

regimes199.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample1.3s

Profiling