Details

sample42.0ms

Algorithm

intervals

Results

22.0ms	264×	body	80	valid
2.0ms	4×	body	1280	valid
1.0ms	3×	body	640	valid
1.0ms	3×	body	160	valid
0.0ms	1×	body	320	valid

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

prune12.0ms

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: 14.3b

Counts

2 → 1

localize22.0ms

Local error

Found 4 expressions with local error:

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

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

24×	`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`
5×	`difference-of-squares`
4×	`associate-r`
3×	`pow-unpow` `times-frac` `associate-l`
2×	`+-commutative` `distribute-rgt-in` `sub-neg` `cos-sum` `distribute-lft-in` `associate-*r/` `distribute-lft-out--` `unswap-sqr`
1×	`cos-diff` `pow-to-exp` `flip3--` `pow-pow` `flip3-+` `diff-log` `pow-prod-down` `pow-exp` `prod-exp` `*-commutative` `flip--` `cbrt-unprod` `flip-+` `distribute-lft-out` `sqr-pow`

Counts

4 → 71

Calls

4 calls:

6.0ms	(* K (+ m n))
24.0ms	(- (/ (* K (+ m n)) 2.0) M)
10.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
23.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

series409.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(* K (+ m n))
56.0ms	(- (/ (* K (+ m n)) 2.0) M)
271.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
54.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

simplify40.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	383	519
1	1254	481
2	5001	477

prune267.0ms

Filtered

83 candidates to 59 candidates (28.9%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	78	5	83
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	79	5	84

Merged error: 1.1b

Counts

84 → 5

localize15.0ms

Local error

Found 3 expressions with local error:

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

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 59

Calls

3 calls:

14.0ms	(- (/ (+ m n) 2.0) M)
21.0ms	(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
10.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

series483.0ms

Counts

3 → 9

Calls

3 calls:

30.0ms	(- (/ (+ m n) 2.0) M)
186.0ms	(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
266.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

simplify100.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 3 (93.0ms)

Iter	Nodes	Cost
0	327	577
1	978	545
2	4160	531
3	5003	528

prune175.0ms

Filtered

68 candidates to 47 candidates (30.9%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	68	0	68
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	68	5	73

Merged error: 1.1b

Counts

73 → 5

localize27.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ (+ (* K m) (* K n)) 2.0) M)
0.0b	(pow (- (/ (+ m n) 2.0) M) 2.0)
1.6b	(+ (* K m) (* K n))
32.9b	(cos (- (/ (+ (* K m) (* K n)) 2.0) M))

rewrite83.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 65

Calls

4 calls:

31.0ms	(- (/ (+ (* K m) (* K n)) 2.0) M)
10.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
12.0ms	(+ (* K m) (* K n))
28.0ms	(cos (- (/ (+ (* K m) (* K n)) 2.0) M))

series413.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(- (/ (+ (* K m) (* K n)) 2.0) M)
264.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
35.0ms	(+ (* K m) (* K n))
53.0ms	(cos (- (/ (+ (* K m) (* K n)) 2.0) M))

simplify101.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 3 (94.0ms)

Iter	Nodes	Cost
0	372	540
1	1025	496
2	3624	487
3	5002	480

prune262.0ms

Filtered

77 candidates to 56 candidates (27.3%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	74	3	77
Fresh	3	0	3
Picked	0	1	1
Done	0	1	1
Total	77	5	82

Merged error: 1.1b

Counts

82 → 5

localize29.0ms

Local error

Found 4 expressions with local error:

1.6b	(+ (* K m) (* K n))
32.9b	(cos (- (/ (+ (* K m) (* K n)) 2.0) M))
32.9b	(cos (- (/ (+ (* K m) (* K n)) 2.0) M))
32.9b	(cos (- (/ (+ (* K m) (* K n)) 2.0) M))

rewrite105.0ms

Algorithm

rewrite-expression-head

Rules

14×	`*-un-lft-identity`
8×	`associate-l` `distribute-lft-out`
6×	`add-sqr-sqrt` `add-cube-cbrt` `cos-sum` `add-log-exp`
4×	`pow1` `add-exp-log` `add-cbrt-cube`
3×	`cos-diff` `sub-neg`
2×	`associate-r` `*-commutative`
1×	`+-commutative` `distribute-rgt-out` `flip3-+` `sum-log` `flip-+`

Counts

4 → 50

Calls

4 calls:

15.0ms	(+ (* K m) (* K n))
29.0ms	(cos (- (/ (+ (* K m) (* K n)) 2.0) M))
29.0ms	(cos (- (/ (+ (* K m) (* K n)) 2.0) M))
32.0ms	(cos (- (/ (+ (* K m) (* K n)) 2.0) M))

series200.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(+ (* K m) (* K n))
53.0ms	(cos (- (/ (+ (* K m) (* K n)) 2.0) M))
57.0ms	(cos (- (/ (+ (* K m) (* K n)) 2.0) M))
54.0ms	(cos (- (/ (+ (* K m) (* K n)) 2.0) M))

simplify135.0ms

Algorithm

egg-herbie

Counts

62 → 62

Iterations

Useful iterations: 2 (15.0ms)

Iter	Nodes	Cost
0	157	473
1	425	423
2	1321	421
3	3843	421
4	5001	421

prune282.0ms

Filtered

62 candidates to 48 candidates (22.6%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	59	3	62
Fresh	1	1	2
Picked	1	0	1
Done	1	1	2
Total	62	5	67

Merged error: 1.1b

Counts

67 → 5

regimes211.0ms

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

sample1.1s

Algorithm

intervals

Results

673.0ms	8116×	body	80	valid
58.0ms	154×	body	640	valid
51.0ms	101×	body	1280	valid
30.0ms	101×	body	320	valid
9.0ms	52×	body	160	valid
2.0ms	2×	body	2560	valid