Details

sample43.0ms

Algorithm

intervals

Results

22.0ms	263×	body	80	valid
1.0ms	5×	body	320	valid
1.0ms	3×	body	640	valid
1.0ms	1×	body	1280	valid
1.0ms	4×	body	160	valid

simplify49.0ms

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

prune15.0ms

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: 13.4b

Counts

2 → 2

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
0.0b	(* K (+ m n))
0.0b	(pow (- (/ (+ m n) 2.0) M) 2.0)
33.5b	(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 77

Calls

4 calls:

20.0ms	(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
6.0ms	(* K (+ m n))
10.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
8.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

series527.0ms

Counts

4 → 12

Calls

4 calls:

185.0ms	(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
24.0ms	(* K (+ m n))
263.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
55.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

simplify44.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	435	667
1	1447	621
2	5001	620

prune296.0ms

Filtered

89 candidates to 60 candidates (67.4%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	85	4	89
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	86	5	91

Merged error: 0.8b

Counts

91 → 5

localize14.0ms

Local error

Found 2 expressions with local error:

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

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 44

Calls

2 calls:

20.0ms	(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
14.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

series443.0ms

Counts

2 → 6

Calls

2 calls:

181.0ms	(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
262.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

simplify80.0ms

Algorithm

egg-herbie

Counts

50 → 50

Iterations

Useful iterations: 3 (74.0ms)

Iter	Nodes	Cost
0	277	469
1	798	444
2	3368	435
3	5001	432

prune138.0ms

Filtered

50 candidates to 34 candidates (68.0%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	50	0	50
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	50	5	55

Merged error: 0.8b

Counts

55 → 5

localize25.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))
0.0b	(* K (+ m n))
0.0b	(pow (- (/ (+ m n) 2.0) M) 2.0)
33.5b	(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 70

Calls

4 calls:

16.0ms	(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))
6.0ms	(* K (+ m n))
10.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
8.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

series517.0ms

Counts

4 → 12

Calls

4 calls:

175.0ms	(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))
24.0ms	(* K (+ m n))
262.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
55.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

simplify41.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	411	566
1	1369	528
2	5001	523

prune263.0ms

Filtered

82 candidates to 58 candidates (70.7%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	80	2	82
Fresh	2	1	3
Picked	1	0	1
Done	0	1	1
Total	83	4	87

Merged error: 0.8b

Counts

87 → 4

localize30.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt K)
0.6b	(cbrt K)
0.6b	(cbrt K)
33.4b	(cos (- (/ (* (* (cbrt K) (cbrt K)) (* (cbrt K) (+ m n))) 2.0) M))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 43

Calls

4 calls:

1.0ms	(cbrt K)
1.0ms	(cbrt K)
1.0ms	(cbrt K)
13.0ms	(cos (- (/ (* (* (cbrt K) (cbrt K)) (* (cbrt K) (+ m n))) 2.0) M))

series627.0ms

Counts

4 → 12

Calls

4 calls:

175.0ms	(cbrt K)
180.0ms	(cbrt K)
173.0ms	(cbrt K)
98.0ms	(cos (- (/ (* (* (cbrt K) (cbrt K)) (* (cbrt K) (+ m n))) 2.0) M))

simplify97.0ms

Algorithm

egg-herbie

Counts

55 → 55

Iterations

Useful iterations: 2 (9.0ms)

Iter	Nodes	Cost
0	111	309
1	265	279
2	681	273
3	3070	273
4	5001	273

prune277.0ms

Filtered

55 candidates to 46 candidates (83.6%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	52	3	55
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	53	6	59

Merged error: 0.8b

Counts

59 → 6

regimes218.0ms

Accuracy

0% (0.2b remaining)

Error of 1.3b against oracle of 1.0b and baseline of 1.3b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

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

end0.0ms

sample1.2s

Algorithm

intervals

Results

710.0ms	8104×	body	80	valid
68.0ms	124×	body	1280	valid
53.0ms	145×	body	640	valid
29.0ms	106×	body	320	valid
12.0ms	63×	body	160	valid
1.0ms	1×	body	2560	valid