Details

sample45.0ms

Algorithm

intervals

Results

22.0ms	257×	body	80	valid
3.0ms	8×	body	640	valid
1.0ms	4×	body	320	valid
1.0ms	3×	body	160	valid
1.0ms	1×	body	1280	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

prune10.0ms

Filtered

1 candidates to 1 candidates (100.0%)

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: 15.5b

Counts

2 → 1

localize40.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (- (/ (+ m n) 2.0) M) 2.0)
0.0b	(* K (+ m n))
0.0b	(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
34.5b	(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:

10.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
6.0ms	(* K (+ m n))
21.0ms	(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
9.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

series522.0ms

Counts

4 → 12

Calls

4 calls:

260.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
24.0ms	(* K (+ m n))
181.0ms	(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
57.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

simplify43.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	435	667
1	1447	621
2	5002	620

prune295.0ms

Filtered

89 candidates to 60 candidates (67.4%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	85	4	89
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	86	4	90

Merged error: 1.0b

Counts

90 → 4

localize15.0ms

Local error

Found 2 expressions with local error:

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

rewrite35.0ms

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:

10.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
24.0ms	(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))

series461.0ms

Counts

2 → 6

Calls

2 calls:

271.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
189.0ms	(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))

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

prune137.0ms

Filtered

50 candidates to 34 candidates (68.0%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	50	0	50
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	50	4	54

Merged error: 1.0b

Counts

54 → 4

localize27.0ms

Local error

Found 4 expressions with local error:

16.4b	(cbrt (* K (+ m n)))
16.4b	(cbrt (* K (+ m n)))
16.4b	(cbrt (* K (+ m n)))
34.7b	(cos (- (/ (* (* (cbrt (* K (+ m n))) (cbrt (* K (+ m n)))) (cbrt (* K (+ m n)))) 2.0) M))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 43

Calls

4 calls:

4.0ms	(cbrt (* K (+ m n)))
4.0ms	(cbrt (* K (+ m n)))
4.0ms	(cbrt (* K (+ m n)))
13.0ms	(cos (- (/ (* (* (cbrt (* K (+ m n))) (cbrt (* K (+ m n)))) (cbrt (* K (+ m n)))) 2.0) M))

series373.0ms

Counts

4 → 12

Calls

4 calls:

105.0ms	(cbrt (* K (+ m n)))
109.0ms	(cbrt (* K (+ m n)))
105.0ms	(cbrt (* K (+ m n)))
54.0ms	(cos (- (/ (* (* (cbrt (* K (+ m n))) (cbrt (* K (+ m n)))) (cbrt (* K (+ m n)))) 2.0) M))

simplify52.0ms

Algorithm

egg-herbie

Counts

55 → 55

Iterations

Useful iterations: 4 (47.0ms)

Iter	Nodes	Cost
0	186	496
1	357	446
2	740	422
3	1608	419
4	5001	407

prune277.0ms

Filtered

55 candidates to 46 candidates (83.6%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	51	4	55
Fresh	1	1	2
Picked	1	0	1
Done	0	1	1
Total	53	6	59

Merged error: 1.0b

Counts

59 → 6

localize39.0ms

Local error

Found 4 expressions with local error:

16.4b	(cbrt (* K (+ m n)))
34.7b	(cos (- (/ (* (* (cbrt (* K (+ m n))) (cbrt (* K (+ m n)))) (cbrt (* K (+ m n)))) 2.0) M))
34.7b	(cos (- (/ (* (* (cbrt (* K (+ m n))) (cbrt (* K (+ m n)))) (cbrt (* K (+ m n)))) 2.0) M))
34.7b	(cos (- (/ (* (* (cbrt (* K (+ m n))) (cbrt (* K (+ m n)))) (cbrt (* K (+ m n)))) 2.0) M))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 41

Calls

4 calls:

5.0ms	(cbrt (* K (+ m n)))
10.0ms	(cos (- (/ (* (* (cbrt (* K (+ m n))) (cbrt (* K (+ m n)))) (cbrt (* K (+ m n)))) 2.0) M))
10.0ms	(cos (- (/ (* (* (cbrt (* K (+ m n))) (cbrt (* K (+ m n)))) (cbrt (* K (+ m n)))) 2.0) M))
10.0ms	(cos (- (/ (* (* (cbrt (* K (+ m n))) (cbrt (* K (+ m n)))) (cbrt (* K (+ m n)))) 2.0) M))

series283.0ms

Counts

4 → 12

Calls

4 calls:

107.0ms	(cbrt (* K (+ m n)))
59.0ms	(cos (- (/ (* (* (cbrt (* K (+ m n))) (cbrt (* K (+ m n)))) (cbrt (* K (+ m n)))) 2.0) M))
56.0ms	(cos (- (/ (* (* (cbrt (* K (+ m n))) (cbrt (* K (+ m n)))) (cbrt (* K (+ m n)))) 2.0) M))
60.0ms	(cos (- (/ (* (* (cbrt (* K (+ m n))) (cbrt (* K (+ m n)))) (cbrt (* K (+ m n)))) 2.0) M))

simplify56.0ms

Algorithm

egg-herbie

Counts

53 → 53

Iterations

Useful iterations: 4 (47.0ms)

Iter	Nodes	Cost
0	186	848
1	357	754
2	740	746
3	1608	745
4	5001	741

prune307.0ms

Filtered

53 candidates to 45 candidates (84.9%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	52	1	53
Fresh	1	3	4
Picked	0	1	1
Done	0	1	1
Total	53	6	59

Merged error: 1.0b

Counts

59 → 6

regimes242.0ms

Accuracy

0% (0.3b remaining)

Error of 1.5b against oracle of 1.2b and baseline of 1.5b

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

sample1.1s

Algorithm

intervals

Results

688.0ms	8075×	body	80	valid
61.0ms	121×	body	1280	valid
57.0ms	150×	body	640	valid
34.0ms	133×	body	320	valid
8.0ms	43×	body	160	valid
2.0ms	3×	body	2560	valid