Details

sample64.0ms

Algorithm

intervals

Results

30.0ms	263×	body	80	valid
3.0ms	5×	body	1280	valid
1.0ms	5×	body	320	valid
1.0ms	3×	body	640	valid

simplify48.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 3 (7.0ms)

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 (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 15.8b

Counts

2 → 1

localize21.0ms

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)
35.0b	(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite44.0ms

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

series104.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))
6.0ms	(* K (+ m n))
38.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
20.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

simplify42.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	442	576
1	1444	538
2	5002	530

prune562.0ms

Filtered

82 candidates to 58 candidates (29.3%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	78	4	82
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	79	4	83

Merged error: 1.0b

Counts

83 → 4

localize13.0ms

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)

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 37

Calls

2 calls:

16.0ms	(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))
10.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

series78.0ms

Counts

2 → 6

Calls

2 calls:

37.0ms	(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))
40.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

simplify79.0ms

Algorithm

egg-herbie

Counts

43 → 43

Iterations

Useful iterations: 3 (74.0ms)

Iter	Nodes	Cost
0	284	378
1	795	361
2	3218	353
3	5001	350

prune202.0ms

Filtered

43 candidates to 31 candidates (27.9%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	43	0	43
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	43	4	47

Merged error: 1.0b

Counts

47 → 4

localize28.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt K)
0.6b	(cbrt K)
0.6b	(cbrt K)
34.6b	(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)
14.0ms	(cos (- (/ (* (* (cbrt K) (cbrt K)) (* (cbrt K) (+ m n))) 2.0) M))

series93.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(cbrt K)
24.0ms	(cbrt K)
21.0ms	(cbrt K)
26.0ms	(cos (- (/ (* (* (cbrt K) (cbrt K)) (* (cbrt K) (+ m n))) 2.0) M))

simplify43.0ms

Algorithm

egg-herbie

Counts

55 → 55

Iterations

Useful iterations: 4 (39.0ms)

Iter	Nodes	Cost
0	130	345
1	254	312
2	453	282
3	1029	279
4	5001	267

prune363.0ms

Filtered

55 candidates to 43 candidates (21.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	52	3	55
Fresh	1	1	2
Picked	1	0	1
Done	0	1	1
Total	54	5	59

Merged error: 1.0b

Counts

59 → 5

localize28.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt K)
0.6b	(cbrt K)
0.6b	(pow (cos (- (/ (* (* (cbrt K) (cbrt K)) (* (cbrt K) (+ m n))) 2.0) M)) 3)
34.6b	(cos (- (/ (* (* (cbrt K) (cbrt K)) (* (cbrt K) (+ m n))) 2.0) M))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`cbrt-prod`
5×	`pow1` `add-exp-log` `add-cbrt-cube`
4×	`add-log-exp`
3×	`unpow-prod-down` `pow-unpow` `cube-prod`
2×	`cos-sum` `pow1/3`
1×	`cos-diff` `cube-mult` `pow-to-exp` `sub-neg` `pow-pow` `unpow3` `pow-exp` `rem-cube-cbrt` `sqr-pow`

Counts

4 → 55

Calls

4 calls:

1.0ms	(cbrt K)
1.0ms	(cbrt K)
3.0ms	(pow (cos (- (/ (* (* (cbrt K) (cbrt K)) (* (cbrt K) (+ m n))) 2.0) M)) 3)
13.0ms	(cos (- (/ (* (* (cbrt K) (cbrt K)) (* (cbrt K) (+ m n))) 2.0) M))

series126.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(cbrt K)
21.0ms	(cbrt K)
55.0ms	(pow (cos (- (/ (* (* (cbrt K) (cbrt K)) (* (cbrt K) (+ m n))) 2.0) M)) 3)
29.0ms	(cos (- (/ (* (* (cbrt K) (cbrt K)) (* (cbrt K) (+ m n))) 2.0) M))

simplify136.0ms

Algorithm

egg-herbie

Counts

67 → 67

Iterations

Useful iterations: 2 (19.0ms)

Iter	Nodes	Cost
0	198	647
1	586	576
2	3195	552
3	5001	552

prune446.0ms

Filtered

67 candidates to 46 candidates (31.3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	65	2	67
Fresh	1	2	3
Picked	1	0	1
Done	0	1	1
Total	67	5	72

Merged error: 1.0b

Counts

72 → 5

regimes462.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	10
1	20	10

end0.0ms

sample1.5s

Algorithm

intervals

Results

783.0ms	8108×	body	80	valid
70.0ms	119×	body	1280	valid
65.0ms	146×	body	640	valid
32.0ms	109×	body	320	valid
10.0ms	49×	body	160	valid
2.0ms	2×	body	2560	valid

Details

sample64.0ms

simplify48.0ms

prune15.0ms

localize21.0ms

rewrite44.0ms

series104.0ms

simplify42.0ms

prune562.0ms

localize13.0ms

rewrite27.0ms

series78.0ms

simplify79.0ms

prune202.0ms

localize28.0ms

rewrite18.0ms

series93.0ms

simplify43.0ms

prune363.0ms

localize28.0ms

rewrite20.0ms

series126.0ms

simplify136.0ms

prune446.0ms

regimes462.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample1.5s

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