Details

sample45.0ms

Algorithm

intervals

Results

21.0ms	258×	body	80	valid
3.0ms	7×	body	1280	valid
1.0ms	4×	body	320	valid
1.0ms	1×	body	2560	valid
1.0ms	2×	body	640	valid

simplify51.0ms

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

prune13.0ms

Filtered

1 candidates to 1 candidates (100.0%)

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: 16.4b

Counts

2 → 1

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))
0.0b	(pow (- (/ (+ m n) 2.0) M) 2.0)
0.0b	(* K (+ m n))
35.9b	(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:

17.0ms	(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))
10.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
6.0ms	(* K (+ m n))
8.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

series535.0ms

Counts

4 → 12

Calls

4 calls:

181.0ms	(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))
271.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
26.0ms	(* K (+ m n))
57.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

simplify43.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (35.0ms)

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

prune348.0ms

Filtered

82 candidates to 58 candidates (70.7%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	77	5	82
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	78	5	83

Merged error: 1.0b

Counts

83 → 5

localize15.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ 1 (exp (+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))))
0.0b	(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))
0.0b	(pow (- (/ (+ m n) 2.0) M) 2.0)

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

27×	`*-un-lft-identity`
20×	`add-sqr-sqrt`
15×	`add-cube-cbrt`
13×	`times-frac`
8×	`add-log-exp`
6×	`unpow-prod-down` `pow-flip`
5×	`pow1` `add-exp-log` `exp-prod` `add-cbrt-cube`
4×	`exp-sum` `associate-/r*` `distribute-lft-out`
3×	`pow-unpow` `associate-/l*` `distribute-lft-out--`
2×	`associate-+r-` `associate-+r+` `div-exp` `sum-log` `difference-of-squares`
1×	`cbrt-undiv` `+-commutative` `pow-to-exp` `sub-neg` `rec-exp` `pow-pow` `frac-2neg` `flip3-+` `exp-diff` `diff-log` `1-exp` `pow-exp` `clear-num` `associate-/r/` `flip-+` `div-inv` `inv-pow` `sqr-pow`

Counts

3 → 78

Calls

3 calls:

20.0ms	(/ 1 (exp (+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))))
20.0ms	(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))
10.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

series628.0ms

Counts

3 → 9

Calls

3 calls:

165.0ms	(/ 1 (exp (+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))))
185.0ms	(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))
278.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

simplify47.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	412	1005
1	1568	934
2	5001	910

prune277.0ms

Filtered

87 candidates to 55 candidates (63.2%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	86	1	87
Fresh	1	3	4
Picked	1	0	1
Done	0	0	0
Total	88	4	92

Merged error: 1.0b

Counts

92 → 4

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (cbrt (pow (pow (- (/ (+ m n) 2.0) M) 2.0) 3)) (- l (fabs (- m n))))
0.0b	(pow (- (/ (+ m n) 2.0) M) 2.0)
0.1b	(pow (pow (- (/ (+ m n) 2.0) M) 2.0) 3)
13.8b	(cbrt (pow (pow (- (/ (+ m n) 2.0) M) 2.0) 3))

rewrite68.0ms

Algorithm

rewrite-expression-head

Rules

50×	`unpow-prod-down`
41×	`add-sqr-sqrt`
31×	`*-un-lft-identity`
26×	`cbrt-prod`
20×	`cube-prod`
16×	`add-cube-cbrt`
10×	`difference-of-squares`
9×	`add-log-exp`
7×	`add-exp-log` `sqr-pow`
6×	`pow-unpow` `distribute-lft-out--`
5×	`pow1` `times-frac` `pow-exp` `add-cbrt-cube`
3×	`pow-to-exp`
2×	`cube-mult` `associate-+r+` `pow-pow` `unpow3` `sum-log` `distribute-lft-out`
1×	`+-commutative` `associate-+r-` `sub-neg` `flip3-+` `pow1/3` `diff-log` `rem-cbrt-cube` `flip-+` `rem-cube-cbrt`

Counts

4 → 111

Calls

4 calls:

28.0ms	(+ (cbrt (pow (pow (- (/ (+ m n) 2.0) M) 2.0) 3)) (- l (fabs (- m n))))
10.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
13.0ms	(pow (pow (- (/ (+ m n) 2.0) M) 2.0) 3)
13.0ms	(cbrt (pow (pow (- (/ (+ m n) 2.0) M) 2.0) 3))

series1.4s

Counts

4 → 12

Calls

4 calls:

186.0ms	(+ (cbrt (pow (pow (- (/ (+ m n) 2.0) M) 2.0) 3)) (- l (fabs (- m n))))
282.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
607.0ms	(pow (pow (- (/ (+ m n) 2.0) M) 2.0) 3)
317.0ms	(cbrt (pow (pow (- (/ (+ m n) 2.0) M) 2.0) 3))

simplify56.0ms

Algorithm

egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	452	1091
1	1685	1041
2	5002	1035

prune399.0ms

Filtered

123 candidates to 70 candidates (56.9%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	122	1	123
Fresh	0	3	3
Picked	1	0	1
Done	0	0	0
Total	123	4	127

Merged error: 1.0b

Counts

127 → 4

localize28.0ms

Local error

Found 4 expressions with local error:

13.8b	(cbrt (pow (pow (- (/ (+ m n) 2.0) M) 2.0) 3))
40.6b	(cbrt (+ (cbrt (pow (pow (- (/ (+ m n) 2.0) M) 2.0) 3)) (- l (fabs (- m n)))))
40.6b	(cbrt (+ (cbrt (pow (pow (- (/ (+ m n) 2.0) M) 2.0) 3)) (- l (fabs (- m n)))))
40.6b	(cbrt (+ (cbrt (pow (pow (- (/ (+ m n) 2.0) M) 2.0) 3)) (- l (fabs (- m n)))))

rewrite90.0ms

Algorithm

rewrite-expression-head

Rules

41×	`cbrt-prod`
31×	`*-un-lft-identity`
22×	`add-sqr-sqrt` `unpow-prod-down`
12×	`add-cube-cbrt`
10×	`cube-prod`
6×	`cbrt-div` `distribute-lft-out`
5×	`distribute-lft-out--`
4×	`pow1` `add-exp-log` `pow1/3` `add-cbrt-cube` `add-log-exp` `difference-of-squares`
3×	`flip3-+` `flip-+` `sqr-pow`
2×	`times-frac`
1×	`cube-mult` `unpow3` `rem-cbrt-cube`

Counts

4 → 80

Calls

4 calls:

13.0ms	(cbrt (pow (pow (- (/ (+ m n) 2.0) M) 2.0) 3))
27.0ms	(cbrt (+ (cbrt (pow (pow (- (/ (+ m n) 2.0) M) 2.0) 3)) (- l (fabs (- m n)))))
24.0ms	(cbrt (+ (cbrt (pow (pow (- (/ (+ m n) 2.0) M) 2.0) 3)) (- l (fabs (- m n)))))
23.0ms	(cbrt (+ (cbrt (pow (pow (- (/ (+ m n) 2.0) M) 2.0) 3)) (- l (fabs (- m n)))))

series1.6s

Counts

4 → 12

Calls

4 calls:

325.0ms	(cbrt (pow (pow (- (/ (+ m n) 2.0) M) 2.0) 3))
437.0ms	(cbrt (+ (cbrt (pow (pow (- (/ (+ m n) 2.0) M) 2.0) 3)) (- l (fabs (- m n)))))
434.0ms	(cbrt (+ (cbrt (pow (pow (- (/ (+ m n) 2.0) M) 2.0) 3)) (- l (fabs (- m n)))))
427.0ms	(cbrt (+ (cbrt (pow (pow (- (/ (+ m n) 2.0) M) 2.0) 3)) (- l (fabs (- m n)))))

simplify135.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	399	1404
1	1262	1333
2	4973	1320
3	5002	1320

prune483.0ms

Filtered

92 candidates to 65 candidates (70.7%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	92	0	92
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	92	4	96

Merged error: 1.0b

Counts

96 → 4

regimes171.0ms

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	27	37
1	27	37

end0.0ms

sample1.3s

Algorithm

intervals

Results

873.0ms	8071×	body	80	valid
69.0ms	127×	body	1280	valid
57.0ms	153×	body	640	valid
30.0ms	118×	body	320	valid
8.0ms	41×	body	160	valid
4.0ms	5×	body	2560	valid