Details

sample52.0ms

Algorithm

intervals

Results

25.0ms	256×	body	80	valid
2.0ms	7×	body	320	valid
2.0ms	3×	body	1280	valid
1.0ms	3×	body	640	valid
0.0ms	1×	body	160	valid

simplify50.0ms

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

prune13.0ms

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: 18.1b

Counts

2 → 1

localize26.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (- (/ (+ m n) 2.0) M) 2.0)
0.0b	(* K (+ m n))
0.2b	(/ (* K (+ m n)) 2.0)
38.0b	(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 76

Calls

4 calls:

10.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
6.0ms	(* K (+ m n))
7.0ms	(/ (* K (+ m n)) 2.0)
8.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

series78.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
6.0ms	(* K (+ m n))
8.0ms	(/ (* K (+ m n)) 2.0)
21.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

simplify50.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 1 (11.0ms)

Iter	Nodes	Cost
0	425	497
1	1759	447
2	5001	447

prune201.0ms

Filtered

63 candidates to 88 candidates (-39.7%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	82	6	88
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	83	6	89

Merged error: 1.8b

Counts

89 → 6

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)

rewrite29.0ms

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:

17.0ms	(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))
10.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

series81.0ms

Counts

2 → 6

Calls

2 calls:

41.0ms	(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))
40.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

simplify83.0ms

Algorithm

egg-herbie

Counts

43 → 43

Iterations

Useful iterations: 3 (77.0ms)

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

prune101.0ms

Filtered

31 candidates to 43 candidates (-38.7%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	43	0	43
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	43	6	49

Merged error: 1.8b

Counts

49 → 6

localize25.0ms

Local error

Found 4 expressions with local error:

1.0b	(cbrt 2.0)
1.0b	(cbrt 2.0)
1.0b	(cbrt 2.0)
38.0b	(cos (- (* (/ K (* (cbrt 2.0) (cbrt 2.0))) (/ (+ m n) (cbrt 2.0))) M))

rewrite17.0ms

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

series35.0ms

Counts

4 → 6

Calls

4 calls:

0.0ms	(cbrt 2.0)
0.0ms	(cbrt 2.0)
0.0ms	(cbrt 2.0)
35.0ms	(cos (- (* (/ K (* (cbrt 2.0) (cbrt 2.0))) (/ (+ m n) (cbrt 2.0))) M))

simplify75.0ms

Algorithm

egg-herbie

Counts

49 → 49

Iterations

Useful iterations: 2 (6.0ms)

Iter	Nodes	Cost
0	82	309
1	139	279
2	219	273
3	308	273
4	458	273
5	812	273
6	2301	273
7	5001	273

prune182.0ms

Filtered

40 candidates to 49 candidates (-22.5%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	45	4	49
Fresh	1	3	4
Picked	1	0	1
Done	0	1	1
Total	47	8	55

Merged error: 1.7b

Counts

55 → 8

localize29.0ms

Local error

Found 4 expressions with local error:

1.0b	(cbrt 2.0)
1.0b	(cbrt 2.0)
1.0b	(cbrt 2.0)
38.0b	(cos (- (* (/ K (* (cbrt 2.0) (cbrt 2.0))) (/ (+ m n) (cbrt 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 2.0)
1.0ms	(cbrt 2.0)
1.0ms	(cbrt 2.0)
14.0ms	(cos (- (* (/ K (* (cbrt 2.0) (cbrt 2.0))) (/ (+ m n) (cbrt 2.0))) M))

series36.0ms

Counts

4 → 6

Calls

4 calls:

0.0ms	(cbrt 2.0)
0.0ms	(cbrt 2.0)
0.0ms	(cbrt 2.0)
36.0ms	(cos (- (* (/ K (* (cbrt 2.0) (cbrt 2.0))) (/ (+ m n) (cbrt 2.0))) M))

simplify63.0ms

Algorithm

egg-herbie

Counts

49 → 49

Iterations

Useful iterations: 2 (7.0ms)

Iter	Nodes	Cost
0	113	333
1	207	321
2	353	315
3	662	315
4	2013	315
5	5001	315

prune159.0ms

Filtered

42 candidates to 49 candidates (-16.7%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	47	2	49
Fresh	2	4	6
Picked	0	1	1
Done	0	1	1
Total	49	8	57

Merged error: 1.7b

Counts

57 → 8

regimes518.0ms

Accuracy

0% (0.3b remaining)

Error of 1.4b against oracle of 1.1b and baseline of 1.4b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	10
1	20	10

end0.0ms

sample1.4s

Algorithm

intervals

Results

786.0ms	8078×	body	80	valid
68.0ms	116×	body	1280	valid
60.0ms	139×	body	640	valid
34.0ms	112×	body	320	valid
10.0ms	50×	body	160	valid
2.0ms	2×	body	2560	valid

Details

sample52.0ms

simplify50.0ms

prune13.0ms

localize26.0ms

rewrite33.0ms

series78.0ms

simplify50.0ms

prune201.0ms

localize14.0ms

rewrite29.0ms

series81.0ms

simplify83.0ms

prune101.0ms

localize25.0ms

rewrite17.0ms

series35.0ms

simplify75.0ms

prune182.0ms

localize29.0ms

rewrite18.0ms

series36.0ms

simplify63.0ms

prune159.0ms

regimes518.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample1.4s

Profiling