Details

sample42.0ms

Algorithm

intervals

Results

21.0ms	260×	body	80	valid
2.0ms	5×	body	1280	valid
1.0ms	3×	body	640	valid
0.0ms	1×	body	320	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

prune9.0ms

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: 13.5b

Counts

2 → 1

localize28.0ms

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)
36.1b	(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite51.0ms

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:

23.0ms	(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
6.0ms	(* K (+ m n))
11.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
9.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

series521.0ms

Counts

4 → 12

Calls

4 calls:

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

prune519.0ms

Filtered

89 candidates to 60 candidates (67.4%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	86	3	89
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	87	3	90

Merged error: 0.6b

Counts

90 → 3

localize15.0ms

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)

rewrite37.0ms

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:

25.0ms	(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
11.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

series432.0ms

Counts

2 → 6

Calls

2 calls:

176.0ms	(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
256.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

simplify82.0ms

Algorithm

egg-herbie

Counts

50 → 50

Iterations

Useful iterations: 3 (76.0ms)

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

prune152.0ms

Filtered

50 candidates to 34 candidates (68.0%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	50	0	50
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	50	3	53

Merged error: 0.6b

Counts

53 → 3

localize27.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (+ m n))
0.5b	(cbrt (+ m n))
0.5b	(* (cbrt (+ m n)) (cbrt (+ m n)))
36.1b	(cos (- (/ (* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (cbrt (+ m n))) 2.0) M))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

32×	`cbrt-prod` `*-un-lft-identity`
22×	`add-sqr-sqrt`
16×	`cbrt-div`
14×	`add-cube-cbrt`
11×	`pow1`
9×	`swap-sqr`
8×	`flip3-+` `pow1/3` `flip-+` `distribute-lft-out`
7×	`associate-r` `associate-l`
6×	`add-exp-log`
4×	`frac-times` `add-cbrt-cube` `add-log-exp` `unswap-sqr`
2×	`cos-sum` `associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `pow-prod-up`
1×	`pow2` `cos-diff` `sub-neg` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 91

Calls

4 calls:

3.0ms	(cbrt (+ m n))
5.0ms	(cbrt (+ m n))
10.0ms	(* (cbrt (+ m n)) (cbrt (+ m n)))
17.0ms	(cos (- (/ (* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (cbrt (+ m n))) 2.0) M))

series499.0ms

Counts

4 → 12

Calls

4 calls:

120.0ms	(cbrt (+ m n))
121.0ms	(cbrt (+ m n))
159.0ms	(* (cbrt (+ m n)) (cbrt (+ m n)))
98.0ms	(cos (- (/ (* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (cbrt (+ m n))) 2.0) M))

simplify158.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 3 (145.0ms)

Iter	Nodes	Cost
0	308	808
1	1031	751
2	4783	705
3	5001	701

prune452.0ms

Filtered

103 candidates to 71 candidates (68.9%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	100	3	103
Fresh	1	0	1
Picked	1	0	1
Done	0	1	1
Total	102	4	106

Merged error: 0.6b

Counts

106 → 4

localize30.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (cbrt (+ m n)))
0.5b	(cbrt (cbrt (+ m n)))
0.6b	(* (cbrt (cbrt (+ m n))) (cbrt (cbrt (+ m n))))
36.2b	(cos (- (/ (* (* K (* (cbrt (+ m n)) (* (* (cbrt (cbrt (+ m n))) (cbrt (cbrt (+ m n)))) (cbrt (cbrt (+ m n)))))) (cbrt (+ m n))) 2.0) M))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

92×	`cbrt-prod`
38×	`add-sqr-sqrt` `*-un-lft-identity`
32×	`cbrt-div`
20×	`add-cube-cbrt`
12×	`swap-sqr`
11×	`pow1`
10×	`associate-r` `associate-l`
9×	`unswap-sqr`
8×	`flip3-+` `pow1/3` `flip-+` `distribute-lft-out`
6×	`add-exp-log`
4×	`frac-times` `add-cbrt-cube` `add-log-exp`
2×	`cos-sum` `associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `pow-prod-up`
1×	`pow2` `cos-diff` `sub-neg` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 111

Calls

4 calls:

4.0ms	(cbrt (cbrt (+ m n)))
4.0ms	(cbrt (cbrt (+ m n)))
14.0ms	(* (cbrt (cbrt (+ m n))) (cbrt (cbrt (+ m n))))
29.0ms	(cos (- (/ (* (* K (* (cbrt (+ m n)) (* (* (cbrt (cbrt (+ m n))) (cbrt (cbrt (+ m n)))) (cbrt (cbrt (+ m n)))))) (cbrt (+ m n))) 2.0) M))

series722.0ms

Counts

4 → 12

Calls

4 calls:

190.0ms	(cbrt (cbrt (+ m n)))
189.0ms	(cbrt (cbrt (+ m n)))
246.0ms	(* (cbrt (cbrt (+ m n))) (cbrt (cbrt (+ m n))))
97.0ms	(cos (- (/ (* (* K (* (cbrt (+ m n)) (* (* (cbrt (cbrt (+ m n))) (cbrt (cbrt (+ m n)))) (cbrt (cbrt (+ m n)))))) (cbrt (+ m n))) 2.0) M))

simplify144.0ms

Algorithm

egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 3 (127.0ms)

Iter	Nodes	Cost
0	343	1364
1	1038	1277
2	4738	1186
3	5001	1181

prune590.0ms

Filtered

123 candidates to 84 candidates (68.3%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	121	2	123
Fresh	2	0	2
Picked	0	1	1
Done	0	1	1
Total	123	4	127

Merged error: 0.6b

Counts

127 → 4

regimes169.0ms

Accuracy

0% (0.2b remaining)

Error of 1.4b against oracle of 1.2b and baseline of 1.4b

bsearch0.0ms

simplify2.0ms

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

676.0ms	8087×	body	80	valid
67.0ms	132×	body	1280	valid
55.0ms	145×	body	640	valid
28.0ms	108×	body	320	valid
7.0ms	43×	body	160	valid
1.0ms	2×	body	2560	valid