Details

sample81.0ms

Algorithm

intervals

Results

24.0ms	195×	body	80	valid
17.0ms	21×	body	1280	valid
10.0ms	19×	body	640	valid
8.0ms	11×	body	320	valid
3.0ms	10×	body	160	valid

simplify41.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	52	16
1	131	16
2	342	16
3	1202	16
4	5002	16

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (sin ky) 2.0)
0.3b	(pow (sin kx) 2.0)
3.4b	(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
9.4b	(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-sqr-sqrt`
18×	`add-exp-log`
17×	`*-un-lft-identity`
16×	`unpow-prod-down`
13×	`add-cube-cbrt`
11×	`associate-l`
7×	`pow1`
6×	`pow-unpow` `prod-exp` `add-cbrt-cube`
5×	`associate-r` `pow-exp`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp` `sqr-pow`
3×	`pow-to-exp` `times-frac` `sqrt-prod` `unswap-sqr`
2×	`pow-pow` `flip3-+` `sqrt-div` `associate-*r/` `div-exp` `flip-+` `distribute-lft-out`
1×	`distribute-rgt-in` `rem-sqrt-square` `distribute-lft-in` `sqrt-pow1` `pow1/2` `*-commutative` `cbrt-unprod` `div-inv`

Counts

4 → 94

Calls

4 calls:

3.0ms	(pow (sin ky) 2.0)
3.0ms	(pow (sin kx) 2.0)
14.0ms	(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
3.0ms	(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

series872.0ms

Counts

4 → 12

Calls

4 calls:

98.0ms	(pow (sin ky) 2.0)
102.0ms	(pow (sin kx) 2.0)
363.0ms	(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
308.0ms	(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

simplify58.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 1 (11.0ms)

Iter	Nodes	Cost
0	489	888
1	1948	857
2	5001	857

prune437.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.4b

localize28.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (sin kx) 2.0)
0.9b	(* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
1.6b	(* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
9.4b	(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

124×	`add-exp-log`
72×	`prod-exp`
37×	`pow-exp`
24×	`div-exp`
22×	`associate-l`
20×	`add-sqr-sqrt` `unpow-prod-down`
18×	`*-un-lft-identity`
14×	`add-cube-cbrt`
13×	`pow-to-exp`
11×	`add-cbrt-cube`
6×	`pow1` `times-frac` `associate-r/` `associate-r*`
5×	`distribute-rgt-in` `distribute-lft-in`
4×	`expm1-log1p-u` `cbrt-unprod` `log1p-expm1-u` `add-log-exp` `sqr-pow`
3×	`pow-unpow` `flip3-+` `sqrt-prod` `flip-+` `unswap-sqr`
2×	`sqrt-div` `*-commutative` `div-inv` `distribute-lft-out`
1×	`rem-sqrt-square` `pow-pow` `sqrt-pow1` `pow1/2`

Counts

4 → 135

Calls

4 calls:

3.0ms	(pow (sin kx) 2.0)
18.0ms	(* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
14.0ms	(* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
3.0ms	(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))

series1.2s

Counts

4 → 12

Calls

4 calls:

104.0ms	(pow (sin kx) 2.0)
369.0ms	(* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
379.0ms	(* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
304.0ms	(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))

simplify83.0ms

Algorithm

egg-herbie

Counts

147 → 147

Iterations

Useful iterations: 2 (64.0ms)

Iter	Nodes	Cost
0	636	2017
1	2648	1796
2	5002	1765

prune539.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.4b

localize8.0ms

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms

Counts: 0 → 0

simplify2.0ms

Algorithm

egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	0	0

prune0.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0.4b

regimes227.0ms

Accuracy

0% (0.1b remaining)

Error of 0.8b against oracle of 0.7b and baseline of 0.8b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	22
1	32	22

end0.0ms

sample2.1s

Algorithm

intervals

Results

765.0ms	6230×	body	80	valid
499.0ms	587×	body	1280	valid
335.0ms	605×	body	640	valid
137.0ms	353×	body	320	valid
58.0ms	225×	body	160	valid