Details

sample85.0ms

Algorithm

intervals

Results

24.0ms	190×	body	80	valid
22.0ms	28×	body	1280	valid
10.0ms	19×	body	640	valid
5.0ms	13×	body	320	valid
2.0ms	6×	body	160	valid

simplify42.0ms

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: 0.8b

localize24.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (/ (* 2.0 l) Om) 2.0)
0.3b	(pow (sin ky) 2.0)
2.0b	(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
10.1b	(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 100

Calls

4 calls:

6.0ms	(pow (/ (* 2.0 l) Om) 2.0)
3.0ms	(pow (sin ky) 2.0)
20.0ms	(* (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:

85.0ms	(pow (/ (* 2.0 l) Om) 2.0)
102.0ms	(pow (sin ky) 2.0)
371.0ms	(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
315.0ms	(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

simplify63.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 1 (12.0ms)

Iter	Nodes	Cost
0	515	957
1	2069	914
2	5001	914

prune466.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.6b

localize27.0ms

Local error

Found 4 expressions with local error:

1.1b	(* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
2.2b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
2.2b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
10.1b	(sqrt (+ 1.0 (* (* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

50×	`add-sqr-sqrt`
27×	`unpow-prod-down`
24×	`*-un-lft-identity`
21×	`sqrt-prod`
19×	`hypot-def`
16×	`add-exp-log`
15×	`sqr-pow`
12×	`add-cube-cbrt`
11×	`associate-l`
8×	`sqrt-div` `associate-r`
7×	`pow1`
6×	`prod-exp` `add-cbrt-cube` `distribute-lft-out` `unswap-sqr`
4×	`expm1-log1p-u` `flip3-+` `flip-+` `log1p-expm1-u` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `times-frac` `pow1/2` `pow-exp`
2×	`associate-*r/` `div-exp`
1×	`pow-to-exp` `*-commutative` `cbrt-unprod` `div-inv`

Counts

4 → 117

Calls

4 calls:

18.0ms	(* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
8.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
8.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
3.0ms	(sqrt (+ 1.0 (* (* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))))

series943.0ms

Counts

4 → 12

Calls

4 calls:

481.0ms	(* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
74.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
79.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
309.0ms	(sqrt (+ 1.0 (* (* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))))

simplify51.0ms

Algorithm

egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	378	1613
1	1232	1509
2	5001	1507

prune668.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.6b

localize7.0ms

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: 0.6b

regimes240.0ms

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	30
1	32	30

end0.0ms

sample2.0s

Algorithm

intervals

Results

796.0ms	6257×	body	80	valid
443.0ms	540×	body	1280	valid
340.0ms	631×	body	640	valid
145.0ms	374×	body	320	valid
51.0ms	198×	body	160	valid