Details

sample80.0ms

Algorithm

intervals

Results

24.0ms	194×	body	80	valid
17.0ms	33×	body	640	valid
11.0ms	13×	body	1280	valid
6.0ms	6×	body	160	valid
4.0ms	10×	body	320	valid

simplify40.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	52	16
1	123	16
2	294	16
3	1083	16
4	5001	16

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.2b

localize23.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (sin kx) 2.0)
0.7b	(/ 1.0 (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
2.9b	(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
10.3b	(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt`
30×	`*-un-lft-identity`
26×	`add-cube-cbrt`
21×	`times-frac`
19×	`add-exp-log`
15×	`sqrt-prod`
13×	`unpow-prod-down`
11×	`associate-l`
8×	`add-cbrt-cube`
6×	`pow1` `prod-exp` `associate-/r*`
5×	`associate-r`
4×	`sqrt-div` `pow-exp` `add-log-exp`
3×	`pow-unpow` `flip3-+` `div-exp` `flip-+` `associate-/l*` `unswap-sqr` `sqr-pow`
2×	`pow-to-exp` `associate-*r/` `associate-/r/` `div-inv` `distribute-lft-out`
1×	`cbrt-undiv` `distribute-rgt-in` `rem-sqrt-square` `pow-pow` `frac-2neg` `distribute-lft-in` `sqrt-pow1` `pow1/2` `clear-num` `*-commutative` `cbrt-unprod`

Counts

4 → 110

Calls

4 calls:

3.0ms	(pow (sin kx) 2.0)
9.0ms	(/ 1.0 (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 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)))))

series1.2s

Counts

4 → 12

Calls

4 calls:

101.0ms	(pow (sin kx) 2.0)
373.0ms	(/ 1.0 (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
370.0ms	(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
310.0ms	(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

simplify65.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	505	1608
1	2047	1504
2	5001	1501

prune493.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.8b

localize31.0ms

Local error

Found 4 expressions with local error:

2.9b	(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
2.9b	(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
15.5b	(cbrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
15.5b	(cbrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-exp-log`
24×	`add-sqr-sqrt`
22×	`-un-lft-identity` `associate-l*`
20×	`unpow-prod-down`
14×	`add-cube-cbrt`
12×	`prod-exp`
10×	`associate-r`
8×	`add-cbrt-cube`
6×	`cbrt-prod` `times-frac` `pow-exp` `unswap-sqr`
4×	`pow1` `cbrt-div` `flip3-+` `associate-*r/` `div-exp` `flip-+` `distribute-lft-out` `add-log-exp` `sqr-pow`
2×	`distribute-rgt-in` `pow-to-exp` `distribute-lft-in` `pow1/3` `*-commutative` `cbrt-unprod` `div-inv`

Counts

4 → 100

Calls

4 calls:

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

series1.3s

Counts

4 → 12

Calls

4 calls:

367.0ms	(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
372.0ms	(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
276.0ms	(cbrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
276.0ms	(cbrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

simplify53.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	358	1412
1	1384	1334
2	5002	1328

prune616.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.8b

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: 0.8b

regimes327.0ms

Accuracy

0% (0.3b remaining)

Error of 0.9b against oracle of 0.6b and baseline of 0.9b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	31
1	36	31

end0.0ms

sample2.0s

Algorithm

intervals

Results

728.0ms	6174×	body	80	valid
425.0ms	527×	body	1280	valid
359.0ms	664×	body	640	valid
168.0ms	417×	body	320	valid
63.0ms	218×	body	160	valid