Details

sample333.0ms

Algorithm

intervals

Results

281.0ms

256×

body

valid

simplify6.7s

Counts

1 → 1

Iterations

Useful iterations: 0 (8.0ms)

Iter	Nodes	Cost
0	22	1196
1	52	1196
2	121	1196
3	263	1196
4	920	1196
5	4017	1196
done	5001	1196

prune17.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.8b

localize56.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ 1.0 (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
0.3b	(pow (sin kx) 2.0)
2.0b	(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
10.8b	(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

rewrite99.0ms

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` `associate-/r*` `prod-exp`
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×	`distribute-rgt-in` `cbrt-undiv` `rem-sqrt-square` `clear-num` `pow-pow` `frac-2neg` `distribute-lft-in` `sqrt-pow1` `pow1/2` `*-commutative` `cbrt-unprod`

Counts

4 → 110

Calls

4 calls:

8.0ms	(/ 1.0 (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
4.0ms	(pow (sin kx) 2.0)
66.0ms	(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
16.0ms	(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

series2.2s

Counts

4 → 12

Calls

4 calls:

637.0ms	(/ 1.0 (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
130.0ms	(pow (sin kx) 2.0)
984.0ms	(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
438.0ms	(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

simplify2.7s

Counts

122 → 122

Iterations

Useful iterations: 2 (950.0ms)

Iter	Nodes	Cost
0	222	123994
1	584	119744
2	1868	119533
done	5001	119533

prune1.2s

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.4b

localize107.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (sin kx) 2.0)
0.4b	(* (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))))
2.1b	(* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
10.8b	(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))))))

rewrite248.0ms

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×	`cbrt-unprod` `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 → 127

Calls

4 calls:

5.0ms	(pow (sin kx) 2.0)
101.0ms	(* (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))))
124.0ms	(* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
8.0ms	(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))))))

series1.9s

Counts

4 → 12

Calls

4 calls:

157.0ms	(pow (sin kx) 2.0)
540.0ms	(* (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))))
629.0ms	(* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
559.0ms	(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))))))

simplify3.4s

Counts

139 → 139

Iterations

Useful iterations: 2 (1.1s)

Iter	Nodes	Cost
0	227	138921
1	654	127605
2	2241	126675
done	5004	126675

prune1.3s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.4b

localize25.0ms

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms

Counts: 0 → 0

simplify0.0ms

Counts

0 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0
done	0	0

prune1.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0.4b

regimes828.0ms

Accuracy

0% (0.1b remaining)

Error of 1.3b against oracle of 1.3b and baseline of 1.3b

bsearch0.0ms

simplify9.0ms

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	25	1277
1	32	1277
done	32	1277

end0.0ms

sample2.9s

Algorithm

intervals

Results

2.6s	7999×	body	80	valid
0.0ms	1×	body	160	valid