Details

sample59.0ms

Algorithm

intervals

Results

35.0ms

256×

body

valid

simplify5.3s

Counts

1 → 1

Iterations

Useful iterations: 2 (54.0ms)

Iter	Nodes	Cost
0	22	29
1	52	29
2	131	28
3	330	28
4	1152	28
5	4772	28
done	5000	28

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 2.5b

localize39.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (sin kx) 2.0)
0.3b	(pow (/ (* 2.0 l) Om) 2.0)
2.9b	(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
9.6b	(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

rewrite164.0ms

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:

4.0ms	(pow (sin kx) 2.0)
12.0ms	(pow (/ (* 2.0 l) Om) 2.0)
135.0ms	(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
9.0ms	(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

series1.4s

Counts

4 → 12

Calls

4 calls:

145.0ms	(pow (sin kx) 2.0)
116.0ms	(pow (/ (* 2.0 l) Om) 2.0)
557.0ms	(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
624.0ms	(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

simplify1.3s

Counts

112 → 112

Iterations

Useful iterations: 2 (345.0ms)

Iter	Nodes	Cost
0	213	1892
1	507	1724
2	1687	1645
done	5001	1645

prune874.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 1.9b

localize34.0ms

Local error

Found 4 expressions with local error:

5.3b	(cbrt (sqrt (fma (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)) (pow (/ (* 2.0 l) Om) 2.0) 1.0)))
9.6b	(sqrt (fma (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)) (pow (/ (* 2.0 l) Om) 2.0) 1.0))
9.6b	(sqrt (fma (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)) (pow (/ (* 2.0 l) Om) 2.0) 1.0))
9.6b	(sqrt (fma (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)) (pow (/ (* 2.0 l) Om) 2.0) 1.0))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `sqrt-prod`
9×	`add-cube-cbrt` `*-un-lft-identity`
7×	`pow1`
6×	`cbrt-prod`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`pow1/3`

Counts

4 → 61

Calls

4 calls:

3.0ms	(cbrt (sqrt (fma (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)) (pow (/ (* 2.0 l) Om) 2.0) 1.0)))
4.0ms	(sqrt (fma (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)) (pow (/ (* 2.0 l) Om) 2.0) 1.0))
3.0ms	(sqrt (fma (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)) (pow (/ (* 2.0 l) Om) 2.0) 1.0))
14.0ms	(sqrt (fma (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)) (pow (/ (* 2.0 l) Om) 2.0) 1.0))

series1.9s

Counts

4 → 12

Calls

4 calls:

476.0ms	(cbrt (sqrt (fma (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)) (pow (/ (* 2.0 l) Om) 2.0) 1.0)))
455.0ms	(sqrt (fma (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)) (pow (/ (* 2.0 l) Om) 2.0) 1.0))
487.0ms	(sqrt (fma (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)) (pow (/ (* 2.0 l) Om) 2.0) 1.0))
483.0ms	(sqrt (fma (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)) (pow (/ (* 2.0 l) Om) 2.0) 1.0))

simplify3.6s

Counts

73 → 73

Iterations

Useful iterations: done (3.6s)

Iter	Nodes	Cost
0	50	1625
1	73	1470
2	110	1379
3	198	1376
4	687	1376
5	3105	1376
done	5000	1288

prune557.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 1.9b

localize62.0ms

Local error

Found 4 expressions with local error:

9.6b	(sqrt (fma (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)) (pow (/ (* 2.0 l) Om) 2.0) 1.0))
9.6b	(sqrt (fma (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)) (pow (/ (* 2.0 l) Om) 2.0) 1.0))
13.8b	(cbrt (fma (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)) (pow (/ (* 2.0 l) Om) 2.0) 1.0))
13.8b	(cbrt (fma (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)) (pow (/ (* 2.0 l) Om) 2.0) 1.0))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
8×	`add-cube-cbrt` `*-un-lft-identity`
6×	`pow1` `cbrt-prod` `sqrt-prod`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow1/3`

Counts

4 → 56

Calls

4 calls:

2.0ms	(sqrt (fma (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)) (pow (/ (* 2.0 l) Om) 2.0) 1.0))
2.0ms	(sqrt (fma (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)) (pow (/ (* 2.0 l) Om) 2.0) 1.0))
1.0ms	(cbrt (fma (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)) (pow (/ (* 2.0 l) Om) 2.0) 1.0))
1.0ms	(cbrt (fma (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)) (pow (/ (* 2.0 l) Om) 2.0) 1.0))

series1.9s

Counts

4 → 12

Calls

4 calls:

469.0ms	(sqrt (fma (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)) (pow (/ (* 2.0 l) Om) 2.0) 1.0))
455.0ms	(sqrt (fma (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)) (pow (/ (* 2.0 l) Om) 2.0) 1.0))
509.0ms	(cbrt (fma (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)) (pow (/ (* 2.0 l) Om) 2.0) 1.0))
511.0ms	(cbrt (fma (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)) (pow (/ (* 2.0 l) Om) 2.0) 1.0))

simplify2.3s

Counts

68 → 68

Iterations

Useful iterations: 3 (73.0ms)

Iter	Nodes	Cost
0	45	1480
1	69	1384
2	106	1274
3	194	1268
4	579	1268
5	2212	1268
done	5000	1268

prune758.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 1.9b

localize17.0ms

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms

Counts: 0 → 0

simplify1.0ms

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: 1.9b

regimes536.0ms

Accuracy

0% (0.4b remaining)

Error of 1.8b against oracle of 1.4b and baseline of 1.8b

bsearch0.0ms

simplify10.0ms

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	30	94
1	36	94
done	36	94

end0.0ms

sample3.0s

Algorithm

intervals

Results

2.6s

8000×

body

valid