Details

sample69.0ms

Algorithm

intervals

Results

24.0ms	207×	body	80	valid
10.0ms	20×	body	640	valid
9.0ms	12×	body	1280	valid
6.0ms	13×	body	320	valid
1.0ms	4×	body	160	valid

simplify39.0ms

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

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 0.3b

Counts

2 → 1

localize23.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (sin ky) 2.0)
0.3b	(/ 1.0 (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
2.3b	(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
8.7b	(sqrt (+ 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

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 ky) 2.0)
6.0ms	(/ 1.0 (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
21.0ms	(* (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:

104.0ms	(pow (sin ky) 2.0)
380.0ms	(/ 1.0 (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
373.0ms	(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
314.0ms	(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

simplify67.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 2 (51.0ms)

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

prune503.0ms

Filtered

122 candidates to 83 candidates (68.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	120	2	122
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	121	2	123

Merged error: 0.2b

Counts

123 → 2

localize30.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
3.2b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
3.2b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
8.7b	(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)))))))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
24×	`*-un-lft-identity`
21×	`sqrt-prod`
16×	`add-exp-log`
15×	`unpow-prod-down`
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×	`flip3-+` `flip-+` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `times-frac` `pow1/2` `pow-exp` `sqr-pow`
2×	`associate-*r/` `div-exp`
1×	`pow-to-exp` `*-commutative` `cbrt-unprod` `div-inv`

Counts

4 → 90

Calls

4 calls:

17.0ms	(* (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)))))))

series945.0ms

Counts

4 → 12

Calls

4 calls:

476.0ms	(* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
76.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
77.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
315.0ms	(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)))))))

simplify50.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 1 (8.0ms)

Iter	Nodes	Cost
0	363	1506
1	1159	1433
2	5002	1433

prune484.0ms

Filtered

102 candidates to 69 candidates (67.6%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	101	1	102
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	103	1	104

Merged error: 0.2b

Counts

104 → 1

localize33.0ms

Local error

Found 4 expressions with local error:

5.5b	(sqrt (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))))))))
5.5b	(sqrt (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))))))))
8.7b	(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)))))))
8.7b	(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)))))))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

26×	`sqrt-prod`
16×	`add-sqr-sqrt`
12×	`sqrt-div`
10×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `sqrt-pow1`
6×	`rem-sqrt-square` `pow1/2`
4×	`add-exp-log` `flip3-+` `add-cbrt-cube` `flip-+` `add-log-exp`

Counts

4 → 72

Calls

4 calls:

4.0ms	(sqrt (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))))))))
4.0ms	(sqrt (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))))))))
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)))))))
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)))))))

series1.2s

Counts

4 → 12

Calls

4 calls:

290.0ms	(sqrt (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))))))))
291.0ms	(sqrt (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))))))))
318.0ms	(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)))))))
322.0ms	(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)))))))

simplify107.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 1 (5.0ms)

Iter	Nodes	Cost
0	134	2532
1	388	2434
2	2237	2434
3	5002	2434

prune492.0ms

Filtered

84 candidates to 62 candidates (73.8%)

Pruning

1 alts after pruning (0 fresh and 1 done)

	Pruned	Kept	Total
New	84	0	84
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	84	1	85

Merged error: 0.2b

Counts

85 → 1

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	58
1	34	58

end0.0ms

sample2.0s

Algorithm

intervals

Results

787.0ms	6238×	body	80	valid
410.0ms	496×	body	1280	valid
371.0ms	672×	body	640	valid
148.0ms	386×	body	320	valid
53.0ms	208×	body	160	valid