Details

sample73.0ms

Algorithm

intervals

Results

24.0ms	199×	body	80	valid
16.0ms	20×	body	1280	valid
10.0ms	18×	body	640	valid
5.0ms	12×	body	320	valid
2.0ms	7×	body	160	valid

simplify41.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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

prune9.0ms

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: 0.5b

Counts

2 → 1

localize23.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (sin kx) 2.0)
0.5b	(/ 1.0 (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
1.9b	(* (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)))))

rewrite100.0ms

Algorithm

rewrite-expression-head

Rules

72×	`*-un-lft-identity`
67×	`add-sqr-sqrt`
62×	`times-frac`
58×	`associate-l`
48×	`add-cube-cbrt` `unpow-prod-down`
25×	`sqrt-prod`
19×	`add-exp-log`
14×	`associate-r`
12×	`distribute-lft-out`
9×	`unswap-sqr`
8×	`pow1` `associate-/r*` `add-cbrt-cube`
6×	`prod-exp`
4×	`sqrt-div` `pow-exp` `*-commutative` `add-log-exp`
3×	`pow-unpow` `flip3-+` `div-exp` `flip-+` `associate-/l*` `sqr-pow`
2×	`+-commutative` `distribute-rgt-in` `pow-to-exp` `distribute-lft-in` `associate-*r/` `associate-/r/` `div-inv`
1×	`cbrt-undiv` `rem-sqrt-square` `pow-pow` `frac-2neg` `sqrt-pow1` `pow1/2` `pow-prod-down` `clear-num` `cbrt-unprod`

Counts

4 → 158

Calls

4 calls:

2.0ms	(pow (sin kx) 2.0)
33.0ms	(/ 1.0 (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
26.0ms	(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
31.0ms	(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:

108.0ms	(pow (sin kx) 2.0)
385.0ms	(/ 1.0 (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
376.0ms	(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
323.0ms	(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

simplify95.0ms

Algorithm

egg-herbie

Counts

170 → 170

Iterations

Useful iterations: 2 (74.0ms)

Iter	Nodes	Cost
0	843	2146
1	3337	2024
2	5002	2021

prune557.0ms

Filtered

170 candidates to 116 candidates (68.2%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	167	3	170
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	168	3	171

Merged error: 0.3b

Counts

171 → 3

localize30.0ms

Local error

Found 4 expressions with local error:

0.9b	(* (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)))
9.6b	(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)))))))

rewrite220.0ms

Algorithm

rewrite-expression-head

Rules

65×	`add-sqr-sqrt`
56×	`associate-l`
52×	`unpow-prod-down`
50×	`*-un-lft-identity`
40×	`times-frac`
32×	`add-cube-cbrt`
26×	`sqrt-prod`
17×	`associate-r`
16×	`add-exp-log`
15×	`unswap-sqr`
10×	`pow1`
9×	`distribute-lft-out`
8×	`sqrt-div`
6×	`prod-exp` `add-cbrt-cube`
4×	`sqrt-pow1` `flip3-+` `*-commutative` `flip-+` `add-log-exp`
3×	`rem-sqrt-square` `pow1/2` `pow-exp` `sqr-pow`
2×	`associate-*r/` `div-exp` `pow-prod-down` `div-inv`
1×	`pow-to-exp` `pow-unpow` `cbrt-unprod`

Counts

4 → 132

Calls

4 calls:

30.0ms	(* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
7.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
10.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
165.0ms	(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)))))))

series957.0ms

Counts

4 → 12

Calls

4 calls:

480.0ms	(* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
75.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
77.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
325.0ms	(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)))))))

simplify63.0ms

Algorithm

egg-herbie

Counts

144 → 144

Iterations

Useful iterations: 1 (12.0ms)

Iter	Nodes	Cost
0	554	2117
1	1681	2041
2	5001	2041

prune601.0ms

Filtered

144 candidates to 102 candidates (70.8%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	143	1	144
Fresh	1	1	2
Picked	0	1	1
Done	0	0	0
Total	144	3	147

Merged error: 0.3b

Counts

147 → 3

localize28.0ms

Local error

Found 4 expressions with local error:

5.7b	(cbrt (/ 1.0 (sqrt (+ 1.0 (* (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)))))
9.6b	(sqrt (+ 1.0 (* (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)))))

rewrite137.0ms

Algorithm

rewrite-expression-head

Rules

53×	`*-un-lft-identity`
35×	`sqrt-prod`
30×	`cbrt-prod`
28×	`add-sqr-sqrt`
25×	`add-cube-cbrt`
24×	`times-frac`
14×	`cbrt-div` `distribute-lft-out`
8×	`sqrt-div` `associate-/r*`
7×	`pow1` `associate-l`
4×	`add-exp-log` `flip3-+` `add-cbrt-cube` `flip-+` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-/l*`
2×	`associate-/r/`
1×	`frac-2neg` `pow1/3` `clear-num` `div-inv`

Counts

4 → 103

Calls

4 calls:

35.0ms	(cbrt (/ 1.0 (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))))
33.0ms	(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
31.0ms	(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
33.0ms	(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:

397.0ms	(cbrt (/ 1.0 (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))))
324.0ms	(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
319.0ms	(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
318.0ms	(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

simplify103.0ms

Algorithm

egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 3 (83.0ms)

Iter	Nodes	Cost
0	222	2077
1	617	2020
2	2648	1985
3	5001	1978

prune432.0ms

Filtered

115 candidates to 71 candidates (61.7%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	115	0	115
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	115	3	118

Merged error: 0.3b

Counts

118 → 3

localize7.0ms

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms

Counts: 0 → 0

simplify3.0ms

Algorithm

egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	0	0

prune0.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

	Kept	Total
New	0	0
Fresh	0	0
Picked	1	1
Done	2	2
Total	3	3

Merged error: 0.3b

Counts

3 → 3

regimes618.0ms

Accuracy

0% (0.1b remaining)

Error of 0.7b against oracle of 0.6b and baseline of 0.7b

bsearch0.0ms

simplify2.0ms

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

776.0ms	6195×	body	80	valid
451.0ms	551×	body	1280	valid
360.0ms	640×	body	640	valid
157.0ms	388×	body	320	valid
59.0ms	226×	body	160	valid