Details

sample113.0ms

Algorithm

intervals

Results

34.0ms	193×	body	80	valid
29.0ms	25×	body	1280	valid
15.0ms	18×	body	640	valid
7.0ms	12×	body	320	valid
3.0ms	8×	body	160	valid

simplify57.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4882	29
1	4882	29

prune11.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 1.5b

Counts

2 → 1

localize24.0ms

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))))))
3.7b	(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
8.5b	(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

rewrite30.0ms

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)
5.0ms	(/ 1.0 (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
16.0ms	(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
2.0ms	(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

series420.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(pow (sin kx) 2.0)
165.0ms	(/ 1.0 (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
108.0ms	(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
129.0ms	(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

simplify100.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 0 (85.0ms)

Iter	Nodes	Cost
0	4969	2674
1	4969	2674

prune335.0ms

Filtered

88 candidates to 122 candidates (-38.6%)

Pruning

2 alts after pruning (1 fresh and 1 done)

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

Merged error: 0.2b

Counts

123 → 2

localize27.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (sin ky) 2.0)
0.3b	(pow (sin kx) 2.0)
1.9b	(log (pow (exp (pow (* (/ 2.0 Om) l) 2.0)) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
2.4b	(pow (exp (pow (* (/ 2.0 Om) l) 2.0)) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

17×	`*-un-lft-identity`
15×	`unpow-prod-down`
13×	`add-sqr-sqrt` `add-cube-cbrt`
11×	`pow-unpow`
8×	`log-prod` `pow-pow`
7×	`pow1` `add-exp-log`
5×	`exp-prod` `sqr-pow`
4×	`pow-to-exp` `pow-exp` `add-cbrt-cube` `add-log-exp`
3×	`rem-log-exp`
2×	`unpow-prod-up` `distribute-lft-out`
1×	`log-pow`

Counts

4 → 78

Calls

4 calls:

3.0ms	(pow (sin ky) 2.0)
3.0ms	(pow (sin kx) 2.0)
5.0ms	(log (pow (exp (pow (* (/ 2.0 Om) l) 2.0)) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
11.0ms	(pow (exp (pow (* (/ 2.0 Om) l) 2.0)) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series161.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(pow (sin ky) 2.0)
19.0ms	(pow (sin kx) 2.0)
63.0ms	(log (pow (exp (pow (* (/ 2.0 Om) l) 2.0)) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
61.0ms	(pow (exp (pow (* (/ 2.0 Om) l) 2.0)) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify41.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	4977	1311
1	4977	1311

prune228.0ms

Filtered

62 candidates to 90 candidates (-45.2%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	90	0	90
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	90	2	92

Merged error: 0.2b

Counts

92 → 2

regimes1.2s

Accuracy

89.7% (0.0b remaining)

Error of 0.7b against oracle of 0.7b and baseline of 1.1b

bsearch2.0ms

Steps

Iters	Range		Point
0	0.0	6.5082214919809e-315	3.2541107435201e-315

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	47	72
1	47	72

end0.0ms

sample3.1s

Algorithm

intervals

Results

1.1s	6195×	body	80	valid
676.0ms	563×	body	1280	valid
558.0ms	658×	body	640	valid
218.0ms	356×	body	320	valid
90.0ms	228×	body	160	valid

Details

sample113.0ms

simplify57.0ms

prune11.0ms

localize24.0ms

rewrite30.0ms

series420.0ms

simplify100.0ms

prune335.0ms

localize27.0ms

rewrite23.0ms

series161.0ms

simplify41.0ms

prune228.0ms

regimes1.2s

bsearch2.0ms

simplify1.0ms

end0.0ms

sample3.1s

Profiling