Details

sample153.0ms

Algorithm

intervals

Results

92.0ms	120×	body	1280	valid
29.0ms	62×	body	640	valid
12.0ms	26×	body	320	valid
4.0ms	38×	body	80	valid
2.0ms	10×	body	160	valid

simplify50.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	23	10
1	39	10
2	67	10
3	153	10
4	439	10
5	1817	10
6	5001	10

prune4.0ms

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: 3.2b

Counts

2 → 1

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
0.3b	(pow (sin kx) 2.0)
0.3b	(pow (sin ky) 2.0)
3.0b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

4×	`sqrt-div` `sqr-pow`
3×	`associate-l` `associate-*l/`
2×	`pow-to-exp` `flip3-+` `associate-/r/` `flip-+`
1×	`frac-2neg` `pow1/2` `clear-num` `*-commutative` `hypot-def` `div-inv`

Counts

4 → 15

Calls

4 calls:

6.0ms	(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
2.0ms	(pow (sin kx) 2.0)
2.0ms	(pow (sin ky) 2.0)
12.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series433.0ms

Counts

4 → 12

Calls

4 calls:

150.0ms	(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
101.0ms	(pow (sin kx) 2.0)
107.0ms	(pow (sin ky) 2.0)
74.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify71.0ms

Algorithm

egg-herbie

Counts

27 → 27

Iterations

Useful iterations: 2 (17.0ms)

Iter	Nodes	Cost
0	178	169
1	604	160
2	2428	159
3	5001	159

prune107.0ms

Filtered

27 candidates to 21 candidates (77.8%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	21	6	27
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	22	6	28

Merged error: 0.0b

Counts

28 → 6

localize11.0ms

Local error

Found 3 expressions with local error:

0.1b	(hypot (sin ky) (sin kx))
0.1b	(/ (sin ky) (hypot (sin ky) (sin kx)))
0.2b	(* (/ (sin ky) (hypot (sin ky) (sin kx))) (sin th))

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

3×	`associate-*l/`
2×	`frac-2neg` `clear-num` `div-inv`
1×	`hypot-udef` `associate-l` `*-commutative`

Counts

3 → 9

Calls

3 calls:

1.0ms	(hypot (sin ky) (sin kx))
3.0ms	(/ (sin ky) (hypot (sin ky) (sin kx)))
4.0ms	(* (/ (sin ky) (hypot (sin ky) (sin kx))) (sin th))

series488.0ms

Counts

3 → 9

Calls

3 calls:

112.0ms	(hypot (sin ky) (sin kx))
159.0ms	(/ (sin ky) (hypot (sin ky) (sin kx)))
217.0ms	(* (/ (sin ky) (hypot (sin ky) (sin kx))) (sin th))

simplify147.0ms

Algorithm

egg-herbie

Counts

18 → 18

Iterations

Useful iterations: 3 (39.0ms)

Iter	Nodes	Cost
0	116	105
1	356	97
2	1317	97
3	4953	96
4	5001	96

prune62.0ms

Filtered

18 candidates to 13 candidates (72.2%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	15	3	18
Fresh	2	3	5
Picked	1	0	1
Done	0	0	0
Total	18	6	24

Merged error: 0.0b

Counts

24 → 6

localize15.0ms

Local error

Found 3 expressions with local error:

0.1b	(hypot (sin ky) (sin kx))
0.1b	(/ (hypot (sin ky) (sin kx)) (sin ky))
0.2b	(/ (sin th) (/ (hypot (sin ky) (sin kx)) (sin ky)))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

3×	`frac-2neg` `clear-num` `associate-/r/` `div-inv`
1×	`hypot-udef` `associate-/r*`

Counts

3 → 11

Calls

3 calls:

1.0ms	(hypot (sin ky) (sin kx))
2.0ms	(/ (hypot (sin ky) (sin kx)) (sin ky))
4.0ms	(/ (sin th) (/ (hypot (sin ky) (sin kx)) (sin ky)))

series486.0ms

Counts

3 → 9

Calls

3 calls:

112.0ms	(hypot (sin ky) (sin kx))
140.0ms	(/ (hypot (sin ky) (sin kx)) (sin ky))
233.0ms	(/ (sin th) (/ (hypot (sin ky) (sin kx)) (sin ky)))

simplify35.0ms

Algorithm

egg-herbie

Counts

20 → 20

Iterations

Useful iterations: 2 (9.0ms)

Iter	Nodes	Cost
0	110	126
1	292	111
2	1043	109
3	5001	109

prune63.0ms

Filtered

20 candidates to 13 candidates (65.0%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	19	1	20
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	19	7	26

Merged error: 0.0b

Counts

26 → 7

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(hypot (sin ky) (sin kx))
0.2b	(/ 1 (hypot (sin ky) (sin kx)))
0.2b	(* (* (sin ky) (/ 1 (hypot (sin ky) (sin kx)))) (sin th))
0.3b	(* (sin ky) (/ 1 (hypot (sin ky) (sin kx))))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

6×	`associate-*r/`
5×	`associate-*l/` `clear-num`
4×	`un-div-inv`
3×	`frac-2neg` `associate-l` `*-commutative` `div-inv`
2×	`associate-r`
1×	`hypot-udef` `inv-pow`

Counts

4 → 21

Calls

4 calls:

1.0ms	(hypot (sin ky) (sin kx))
2.0ms	(/ 1 (hypot (sin ky) (sin kx)))
5.0ms	(* (* (sin ky) (/ 1 (hypot (sin ky) (sin kx)))) (sin th))
3.0ms	(* (sin ky) (/ 1 (hypot (sin ky) (sin kx))))

series659.0ms

Counts

4 → 12

Calls

4 calls:

119.0ms	(hypot (sin ky) (sin kx))
139.0ms	(/ 1 (hypot (sin ky) (sin kx)))
236.0ms	(* (* (sin ky) (/ 1 (hypot (sin ky) (sin kx)))) (sin th))
165.0ms	(* (sin ky) (/ 1 (hypot (sin ky) (sin kx))))

simplify48.0ms

Algorithm

egg-herbie

Counts

33 → 33

Iterations

Useful iterations: 3 (45.0ms)

Iter	Nodes	Cost
0	139	147
1	445	136
2	1602	135
3	5001	134

prune70.0ms

Filtered

33 candidates to 21 candidates (63.6%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	32	1	33
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	33	7	40

Merged error: 0.0b

Counts

40 → 7

regimes279.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	7

end0.0ms

sample4.7s

Algorithm

intervals

Results

3.1s	3781×	body	1280	valid
977.0ms	2014×	body	640	valid
237.0ms	686×	body	320	valid
138.0ms	1252×	body	80	valid
56.0ms	267×	body	160	valid