Details

sample188.0ms

Algorithm

intervals

Results

115.0ms	113×	body	1280	valid
40.0ms	66×	body	640	valid
9.0ms	23×	body	320	valid
5.0ms	43×	body	80	valid
3.0ms	11×	body	160	valid

simplify53.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	23	10
1	35	10
2	63	10
3	137	10
4	417	10
5	1798	10
6	5002	10

prune5.0ms

Filtered

1 candidates to 0 candidates (100.0%)

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: 4.5b

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))))
0.2b	(pow (sin ky) 2.0)
0.3b	(pow (sin kx) 2.0)
4.2b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

46×	`*-un-lft-identity`
27×	`add-sqr-sqrt`
26×	`add-cube-cbrt`
25×	`sqrt-prod`
24×	`times-frac`
16×	`unpow-prod-down`
10×	`distribute-lft-out`
8×	`add-exp-log` `associate-/r*`
7×	`pow1`
6×	`pow-unpow` `add-cbrt-cube`
4×	`sqrt-div` `add-log-exp`
3×	`associate-/l*`
2×	`pow-to-exp` `pow-pow` `flip3-+` `pow-exp` `associate-/r/` `flip-+` `sqr-pow`
1×	`cbrt-undiv` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `clear-num` `div-inv`

Counts

4 → 100

Calls

4 calls:

11.0ms	(/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
2.0ms	(pow (sin ky) 2.0)
2.0ms	(pow (sin kx) 2.0)
7.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series99.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
19.0ms	(pow (sin ky) 2.0)
20.0ms	(pow (sin kx) 2.0)
24.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify43.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	363	1053
1	1249	978
2	5001	961

prune253.0ms

Filtered

112 candidates to 70 candidates (37.5%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	101	11	112
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	101	12	113

Merged error: 3.0b

Counts

113 → 12

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (sin ky) 2.0)
0.3b	(pow (sin kx) 2.0)
0.3b	(* (sin ky) (/ 1 (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
4.2b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

43×	`*-un-lft-identity`
38×	`add-sqr-sqrt`
30×	`associate-r`
28×	`times-frac`
25×	`add-cube-cbrt`
22×	`sqrt-prod`
15×	`add-exp-log`
14×	`unpow-prod-down`
9×	`pow1` `add-cbrt-cube`
8×	`distribute-lft-out`
6×	`pow-unpow`
5×	`unswap-sqr`
4×	`sqrt-div` `prod-exp` `add-log-exp`
3×	`associate-l`
2×	`pow-to-exp` `pow-pow` `flip3-+` `div-exp` `pow-exp` `associate-/r/` `cbrt-unprod` `flip-+` `sqr-pow`
1×	`cbrt-undiv` `rem-sqrt-square` `rec-exp` `sqrt-pow1` `pow1/2` `1-exp` `associate-r/` `pow-prod-down` `un-div-inv` `-commutative` `div-inv`

Counts

4 → 106

Calls

4 calls:

2.0ms	(pow (sin ky) 2.0)
3.0ms	(pow (sin kx) 2.0)
19.0ms	(* (sin ky) (/ 1 (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
7.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series95.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(pow (sin ky) 2.0)
19.0ms	(pow (sin kx) 2.0)
35.0ms	(* (sin ky) (/ 1 (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
19.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify57.0ms

Algorithm

egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	482	963
1	2275	882
2	5002	841

prune229.0ms

Filtered

118 candidates to 69 candidates (41.5%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	118	0	118
Fresh	0	10	10
Picked	0	1	1
Done	0	1	1
Total	118	12	130

Merged error: 3.0b

Counts

130 → 12

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))
0.3b	(pow (sin kx) 2)
0.3b	(* (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin ky))
4.4b	(sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

78×	`*-un-lft-identity`
49×	`add-sqr-sqrt` `times-frac`
45×	`sqrt-prod`
36×	`add-cube-cbrt`
24×	`associate-l`
23×	`unpow-prod-down`
20×	`distribute-lft-out`
11×	`add-exp-log`
10×	`pow1`
8×	`add-cbrt-cube`
6×	`associate-/r/`
5×	`associate-/r*`
4×	`add-log-exp` `unswap-sqr`
3×	`rem-sqrt-square` `pow-unpow` `sqrt-pow1` `flip3-+` `associate-r` `flip-+` `div-inv` `associate-/l*`
2×	`pow-flip` `sqrt-div` `div-exp` `inv-pow`
1×	`cbrt-undiv` `pow-to-exp` `rec-exp` `pow-pow` `frac-2neg` `pow1/2` `1-exp` `pow-prod-down` `associate-l/` `pow-exp` `prod-exp` `clear-num` `-commutative` `cbrt-unprod` `unpow2` `sqr-pow`

Counts

4 → 138

Calls

4 calls:

10.0ms	(/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))
2.0ms	(pow (sin kx) 2)
16.0ms	(* (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin ky))
10.0ms	(sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))

series87.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))
4.0ms	(pow (sin kx) 2)
34.0ms	(* (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin ky))
29.0ms	(sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))

simplify51.0ms

Algorithm

egg-herbie

Counts

150 → 150

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	384	1400
1	1350	1277
2	5002	1219

prune256.0ms

Filtered

150 candidates to 81 candidates (46.0%)

Pruning

12 alts after pruning (9 fresh and 3 done)

	Pruned	Kept	Total
New	148	2	150
Fresh	2	7	9
Picked	0	1	1
Done	0	2	2
Total	150	12	162

Merged error: 3.0b

Counts

162 → 12

localize21.0ms

Local error

Found 4 expressions with local error:

0.7b	(cbrt (sin kx))
0.7b	(cbrt (sin kx))
0.7b	(cbrt (sin kx))
4.2b	(sqrt (+ (* (pow (* (cbrt (sin kx)) (cbrt (sin kx))) 2.0) (pow (cbrt (sin kx)) 2.0)) (pow (sin ky) 2.0)))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod` `add-sqr-sqrt`
8×	`add-cube-cbrt` `*-un-lft-identity`
5×	`pow1`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`pow1/3` `sqrt-prod`
2×	`sqrt-div`
1×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`

Counts

4 → 48

Calls

4 calls:

2.0ms	(cbrt (sin kx))
2.0ms	(cbrt (sin kx))
2.0ms	(cbrt (sin kx))
9.0ms	(sqrt (+ (* (pow (* (cbrt (sin kx)) (cbrt (sin kx))) 2.0) (pow (cbrt (sin kx)) 2.0)) (pow (sin ky) 2.0)))

series78.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(cbrt (sin kx))
19.0ms	(cbrt (sin kx))
19.0ms	(cbrt (sin kx))
22.0ms	(sqrt (+ (* (pow (* (cbrt (sin kx)) (cbrt (sin kx))) 2.0) (pow (cbrt (sin kx)) 2.0)) (pow (sin ky) 2.0)))

simplify90.0ms

Algorithm

egg-herbie

Counts

60 → 60

Iterations

Useful iterations: 3 (83.0ms)

Iter	Nodes	Cost
0	189	553
1	571	525
2	2518	507
3	5002	503

prune115.0ms

Filtered

60 candidates to 47 candidates (21.7%)

Pruning

12 alts after pruning (8 fresh and 4 done)

	Pruned	Kept	Total
New	60	0	60
Fresh	0	8	8
Picked	0	1	1
Done	0	3	3
Total	60	12	72

Merged error: 3.0b

Counts

72 → 12

regimes1.0s

Accuracy

57% (0.6b remaining)

Error of 3.0b against oracle of 2.5b and baseline of 3.8b

bsearch2.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	23
1	29	23

end0.0ms

sample6.0s

Algorithm

intervals

Results

3.8s	3705×	body	1280	valid
1.3s	2040×	body	640	valid
274.0ms	694×	body	320	valid
145.0ms	1252×	body	80	valid
89.0ms	309×	body	160	valid

Details

sample188.0ms

simplify53.0ms

prune5.0ms

localize15.0ms

rewrite25.0ms

series99.0ms

simplify43.0ms

prune253.0ms

localize17.0ms

rewrite35.0ms

series95.0ms

simplify57.0ms

prune229.0ms

localize16.0ms

rewrite45.0ms

series87.0ms

simplify51.0ms

prune256.0ms

localize21.0ms

rewrite14.0ms

series78.0ms

simplify90.0ms

prune115.0ms

regimes1.0s

bsearch2.0ms

simplify1.0ms

end0.0ms

sample6.0s

Profiling