Details

sample196.0ms

Algorithm

intervals

Results

113.0ms	114×	body	1280	valid
49.0ms	81×	body	640	valid
8.0ms	20×	body	320	valid
5.0ms	37×	body	80	valid
1.0ms	4×	body	160	valid

simplify51.0ms

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

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: 3.8b

Counts

2 → 1

localize21.0ms

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))
0.2b	(pow (sin ky) 2.0)
0.2b	(pow (sin kx) 2.0)
3.5b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 101

Calls

4 calls:

15.0ms	(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
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)))

series105.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
22.0ms	(pow (sin ky) 2.0)
19.0ms	(pow (sin kx) 2.0)
19.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify44.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	425	1022
1	1522	960
2	5001	946

prune292.0ms

Filtered

78 candidates to 113 candidates (-44.9%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	100	13	113
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	101	13	114

Merged error: 2.7b

Counts

114 → 13

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (sin kx) 2.0)
0.3b	(* (sin ky) (* (/ 1 (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th)))
0.3b	(* (/ 1 (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
3.5b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

42×	`*-un-lft-identity`
37×	`add-sqr-sqrt`
33×	`associate-l`
29×	`add-exp-log`
28×	`times-frac`
24×	`add-cube-cbrt`
22×	`sqrt-prod`
18×	`add-cbrt-cube`
13×	`pow1` `prod-exp`
11×	`unpow-prod-down`
8×	`distribute-lft-out`
7×	`cbrt-unprod`
5×	`unswap-sqr`
4×	`sqrt-div` `div-exp` `associate-r` `pow-prod-down` `add-log-exp`
3×	`pow-unpow`
2×	`cbrt-undiv` `rec-exp` `flip3-+` `1-exp` `associate-l/` `associate-/r/` `-commutative` `flip-+`
1×	`pow-to-exp` `rem-sqrt-square` `pow-pow` `sqrt-pow1` `pow1/2` `associate-*r/` `pow-exp` `div-inv` `sqr-pow`

Counts

4 → 111

Calls

4 calls:

3.0ms	(pow (sin kx) 2.0)
15.0ms	(* (sin ky) (* (/ 1 (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th)))
16.0ms	(* (/ 1 (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
7.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series126.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(pow (sin kx) 2.0)
44.0ms	(* (sin ky) (* (/ 1 (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th)))
43.0ms	(* (/ 1 (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
19.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify50.0ms

Algorithm

egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	443	1278
1	1781	1120
2	5001	1095

prune272.0ms

Filtered

80 candidates to 123 candidates (-53.8%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	120	3	123
Fresh	2	10	12
Picked	1	0	1
Done	0	0	0
Total	123	13	136

Merged error: 2.7b

Counts

136 → 13

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (sin kx) 2)
0.3b	(* (sin ky) (* (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)))
0.3b	(* (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th))
3.7b	(sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

53×	`*-un-lft-identity`
45×	`sqrt-prod`
40×	`add-sqr-sqrt`
34×	`times-frac`
27×	`add-cube-cbrt` `associate-l`
15×	`unpow-prod-down`
14×	`pow1`
12×	`add-exp-log` `distribute-lft-out`
11×	`add-cbrt-cube`
4×	`associate-r` `pow-prod-down` `prod-exp` `associate-/r/` `cbrt-unprod` `add-log-exp` `unswap-sqr`
3×	`rem-sqrt-square` `pow-unpow` `sqrt-pow1` `sqrt-div`
2×	`flip3-+` `associate-l/` `-commutative` `flip-+` `div-inv`
1×	`pow-to-exp` `pow-flip` `pow-pow` `pow1/2` `associate-*r/` `pow-exp` `unpow2` `inv-pow` `sqr-pow`

Counts

4 → 116

Calls

4 calls:

3.0ms	(pow (sin kx) 2)
15.0ms	(* (sin ky) (* (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)))
15.0ms	(* (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th))
10.0ms	(sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))

series119.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(pow (sin kx) 2)
44.0ms	(* (sin ky) (* (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)))
44.0ms	(* (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th))
28.0ms	(sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))

simplify49.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	379	1283
1	1312	1159
2	5002	1122

prune257.0ms

Filtered

77 candidates to 128 candidates (-66.2%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	127	1	128
Fresh	1	11	12
Picked	0	1	1
Done	0	0	0
Total	128	13	141

Merged error: 2.7b

Counts

141 → 13

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (sin ky) 2)
0.2b	(pow (sin kx) 2)
0.3b	(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
3.7b	(sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

54×	`*-un-lft-identity`
45×	`sqrt-prod`
41×	`add-sqr-sqrt`
34×	`times-frac`
28×	`add-cube-cbrt`
24×	`associate-r`
18×	`unpow-prod-down`
12×	`distribute-lft-out`
10×	`pow1`
8×	`add-exp-log`
6×	`pow-unpow` `add-cbrt-cube`
4×	`associate-/r/` `add-log-exp` `unswap-sqr`
3×	`rem-sqrt-square` `sqrt-pow1` `associate-l`
2×	`pow-to-exp` `pow-pow` `flip3-+` `sqrt-div` `pow-exp` `flip-+` `div-inv` `unpow2` `sqr-pow`
1×	`pow-flip` `pow1/2` `associate-r/` `pow-prod-down` `prod-exp` `-commutative` `cbrt-unprod` `inv-pow`

Counts

4 → 115

Calls

4 calls:

3.0ms	(pow (sin ky) 2)
3.0ms	(pow (sin kx) 2)
16.0ms	(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
10.0ms	(sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))

series71.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(pow (sin ky) 2)
3.0ms	(pow (sin kx) 2)
34.0ms	(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
30.0ms	(sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))

simplify47.0ms

Algorithm

egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	379	1045
1	1313	916
2	5001	861

prune175.0ms

Filtered

70 candidates to 127 candidates (-81.4%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	126	1	127
Fresh	1	10	11
Picked	1	0	1
Done	0	1	1
Total	128	12	140

Merged error: 2.7b

Counts

140 → 12

regimes1.2s

Accuracy

0% (1.7b remaining)

Error of 4.4b against oracle of 2.7b and baseline of 4.4b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	11
1	20	11

end0.0ms

sample6.0s

Algorithm

intervals

Results

3.8s	3684×	body	1280	valid
1.3s	2072×	body	640	valid
291.0ms	692×	body	320	valid
146.0ms	1246×	body	80	valid
81.0ms	306×	body	160	valid

Details

sample196.0ms

simplify51.0ms

prune5.0ms

localize21.0ms

rewrite31.0ms

series105.0ms

simplify44.0ms

prune292.0ms

localize17.0ms

rewrite45.0ms

series126.0ms

simplify50.0ms

prune272.0ms

localize19.0ms

rewrite48.0ms

series119.0ms

simplify49.0ms

prune257.0ms

localize17.0ms

rewrite36.0ms

series71.0ms

simplify47.0ms

prune175.0ms

regimes1.2s

bsearch0.0ms

simplify1.0ms

end0.0ms

sample6.0s

Profiling