Details

sample193.0ms

Algorithm

intervals

Results

127.0ms	128×	body	1280	valid
38.0ms	63×	body	640	valid
7.0ms	19×	body	320	valid
4.0ms	37×	body	80	valid
2.0ms	9×	body	160	valid

simplify53.0ms

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	1830	10
6	5001	10

prune3.0ms

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: 3.3b

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))))
0.3b	(pow (sin ky) 2.0)
0.3b	(pow (sin kx) 2.0)
3.0b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

46×	`*-un-lft-identity`
39×	`add-sqr-sqrt`
26×	`add-cube-cbrt`
25×	`sqrt-prod`
24×	`times-frac`
22×	`unpow-prod-down`
10×	`distribute-lft-out`
9×	`hypot-def`
8×	`add-exp-log` `associate-/r*` `sqr-pow`
7×	`pow1`
6×	`pow-unpow` `add-cbrt-cube`
4×	`expm1-log1p-u` `sqrt-div` `log1p-expm1-u` `add-log-exp`
3×	`associate-/l*`
2×	`pow-to-exp` `pow-pow` `flip3-+` `pow-exp` `associate-/r/` `flip-+`
1×	`cbrt-undiv` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `clear-num` `div-inv`

Counts

4 → 117

Calls

4 calls:

11.0ms	(/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
3.0ms	(pow (sin ky) 2.0)
3.0ms	(pow (sin kx) 2.0)
8.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series403.0ms

Counts

4 → 12

Calls

4 calls:

123.0ms	(/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
104.0ms	(pow (sin ky) 2.0)
99.0ms	(pow (sin kx) 2.0)
77.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify41.0ms

Algorithm

egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	341	1065
1	1159	981
2	5001	976

prune405.0ms

Filtered

129 candidates to 87 candidates (67.4%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	118	11	129
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	119	11	130

Merged error: 0.0b

Counts

130 → 11

localize12.0ms

Local error

Found 3 expressions with local error:

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

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
19×	`add-cube-cbrt` `*-un-lft-identity` `times-frac`
13×	`associate-l`
10×	`add-exp-log` `add-cbrt-cube`
5×	`pow1`
3×	`expm1-log1p-u` `associate-r` `associate-/r` `log1p-expm1-u` `associate-/l` `add-log-exp`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `div-inv` `unswap-sqr`
1×	`hypot-udef` `frac-2neg` `pow-prod-down` `associate-l/` `clear-num` `-commutative`

Counts

3 → 73

Calls

3 calls:

1.0ms	(hypot (sin ky) (sin kx))
6.0ms	(* (/ (sin ky) (hypot (sin ky) (sin kx))) (sin th))
4.0ms	(/ (sin ky) (hypot (sin ky) (sin kx)))

series496.0ms

Counts

3 → 9

Calls

3 calls:

118.0ms	(hypot (sin ky) (sin kx))
217.0ms	(* (/ (sin ky) (hypot (sin ky) (sin kx))) (sin th))
161.0ms	(/ (sin ky) (hypot (sin ky) (sin kx)))

simplify141.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (27.0ms)

Iter	Nodes	Cost
0	287	725
1	1045	645
2	4962	644
3	5001	644

prune252.0ms

Filtered

82 candidates to 65 candidates (79.3%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	74	8	82
Fresh	6	4	10
Picked	1	0	1
Done	0	0	0
Total	81	12	93

Merged error: 0b

Counts

93 → 12

localize13.0ms

Local error

Found 4 expressions with local error:

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

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

156×	`times-frac`
104×	`add-sqr-sqrt`
92×	`*-un-lft-identity`
90×	`add-cube-cbrt`
44×	`associate-l`
36×	`add-exp-log`
20×	`add-cbrt-cube`
16×	`associate-/r*`
15×	`div-exp`
10×	`div-inv`
7×	`pow1` `cbrt-undiv` `prod-exp`
6×	`associate-/l*`
5×	`unswap-sqr`
4×	`expm1-log1p-u` `rec-exp` `1-exp` `log1p-expm1-u` `add-log-exp`
3×	`associate-r` `cbrt-unprod`
2×	`frac-2neg` `clear-num` `associate-/r/`
1×	`hypot-udef` `pow-flip` `pow-prod-down` `associate-l/` `-commutative` `inv-pow`

Counts

4 → 191

Calls

4 calls:

1.0ms	(hypot (sin ky) (sin kx))
4.0ms	(/ (hypot (sin ky) (sin kx)) (sin ky))
13.0ms	(* (/ 1 (/ (hypot (sin ky) (sin kx)) (sin ky))) (sin th))
6.0ms	(/ 1 (/ (hypot (sin ky) (sin kx)) (sin ky)))

series637.0ms

Counts

4 → 12

Calls

4 calls:

113.0ms	(hypot (sin ky) (sin kx))
135.0ms	(/ (hypot (sin ky) (sin kx)) (sin ky))
225.0ms	(* (/ 1 (/ (hypot (sin ky) (sin kx)) (sin ky))) (sin th))
164.0ms	(/ 1 (/ (hypot (sin ky) (sin kx)) (sin ky)))

simplify81.0ms

Algorithm

egg-herbie

Counts

203 → 203

Iterations

Useful iterations: 2 (57.0ms)

Iter	Nodes	Cost
0	637	2121
1	2915	1881
2	5001	1782

prune476.0ms

Filtered

203 candidates to 137 candidates (67.5%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	202	1	203
Fresh	1	10	11
Picked	1	0	1
Done	0	0	0
Total	204	11	215

Merged error: 0b

Counts

215 → 11

localize12.0ms

Local error

Found 3 expressions with local error:

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

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

84×	`times-frac`
53×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
16×	`associate-/r*`
10×	`add-exp-log` `add-cbrt-cube`
6×	`div-inv` `associate-/l*`
4×	`cbrt-undiv` `div-exp`
3×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`frac-2neg` `clear-num`
1×	`hypot-udef` `associate-/r/`

Counts

3 → 111

Calls

3 calls:

1.0ms	(hypot (sin ky) (sin kx))
3.0ms	(/ (hypot (sin ky) (sin kx)) (sin ky))
6.0ms	(/ (sin th) (/ (hypot (sin ky) (sin kx)) (sin ky)))

series493.0ms

Counts

3 → 9

Calls

3 calls:

115.0ms	(hypot (sin ky) (sin kx))
139.0ms	(/ (hypot (sin ky) (sin kx)) (sin ky))
239.0ms	(/ (sin th) (/ (hypot (sin ky) (sin kx)) (sin ky)))

simplify53.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	426	1414
1	1727	1322
2	5001	1320

prune322.0ms

Filtered

120 candidates to 99 candidates (82.5%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	118	2	120
Fresh	4	6	10
Picked	1	0	1
Done	0	0	0
Total	123	8	131

Merged error: 0b

Counts

131 → 8

regimes364.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	8
1	13	8

end0.0ms

sample5.9s

Algorithm

intervals

Results

3.9s	3746×	body	1280	valid
1.2s	1959×	body	640	valid
309.0ms	738×	body	320	valid
139.0ms	1265×	body	80	valid
80.0ms	292×	body	160	valid

Details

sample193.0ms

simplify53.0ms

prune3.0ms

localize15.0ms

rewrite28.0ms

series403.0ms

simplify41.0ms

prune405.0ms

localize12.0ms

rewrite13.0ms

series496.0ms

simplify141.0ms

prune252.0ms

localize13.0ms

rewrite31.0ms

series637.0ms

simplify81.0ms

prune476.0ms

localize12.0ms

rewrite15.0ms

series493.0ms

simplify53.0ms

prune322.0ms

regimes364.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample5.9s

Profiling