Details

sample191.0ms

Algorithm

intervals

Results

125.0ms	135×	body	1280	valid
33.0ms	56×	body	640	valid
10.0ms	42×	body	80	valid
6.0ms	16×	body	320	valid
2.0ms	7×	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

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: 4.4b

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))
0.2b	(pow (sin ky) 2.0)
0.3b	(pow (sin kx) 2.0)
4.1b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite36.0ms

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:

20.0ms	(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
3.0ms	(pow (sin ky) 2.0)
3.0ms	(pow (sin kx) 2.0)
7.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series441.0ms

Counts

4 → 12

Calls

4 calls:

153.0ms	(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
103.0ms	(pow (sin ky) 2.0)
111.0ms	(pow (sin kx) 2.0)
74.0ms	(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	391	990
1	1382	928
2	5001	927

prune385.0ms

Filtered

113 candidates to 78 candidates (69.0%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	99	14	113
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	100	14	114

Merged error: 2.8b

Counts

114 → 14

localize15.0ms

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) (/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
4.1b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

41×	`*-un-lft-identity`
34×	`add-sqr-sqrt`
30×	`associate-r`
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-l` `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` `associate-r/` `div-exp` `pow-prod-down` `-commutative` `div-inv`

Counts

4 → 101

Calls

4 calls:

3.0ms	(pow (sin ky) 2.0)
3.0ms	(pow (sin kx) 2.0)
17.0ms	(* (sin ky) (/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
7.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series440.0ms

Counts

4 → 12

Calls

4 calls:

107.0ms	(pow (sin ky) 2.0)
107.0ms	(pow (sin kx) 2.0)
147.0ms	(* (sin ky) (/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
79.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify56.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 1 (12.0ms)

Iter	Nodes	Cost
0	437	948
1	1864	870
2	5002	870

prune320.0ms

Filtered

113 candidates to 68 candidates (60.2%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	112	1	113
Fresh	1	12	13
Picked	0	1	1
Done	0	0	0
Total	113	14	127

Merged error: 2.8b

Counts

127 → 14

localize18.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (sin kx) 2.0)
0.5b	(* (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
4.1b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
4.1b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

100×	`sqrt-prod`
52×	`add-sqr-sqrt`
50×	`*-un-lft-identity`
34×	`sqrt-pow1`
30×	`pow1`
28×	`sqrt-div`
20×	`add-cube-cbrt`
19×	`swap-sqr`
18×	`pow1/2`
15×	`unpow-prod-down`
14×	`distribute-lft-out`
11×	`associate-r` `associate-l`
9×	`pow-prod-up` `unswap-sqr`
8×	`flip3-+` `flip-+`
7×	`add-exp-log`
6×	`add-cbrt-cube`
5×	`pow-prod-down` `pow-sqr`
4×	`frac-times` `add-log-exp`
3×	`pow-unpow`
2×	`rem-sqrt-square` `associate-r/` `associate-l/`
1×	`pow2` `pow-to-exp` `pow-pow` `pow-plus` `sqrt-unprod` `pow-exp` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod` `sqr-pow`

Counts

4 → 142

Calls

4 calls:

3.0ms	(pow (sin kx) 2.0)
23.0ms	(* (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
11.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
7.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series346.0ms

Counts

4 → 12

Calls

4 calls:

111.0ms	(pow (sin kx) 2.0)
73.0ms	(* (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
78.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
83.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify56.0ms

Algorithm

egg-herbie

Counts

154 → 154

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	309	1456
1	1174	1355
2	5001	1324

prune385.0ms

Filtered

154 candidates to 72 candidates (46.8%)

Pruning

14 alts after pruning (12 fresh and 2 done)

	Pruned	Kept	Total
New	154	0	154
Fresh	0	12	12
Picked	0	1	1
Done	0	1	1
Total	154	14	168

Merged error: 2.8b

Counts

168 → 14

localize20.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sin ky) (/ (sin th) (sqrt (+ (exp (log (pow (sin kx) 2.0))) (pow (sin ky) 2.0)))))
1.6b	(exp (log (pow (sin kx) 2.0)))
4.1b	(sqrt (+ (exp (log (pow (sin kx) 2.0))) (pow (sin ky) 2.0)))
16.1b	(log (pow (sin kx) 2.0))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 100

Calls

4 calls:

19.0ms	(* (sin ky) (/ (sin th) (sqrt (+ (exp (log (pow (sin kx) 2.0))) (pow (sin ky) 2.0)))))
4.0ms	(exp (log (pow (sin kx) 2.0)))
9.0ms	(sqrt (+ (exp (log (pow (sin kx) 2.0))) (pow (sin ky) 2.0)))
3.0ms	(log (pow (sin kx) 2.0))

series494.0ms

Counts

4 → 12

Calls

4 calls:

148.0ms	(* (sin ky) (/ (sin th) (sqrt (+ (exp (log (pow (sin kx) 2.0))) (pow (sin ky) 2.0)))))
106.0ms	(exp (log (pow (sin kx) 2.0)))
81.0ms	(sqrt (+ (exp (log (pow (sin kx) 2.0))) (pow (sin ky) 2.0)))
158.0ms	(log (pow (sin kx) 2.0))

simplify52.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	422	1121
1	1635	1024
2	5001	1022

prune319.0ms

Filtered

112 candidates to 71 candidates (63.4%)

Pruning

14 alts after pruning (11 fresh and 3 done)

	Pruned	Kept	Total
New	112	0	112
Fresh	0	11	11
Picked	0	1	1
Done	0	2	2
Total	112	14	126

Merged error: 2.8b

Counts

126 → 14

regimes731.0ms

Accuracy

70.3% (0.4b remaining)

Error of 3.1b against oracle of 2.6b and baseline of 4.2b

bsearch3.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	29
1	37	29

end0.0ms

sample5.8s

Algorithm

intervals

Results

3.8s	3820×	body	1280	valid
1.2s	1975×	body	640	valid
288.0ms	691×	body	320	valid
157.0ms	1246×	body	80	valid
80.0ms	268×	body	160	valid

Details

sample191.0ms

simplify53.0ms

prune4.0ms

localize15.0ms

rewrite36.0ms

series441.0ms

simplify44.0ms

prune385.0ms

localize15.0ms

rewrite33.0ms

series440.0ms

simplify56.0ms

prune320.0ms

localize18.0ms

rewrite50.0ms

series346.0ms

simplify56.0ms

prune385.0ms

localize20.0ms

rewrite39.0ms

series494.0ms

simplify52.0ms

prune319.0ms

regimes731.0ms

bsearch3.0ms

simplify1.0ms

end0.0ms

sample5.8s

Profiling