Details

sample118.0ms

Algorithm

intervals

Results

53.0ms	70×	body	1280	valid
31.0ms	72×	body	640	valid
8.0ms	27×	body	320	valid
6.0ms	73×	body	80	valid
2.0ms	14×	body	160	valid

simplify60.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.7b

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)
3.4b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite122.0ms

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:

80.0ms	(* (/ (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)
32.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series408.0ms

Counts

4 → 12

Calls

4 calls:

140.0ms	(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
97.0ms	(pow (sin ky) 2.0)
99.0ms	(pow (sin kx) 2.0)
71.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify41.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	391	990
1	1382	928
2	5001	927

prune414.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 12.3b

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (sin ky) 2.0)
0.3b	(* (sin ky) (/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
0.3b	(pow (sin kx) 2.0)
3.4b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite117.0ms

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)
81.0ms	(* (sin ky) (/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
3.0ms	(pow (sin kx) 2.0)
26.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series401.0ms

Counts

4 → 12

Calls

4 calls:

98.0ms	(pow (sin ky) 2.0)
133.0ms	(* (sin ky) (/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
99.0ms	(pow (sin kx) 2.0)
71.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify53.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 1 (10.0ms)

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

prune393.0ms

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 12.3b

localize18.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ (sin ky) (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))) (/ (sin th) (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
0.4b	(/ (sin ky) (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
3.4b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
3.4b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite277.0ms

Algorithm

rewrite-expression-head

Rules

164×	`sqrt-prod`
130×	`add-sqr-sqrt`
123×	`times-frac`
120×	`*-un-lft-identity`
72×	`add-cube-cbrt`
39×	`associate-r` `associate-l`
24×	`unpow-prod-down` `distribute-lft-out`
18×	`add-exp-log` `add-cbrt-cube`
16×	`sqrt-div` `unswap-sqr`
11×	`associate-/r*`
8×	`pow1`
6×	`associate-/r/`
5×	`cbrt-undiv` `flip3-+` `div-exp` `flip-+`
4×	`prod-exp` `cbrt-unprod` `add-log-exp`
3×	`div-inv` `associate-/l*`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`frac-times` `frac-2neg` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `*-commutative`

Counts

4 → 209

Calls

4 calls:

173.0ms	(* (/ (sin ky) (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))) (/ (sin th) (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
37.0ms	(/ (sin ky) (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
29.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
26.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series445.0ms

Counts

4 → 12

Calls

4 calls:

162.0ms	(* (/ (sin ky) (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))) (/ (sin th) (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
142.0ms	(/ (sin ky) (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
73.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
68.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify86.0ms

Algorithm

egg-herbie

Counts

221 → 221

Iterations

Useful iterations: 2 (53.0ms)

Iter	Nodes	Cost
0	681	4176
1	2877	3811
2	5001	3715

prune755.0ms

Pruning

24 alts after pruning (23 fresh and 1 done)

Merged error: 12.3b

localize21.0ms

Local error

Found 4 expressions with local error:

0.4b	(cbrt (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
3.4b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
3.4b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
3.4b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite105.0ms

Algorithm

rewrite-expression-head

Rules

46×	`*-un-lft-identity`
30×	`cbrt-prod` `sqrt-prod`
25×	`add-sqr-sqrt`
24×	`times-frac`
22×	`add-cube-cbrt`
12×	`unpow-prod-down` `distribute-lft-out`
8×	`sqrt-div`
7×	`pow1`
4×	`add-exp-log` `flip3-+` `add-cbrt-cube` `flip-+` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
2×	`associate-/r/`
1×	`cbrt-div` `pow1/3` `div-inv`

Counts

4 → 90

Calls

4 calls:

17.0ms	(cbrt (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
27.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
26.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
31.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series366.0ms

Counts

4 → 12

Calls

4 calls:

153.0ms	(cbrt (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
66.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
74.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
74.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify94.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 3 (83.0ms)

Iter	Nodes	Cost
0	282	1291
1	819	1231
2	3475	1224
3	5002	1219

prune398.0ms

Pruning

25 alts after pruning (24 fresh and 1 done)

Merged error: 12.3b

regimes1.2s

Accuracy

58.9% (0.6b remaining)

Error of 11.6b against oracle of 11.0b and baseline of 12.5b

bsearch4.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	48	59
1	48	59

end0.0ms

sample3.7s

Algorithm

intervals

Results

2.1s	2700×	body	1280	valid
750.0ms	1885×	body	640	valid
211.0ms	762×	body	320	valid
202.0ms	2290×	body	80	valid
64.0ms	363×	body	160	valid