Details

sample156.0ms

Algorithm

intervals

Results

97.0ms	120×	body	1280	valid
29.0ms	62×	body	640	valid
9.0ms	26×	body	320	valid
4.0ms	38×	body	80	valid
2.0ms	10×	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

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: 3.2b

Counts

2 → 1

localize16.0ms

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

rewrite39.0ms

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:

17.0ms	(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
2.0ms	(pow (sin kx) 2.0)
3.0ms	(pow (sin ky) 2.0)
13.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series453.0ms

Counts

4 → 12

Calls

4 calls:

150.0ms	(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
105.0ms	(pow (sin kx) 2.0)
105.0ms	(pow (sin ky) 2.0)
92.0ms	(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

prune401.0ms

Filtered

113 candidates to 78 candidates (69.0%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	102	11	113
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	103	11	114

Merged error: 1.9b

Counts

114 → 11

localize18.0ms

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

rewrite32.0ms

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:

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

series449.0ms

Counts

4 → 12

Calls

4 calls:

152.0ms	(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
112.0ms	(pow (sin kx) 2.0)
105.0ms	(pow (sin ky) 2.0)
79.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify45.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (34.0ms)

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

prune422.0ms

Filtered

113 candidates to 78 candidates (69.0%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	107	6	113
Fresh	6	4	10
Picked	0	1	1
Done	0	0	0
Total	113	11	124

Merged error: 1.9b

Counts

124 → 11

localize18.0ms

Local error

Found 4 expressions with local error:

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

rewrite39.0ms

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 kx) 2.0)
22.0ms	(* (sin ky) (/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
3.0ms	(pow (sin ky) 2.0)
8.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series444.0ms

Counts

4 → 12

Calls

4 calls:

111.0ms	(pow (sin kx) 2.0)
144.0ms	(* (sin ky) (/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
107.0ms	(pow (sin ky) 2.0)
81.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify56.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 1 (11.0ms)

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

prune386.0ms

Filtered

113 candidates to 71 candidates (62.8%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	109	4	113
Fresh	4	5	9
Picked	0	1	1
Done	0	1	1
Total	113	11	124

Merged error: 1.9b

Counts

124 → 11

localize22.0ms

Local error

Found 4 expressions with local error:

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

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

94×	`*-un-lft-identity`
85×	`times-frac`
84×	`add-sqr-sqrt`
60×	`sqrt-prod`
58×	`add-cube-cbrt`
47×	`cbrt-prod`
39×	`associate-r`
18×	`add-exp-log` `unpow-prod-down` `add-cbrt-cube` `distribute-lft-out`
13×	`associate-l`
11×	`associate-/r*`
8×	`cbrt-div` `unswap-sqr`
6×	`pow1`
5×	`cbrt-undiv` `div-exp`
4×	`flip3-+` `sqrt-div` `prod-exp` `associate-/r/` `cbrt-unprod` `flip-+` `add-log-exp`
3×	`div-inv` `associate-/l*`
2×	`pow1/3`
1×	`frac-times` `frac-2neg` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `*-commutative`

Counts

4 → 171

Calls

4 calls:

27.0ms	(* (/ (sin ky) (fabs (cbrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))) (/ (sin th) (sqrt (cbrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
17.0ms	(/ (sin th) (sqrt (cbrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
7.0ms	(cbrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
7.0ms	(cbrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series572.0ms

Counts

4 → 12

Calls

4 calls:

230.0ms	(* (/ (sin ky) (fabs (cbrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))) (/ (sin th) (sqrt (cbrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
144.0ms	(/ (sin th) (sqrt (cbrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
98.0ms	(cbrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
101.0ms	(cbrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify89.0ms

Algorithm

egg-herbie

Counts

183 → 183

Iterations

Useful iterations: 2 (63.0ms)

Iter	Nodes	Cost
0	728	3415
1	3145	3139
2	5002	3132

prune752.0ms

Filtered

183 candidates to 126 candidates (68.9%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	182	1	183
Fresh	1	7	8
Picked	0	1	1
Done	0	2	2
Total	183	11	194

Merged error: 1.9b

Counts

194 → 11

regimes569.0ms

Accuracy

0% (1.3b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	10
1	23	10
2	23	10

end0.0ms

sample4.9s

Algorithm

intervals

Results

3.2s	3781×	body	1280	valid
1.0s	2014×	body	640	valid
237.0ms	686×	body	320	valid
136.0ms	1252×	body	80	valid
56.0ms	267×	body	160	valid