Details

sample148.0ms

Algorithm

intervals

Results

94.0ms	121×	body	1280	valid
28.0ms	63×	body	640	valid
7.0ms	22×	body	320	valid
4.0ms	45×	body	80	valid
1.0ms	5×	body	160	valid

simplify50.0ms

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

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: 4.0b

Counts

2 → 1

localize22.0ms

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 ky) 2.0)
0.3b	(pow (sin kx) 2.0)
3.6b	(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:

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

series434.0ms

Counts

4 → 12

Calls

4 calls:

150.0ms	(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
103.0ms	(pow (sin ky) 2.0)
104.0ms	(pow (sin kx) 2.0)
77.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify43.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	391	991
1	1380	928
2	5001	927

prune371.0ms

Filtered

113 candidates to 78 candidates (69.0%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	103	10	113
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	103	11	114

Merged error: 2.3b

Counts

114 → 11

localize15.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (sin th) (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)
3.6b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 100

Calls

4 calls:

14.0ms	(/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
2.0ms	(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)))

series409.0ms

Counts

4 → 12

Calls

4 calls:

127.0ms	(/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
101.0ms	(pow (sin ky) 2.0)
108.0ms	(pow (sin kx) 2.0)
72.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify122.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 2 (27.0ms)

Iter	Nodes	Cost
0	329	1020
1	1058	944
2	4205	941
3	5001	941

prune303.0ms

Filtered

112 candidates to 70 candidates (62.5%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	110	2	112
Fresh	1	8	9
Picked	1	0	1
Done	0	1	1
Total	112	11	123

Merged error: 2.3b

Counts

123 → 11

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sin ky) (/ 1 (/ (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))) (sin th))))
0.3b	(pow (sin ky) 2.0)
0.3b	(pow (sin kx) 2.0)
3.6b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

166×	`times-frac`
127×	`*-un-lft-identity`
106×	`add-sqr-sqrt`
89×	`associate-r`
84×	`add-cube-cbrt`
52×	`sqrt-prod`
26×	`unpow-prod-down`
25×	`add-exp-log`
20×	`distribute-lft-out`
13×	`add-cbrt-cube`
9×	`pow1`
7×	`div-exp` `prod-exp` `unswap-sqr`
6×	`pow-unpow`
4×	`div-inv` `add-log-exp`
3×	`cbrt-undiv` `associate-l` `cbrt-unprod`
2×	`pow-to-exp` `rec-exp` `pow-pow` `sqrt-div` `1-exp` `pow-exp` `sqr-pow`
1×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `associate-r/` `pow-prod-down` `associate-/r/` `un-div-inv` `-commutative` `flip-+`

Counts

4 → 171

Calls

4 calls:

34.0ms	(* (sin ky) (/ 1 (/ (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)))

series434.0ms

Counts

4 → 12

Calls

4 calls:

152.0ms	(* (sin ky) (/ 1 (/ (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))) (sin th))))
102.0ms	(pow (sin ky) 2.0)
102.0ms	(pow (sin kx) 2.0)
77.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify94.0ms

Algorithm

egg-herbie

Counts

183 → 183

Iterations

Useful iterations: 2 (77.0ms)

Iter	Nodes	Cost
0	836	1918
1	4320	1702
2	5001	1589

prune446.0ms

Filtered

183 candidates to 102 candidates (55.7%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	182	1	183
Fresh	1	8	9
Picked	0	1	1
Done	1	0	1
Total	184	10	194

Merged error: 2.3b

Counts

194 → 10

localize17.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (sin ky) 2.0)
0.3b	(/ 1 (/ 1 (sin th)))
0.3b	(pow (sin kx) 2.0)
3.6b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

75×	`times-frac`
55×	`*-un-lft-identity`
52×	`add-sqr-sqrt`
51×	`add-cube-cbrt`
25×	`add-exp-log`
14×	`div-exp`
13×	`associate-/r*`
9×	`pow1` `add-cbrt-cube`
8×	`unpow-prod-down`
7×	`rec-exp` `1-exp`
6×	`pow-unpow`
5×	`sqrt-prod` `div-inv`
4×	`pow-flip` `add-log-exp`
3×	`cbrt-undiv` `associate-/l*`
2×	`pow-to-exp` `pow-pow` `sqrt-div` `pow-exp` `distribute-lft-out` `inv-pow` `sqr-pow`
1×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `clear-num` `associate-/r/` `flip-+` `remove-double-div`

Counts

4 → 136

Calls

4 calls:

2.0ms	(pow (sin ky) 2.0)
6.0ms	(/ 1 (/ 1 (sin th)))
3.0ms	(pow (sin kx) 2.0)
7.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series285.0ms

Counts

4 → 12

Calls

4 calls:

100.0ms	(pow (sin ky) 2.0)
6.0ms	(/ 1 (/ 1 (sin th)))
107.0ms	(pow (sin kx) 2.0)
72.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify53.0ms

Algorithm

egg-herbie

Counts

148 → 148

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	538	855
1	2467	692
2	5001	590

prune264.0ms

Filtered

148 candidates to 69 candidates (46.6%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	148	0	148
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	148	10	158

Merged error: 2.3b

Counts

158 → 10

regimes442.0ms

Accuracy

0% (1.6b remaining)

Error of 4.0b against oracle of 2.4b and baseline of 4.0b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	11
1	19	11

end0.0ms

sample4.8s

Algorithm

intervals

Results

3.1s	3674×	body	1280	valid
1.0s	2082×	body	640	valid
224.0ms	700×	body	320	valid
119.0ms	1261×	body	80	valid
63.0ms	283×	body	160	valid