Details

sample194.0ms

Algorithm

intervals

Results

121.0ms	120×	body	1280	valid
38.0ms	66×	body	640	valid
8.0ms	19×	body	320	valid
5.0ms	41×	body	80	valid
3.0ms	10×	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

prune5.0ms

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: 2.4b

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)
2.2b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite30.0ms

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:

15.0ms	(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
2.0ms	(pow (sin ky) 2.0)
2.0ms	(pow (sin kx) 2.0)
7.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series376.0ms

Counts

4 → 12

Calls

4 calls:

145.0ms	(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
76.0ms	(pow (sin ky) 2.0)
78.0ms	(pow (sin kx) 2.0)
77.0ms	(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	420	1024
1	1509	962
2	5002	961

prune555.0ms

Filtered

113 candidates to 82 candidates (72.6%)

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: 1.2b

Counts

114 → 11

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (sin ky) 2.0)
0.3b	(pow (sin kx) 2.0)
0.3b	(* (/ 1 (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
2.2b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

43×	`*-un-lft-identity`
38×	`add-sqr-sqrt`
30×	`associate-l`
28×	`times-frac`
25×	`add-cube-cbrt`
22×	`sqrt-prod`
15×	`add-exp-log`
14×	`unpow-prod-down`
9×	`pow1` `add-cbrt-cube`
8×	`distribute-lft-out`
6×	`pow-unpow`
5×	`unswap-sqr`
4×	`sqrt-div` `prod-exp` `add-log-exp`
3×	`associate-r`
2×	`pow-to-exp` `pow-pow` `flip3-+` `div-exp` `pow-exp` `associate-/r/` `cbrt-unprod` `flip-+` `sqr-pow`
1×	`cbrt-undiv` `rem-sqrt-square` `rec-exp` `sqrt-pow1` `pow1/2` `1-exp` `pow-prod-down` `associate-l/` `-commutative` `div-inv`

Counts

4 → 105

Calls

4 calls:

2.0ms	(pow (sin ky) 2.0)
2.0ms	(pow (sin kx) 2.0)
16.0ms	(* (/ 1 (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
7.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series381.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(pow (sin ky) 2.0)
79.0ms	(pow (sin kx) 2.0)
147.0ms	(* (/ 1 (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
75.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify45.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	423	1014
1	1600	937
2	5002	910

prune545.0ms

Filtered

117 candidates to 83 candidates (70.9%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	116	1	117
Fresh	1	9	10
Picked	0	1	1
Done	0	0	0
Total	117	11	128

Merged error: 1.2b

Counts

128 → 11

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
0.2b	(pow (sin ky) 2.0)
0.3b	(pow (sin kx) 2.0)
2.2b	(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:

11.0ms	(/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
2.0ms	(pow (sin ky) 2.0)
2.0ms	(pow (sin kx) 2.0)
7.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series360.0ms

Counts

4 → 12

Calls

4 calls:

131.0ms	(/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
78.0ms	(pow (sin ky) 2.0)
79.0ms	(pow (sin kx) 2.0)
72.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify135.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	358	1054
1	1185	978
2	4871	974
3	5001	974

prune480.0ms

Filtered

112 candidates to 74 candidates (66.1%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	111	1	112
Fresh	1	8	9
Picked	1	0	1
Done	0	1	1
Total	113	10	123

Merged error: 1.2b

Counts

123 → 10

localize21.0ms

Local error

Found 4 expressions with local error:

0.7b	(cbrt (sin kx))
0.7b	(cbrt (sin kx))
0.7b	(cbrt (sin kx))
2.2b	(sqrt (+ (* (pow (* (cbrt (sin kx)) (cbrt (sin kx))) 2.0) (pow (cbrt (sin kx)) 2.0)) (pow (sin ky) 2.0)))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod` `add-sqr-sqrt`
8×	`add-cube-cbrt` `*-un-lft-identity`
5×	`pow1`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`pow1/3` `sqrt-prod`
2×	`sqrt-div`
1×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`

Counts

4 → 48

Calls

4 calls:

2.0ms	(cbrt (sin kx))
1.0ms	(cbrt (sin kx))
2.0ms	(cbrt (sin kx))
12.0ms	(sqrt (+ (* (pow (* (cbrt (sin kx)) (cbrt (sin kx))) 2.0) (pow (cbrt (sin kx)) 2.0)) (pow (sin ky) 2.0)))

series307.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(cbrt (sin kx))
77.0ms	(cbrt (sin kx))
78.0ms	(cbrt (sin kx))
72.0ms	(sqrt (+ (* (pow (* (cbrt (sin kx)) (cbrt (sin kx))) 2.0) (pow (cbrt (sin kx)) 2.0)) (pow (sin ky) 2.0)))

simplify109.0ms

Algorithm

egg-herbie

Counts

60 → 60

Iterations

Useful iterations: 3 (102.0ms)

Iter	Nodes	Cost
0	211	607
1	688	576
2	3278	555
3	5002	554

prune373.0ms

Filtered

60 candidates to 53 candidates (88.3%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	60	0	60
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	60	10	70

Merged error: 1.2b

Counts

70 → 10

regimes837.0ms

Accuracy

0% (1.4b remaining)

Error of 3.9b against oracle of 2.5b and baseline of 3.9b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	11
1	20	11

end0.0ms

sample5.9s

Algorithm

intervals

Results

3.9s	3778×	body	1280	valid
1.2s	1999×	body	640	valid
291.0ms	707×	body	320	valid
140.0ms	1239×	body	80	valid
70.0ms	277×	body	160	valid

Details

sample194.0ms

simplify50.0ms

prune5.0ms

localize15.0ms

rewrite30.0ms

series376.0ms

simplify45.0ms

prune555.0ms

localize16.0ms

rewrite31.0ms

series381.0ms

simplify45.0ms

prune545.0ms

localize15.0ms

rewrite29.0ms

series360.0ms

simplify135.0ms

prune480.0ms

localize21.0ms

rewrite18.0ms

series307.0ms

simplify109.0ms

prune373.0ms

regimes837.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample5.9s

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