Details

sample194.0ms

Algorithm

intervals

Results

114.0ms	120×	body	1280	valid
45.0ms	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 (100.0%)

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)))

series106.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
18.0ms	(pow (sin ky) 2.0)
20.0ms	(pow (sin kx) 2.0)
24.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify47.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	425	1022
1	1522	960
2	5001	946

prune695.0ms

Filtered

113 candidates to 78 candidates (31.0%)

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: 1.2b

Counts

114 → 11

localize20.0ms

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)
3.0ms	(pow (sin kx) 2.0)
15.0ms	(* (/ 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)))

series100.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(pow (sin ky) 2.0)
18.0ms	(pow (sin kx) 2.0)
45.0ms	(* (/ 1 (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
19.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify46.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	427	1012
1	1607	935
2	5001	895

prune804.0ms

Filtered

117 candidates to 79 candidates (32.5%)

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)))

rewrite26.0ms

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))))
3.0ms	(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)))

series99.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
18.0ms	(pow (sin ky) 2.0)
18.0ms	(pow (sin kx) 2.0)
22.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify148.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	363	1052
1	1201	976
2	4954	952
3	5001	952

prune727.0ms

Filtered

112 candidates to 70 candidates (37.5%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	111	1	112
Fresh	2	7	9
Picked	1	0	1
Done	0	1	1
Total	114	9	123

Merged error: 1.2b

Counts

123 → 9

localize20.0ms

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)))

rewrite16.0ms

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))
2.0ms	(cbrt (sin kx))
2.0ms	(cbrt (sin kx))
11.0ms	(sqrt (+ (* (pow (* (cbrt (sin kx)) (cbrt (sin kx))) 2.0) (pow (cbrt (sin kx)) 2.0)) (pow (sin ky) 2.0)))

series73.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(cbrt (sin kx))
18.0ms	(cbrt (sin kx))
18.0ms	(cbrt (sin kx))
19.0ms	(sqrt (+ (* (pow (* (cbrt (sin kx)) (cbrt (sin kx))) 2.0) (pow (cbrt (sin kx)) 2.0)) (pow (sin ky) 2.0)))

simplify88.0ms

Algorithm

egg-herbie

Counts

60 → 60

Iterations

Useful iterations: 3 (82.0ms)

Iter	Nodes	Cost
0	189	553
1	571	525
2	2518	507
3	5002	503

prune430.0ms

Filtered

60 candidates to 47 candidates (21.7%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	60	0	60
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	60	9	69

Merged error: 1.2b

Counts

69 → 9

regimes787.0ms

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

3.8s	3778×	body	1280	valid
1.2s	1999×	body	640	valid
293.0ms	707×	body	320	valid
133.0ms	1239×	body	80	valid
68.0ms	277×	body	160	valid

Details

sample194.0ms

simplify50.0ms

prune5.0ms

localize15.0ms

rewrite30.0ms

series106.0ms

simplify47.0ms

prune695.0ms

localize20.0ms

rewrite31.0ms

series100.0ms

simplify46.0ms

prune804.0ms

localize15.0ms

rewrite26.0ms

series99.0ms

simplify148.0ms

prune727.0ms

localize20.0ms

rewrite16.0ms

series73.0ms

simplify88.0ms

prune430.0ms

regimes787.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample5.9s

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