Details

sample191.0ms

Algorithm

intervals

Results

112.0ms	108×	body	1280	valid
49.0ms	83×	body	640	valid
11.0ms	28×	body	320	valid
3.0ms	31×	body	80	valid
2.0ms	6×	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

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: 3.6b

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))
0.3b	(pow (sin ky) 2.0)
0.3b	(pow (sin kx) 2.0)
3.5b	(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:

145.0ms	(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
102.0ms	(pow (sin ky) 2.0)
109.0ms	(pow (sin kx) 2.0)
77.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify47.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (33.0ms)

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

prune377.0ms

Filtered

113 candidates to 78 candidates (69.0%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	100	13	113
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	101	13	114

Merged error: 2.7b

Counts

114 → 13

localize15.0ms

Local error

Found 4 expressions with local error:

0.3b	(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)
3.5b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite33.0ms

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

series429.0ms

Counts

4 → 12

Calls

4 calls:

102.0ms	(pow (sin ky) 2.0)
146.0ms	(* (sin ky) (/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
103.0ms	(pow (sin kx) 2.0)
77.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify54.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 1 (11.0ms)

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

prune301.0ms

Filtered

113 candidates to 68 candidates (60.2%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	111	2	113
Fresh	3	9	12
Picked	0	1	1
Done	0	0	0
Total	114	12	126

Merged error: 2.7b

Counts

126 → 12

localize19.0ms

Local error

Found 4 expressions with local error:

3.5b	(sqrt (+ (* (* (cbrt (pow (sin kx) 2.0)) (cbrt (pow (sin kx) 2.0))) (cbrt (pow (sin kx) 2.0))) (pow (sin ky) 2.0)))
14.6b	(cbrt (pow (sin kx) 2.0))
14.6b	(cbrt (pow (sin kx) 2.0))
14.6b	(cbrt (pow (sin kx) 2.0))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 60

Calls

4 calls:

14.0ms	(sqrt (+ (* (* (cbrt (pow (sin kx) 2.0)) (cbrt (pow (sin kx) 2.0))) (cbrt (pow (sin kx) 2.0))) (pow (sin ky) 2.0)))
2.0ms	(cbrt (pow (sin kx) 2.0))
2.0ms	(cbrt (pow (sin kx) 2.0))
2.0ms	(cbrt (pow (sin kx) 2.0))

series668.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(sqrt (+ (* (* (cbrt (pow (sin kx) 2.0)) (cbrt (pow (sin kx) 2.0))) (cbrt (pow (sin kx) 2.0))) (pow (sin ky) 2.0)))
196.0ms	(cbrt (pow (sin kx) 2.0))
195.0ms	(cbrt (pow (sin kx) 2.0))
199.0ms	(cbrt (pow (sin kx) 2.0))

simplify59.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 3 (52.0ms)

Iter	Nodes	Cost
0	204	682
1	478	640
2	1705	640
3	5001	634

prune287.0ms

Filtered

72 candidates to 55 candidates (76.4%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	72	0	72
Fresh	0	10	10
Picked	0	1	1
Done	0	1	1
Total	72	12	84

Merged error: 2.7b

Counts

84 → 12

localize15.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (sin ky) 2.0)
0.3b	(pow (sin kx) 2.0)
2.2b	(/ (* (sin ky) (sin th)) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
3.5b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

25×	`*-un-lft-identity`
15×	`sqrt-prod`
14×	`add-sqr-sqrt`
13×	`add-cube-cbrt`
12×	`unpow-prod-down`
11×	`add-exp-log`
9×	`add-cbrt-cube`
8×	`times-frac` `associate-/r*`
7×	`pow1`
6×	`pow-unpow` `distribute-lft-out`
4×	`sqrt-div` `add-log-exp`
2×	`cbrt-undiv` `pow-to-exp` `pow-pow` `flip3-+` `div-exp` `pow-exp` `associate-/r/` `flip-+` `sqr-pow`
1×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `prod-exp` `clear-num` `cbrt-unprod` `div-inv` `associate-/l/` `sin-mult` `associate-/l*`

Counts

4 → 85

Calls

4 calls:

2.0ms	(pow (sin ky) 2.0)
2.0ms	(pow (sin kx) 2.0)
12.0ms	(/ (* (sin ky) (sin th)) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
7.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series431.0ms

Counts

4 → 12

Calls

4 calls:

103.0ms	(pow (sin ky) 2.0)
109.0ms	(pow (sin kx) 2.0)
142.0ms	(/ (* (sin ky) (sin th)) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
77.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify42.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 1 (9.0ms)

Iter	Nodes	Cost
0	357	792
1	1385	720
2	5001	720

prune235.0ms

Filtered

97 candidates to 60 candidates (61.9%)

Pruning

12 alts after pruning (9 fresh and 3 done)

	Pruned	Kept	Total
New	95	2	97
Fresh	2	7	9
Picked	0	1	1
Done	0	2	2
Total	97	12	109

Merged error: 2.7b

Counts

109 → 12

regimes512.0ms

Accuracy

0% (1.3b remaining)

Error of 3.9b against oracle of 2.6b and baseline of 3.9b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	10
1	14	10

end0.0ms

sample6.0s

Algorithm

intervals

Results

3.9s	3819×	body	1280	valid
1.2s	1952×	body	640	valid
442.0ms	707×	body	320	valid
145.0ms	1225×	body	80	valid
82.0ms	297×	body	160	valid

Details

sample191.0ms

simplify51.0ms

prune3.0ms

localize15.0ms

rewrite31.0ms

series434.0ms

simplify47.0ms

prune377.0ms

localize15.0ms

rewrite33.0ms

series429.0ms

simplify54.0ms

prune301.0ms

localize19.0ms

rewrite23.0ms

series668.0ms

simplify59.0ms

prune287.0ms

localize15.0ms

rewrite27.0ms

series431.0ms

simplify42.0ms

prune235.0ms

regimes512.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample6.0s

Profiling