Details

analyze1.3s

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
0%	99.9%	0.1%	7
25%	74.9%	0.1%	8
54.6%	45.2%	0.1%	9
56.2%	43.7%	0.1%	10
62.4%	37.4%	0.1%	11
65.9%	33.9%	0.1%	12
66.3%	33.5%	0.1%	13
69%	30.8%	0.1%	14

sample209.0ms

Algorithm

intervals

Results

134.0ms	119×	body	1280	valid
41.0ms	63×	body	640	valid
10.0ms	23×	body	320	valid
9.0ms	45×	body	80	valid
2.0ms	6×	body	160	valid

simplify60.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4766	16
1	4766	16

prune14.0ms

Filtered

1 candidates to 1 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: 3.5b

Counts

2 → 2

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)
0.2b	(pow (sin kx) 2.0)
3.3b	(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-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 ky) 2.0)
3.0ms	(pow (sin kx) 2.0)
8.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series251.0ms

Counts

4 → 12

Calls

4 calls:

191.0ms	(* (/ (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)
22.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify77.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	5228	1477

prune257.0ms

Filtered

77 candidates to 113 candidates (-46.8%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	104	9	113
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	105	10	115

Merged error: 2.7b

Counts

115 → 10

localize20.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sin ky) (* (sin th) (sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2))))))
0.3b	(/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2)))
0.3b	(* (sin th) (sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2)))))
3.4b	(sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2))))

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

77×	`*-un-lft-identity`
49×	`times-frac`
48×	`add-sqr-sqrt`
45×	`sqrt-prod`
35×	`add-cube-cbrt`
25×	`associate-r`
20×	`unpow-prod-down` `distribute-lft-out`
15×	`add-exp-log`
14×	`pow1`
13×	`add-cbrt-cube`
6×	`associate-l` `associate-/r/`
5×	`associate-/r*`
4×	`pow-prod-down` `prod-exp` `cbrt-unprod` `add-log-exp` `unswap-sqr`
3×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `sqrt-div` `associate-r/` `flip-+` `div-inv` `associate-/l`
2×	`pow-flip` `div-exp` `*-commutative` `inv-pow`
1×	`cbrt-undiv` `rec-exp` `frac-2neg` `pow1/2` `1-exp` `clear-num`

Counts

4 → 139

Calls

4 calls:

17.0ms	(* (sin ky) (* (sin th) (sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2))))))
10.0ms	(/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2)))
18.0ms	(* (sin th) (sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2)))))
11.0ms	(sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2))))

series134.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(* (sin ky) (* (sin th) (sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2))))))
19.0ms	(/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2)))
40.0ms	(* (sin th) (sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2)))))
30.0ms	(sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2))))

simplify63.0ms

Algorithm

egg-herbie

Counts

151 → 151

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5181	2244

prune260.0ms

Filtered

85 candidates to 151 candidates (-77.6%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	150	1	151
Fresh	1	7	8
Picked	0	1	1
Done	0	1	1
Total	151	10	161

Merged error: 2.7b

Counts

161 → 10

localize25.0ms

Local error

Found 4 expressions with local error:

0.4b	(cbrt (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
3.3b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
3.3b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
3.3b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

46×	`*-un-lft-identity`
30×	`cbrt-prod` `sqrt-prod`
25×	`add-sqr-sqrt`
24×	`times-frac`
22×	`add-cube-cbrt`
12×	`unpow-prod-down` `distribute-lft-out`
8×	`sqrt-div`
7×	`pow1`
4×	`add-exp-log` `flip3-+` `add-cbrt-cube` `flip-+` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
2×	`associate-/r/`
1×	`cbrt-div` `pow1/3` `div-inv`

Counts

4 → 90

Calls

4 calls:

11.0ms	(cbrt (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
8.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
8.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
8.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series113.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(cbrt (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
20.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
22.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
19.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify71.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	5542	1796

prune372.0ms

Filtered

68 candidates to 102 candidates (-50.0%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	102	0	102
Fresh	0	7	7
Picked	0	1	1
Done	0	2	2
Total	102	10	112

Merged error: 2.7b

Counts

112 → 10

localize20.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (sin ky) (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
1.0b	(* (/ 1 (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))) (* (sin th) (/ (sin ky) (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))))
3.3b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
3.3b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

101×	`sqrt-prod`
87×	`*-un-lft-identity`
66×	`times-frac`
53×	`add-sqr-sqrt`
51×	`add-cube-cbrt`
45×	`add-exp-log`
39×	`associate-l`
27×	`add-cbrt-cube`
20×	`prod-exp`
18×	`unpow-prod-down` `distribute-lft-out`
12×	`sqrt-div`
11×	`pow1` `div-exp` `associate-/r*`
10×	`cbrt-unprod`
6×	`cbrt-undiv`
4×	`flip3-+` `associate-/r/` `flip-+` `add-log-exp`
3×	`rec-exp` `1-exp` `associate-r/` `pow-prod-down` `associate-/l`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `div-inv`
1×	`frac-times` `frac-2neg` `associate-r` `associate-l/` `clear-num` `-commutative`

Counts

4 → 166

Calls

4 calls:

13.0ms	(/ (sin ky) (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
35.0ms	(* (/ 1 (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))) (* (sin th) (/ (sin ky) (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))))
7.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
9.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series129.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(/ (sin ky) (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
50.0ms	(* (/ 1 (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))) (* (sin th) (/ (sin ky) (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))))
18.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
18.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify73.0ms

Algorithm

egg-herbie

Counts

178 → 178

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5771	3426

prune403.0ms

Filtered

103 candidates to 178 candidates (-72.8%)

Pruning

11 alts after pruning (7 fresh and 4 done)

	Pruned	Kept	Total
New	177	1	178
Fresh	0	6	6
Picked	0	1	1
Done	0	3	3
Total	177	11	188

Merged error: 2.7b

Counts

188 → 11

regimes867.0ms

Accuracy

0% (1.3b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	16
1	15	16

end0.0ms

sample6.3s

Algorithm

intervals

Results

4.1s	3682×	body	1280	valid
1.4s	2060×	body	640	valid
332.0ms	725×	body	320	valid
173.0ms	1234×	body	80	valid
94.0ms	299×	body	160	valid

Details

analyze1.3s

sample209.0ms

simplify60.0ms

prune14.0ms

localize15.0ms

rewrite33.0ms

series251.0ms

simplify77.0ms

prune257.0ms

localize20.0ms

rewrite62.0ms

series134.0ms

simplify63.0ms

prune260.0ms

localize25.0ms

rewrite37.0ms

series113.0ms

simplify71.0ms

prune372.0ms

localize20.0ms

rewrite72.0ms

series129.0ms

simplify73.0ms

prune403.0ms

regimes867.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample6.3s

Profiling