Details

sample4.1s

Algorithm

intervals

sampling

Space saved by range analysis: 0.146413%

Space saved by search: 0.146413%

Guaranteed chance to sample good point: 0%

Results

134.0ms	122×	body	1280	valid
49.0ms	73×	body	640	valid
10.0ms	20×	body	320	valid
4.0ms	35×	body	80	valid
2.0ms	6×	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

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: 3.3b

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)
2.9b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite34.0ms

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:

19.0ms	(* (/ (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)))

series107.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
19.0ms	(pow (sin ky) 2.0)
19.0ms	(pow (sin kx) 2.0)
20.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify44.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (34.0ms)

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

prune287.0ms

Filtered

78 candidates to 113 candidates (-44.9%)

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: 2.1b

Counts

114 → 13

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin ky) (* (/ 1 (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th)))
0.3b	(pow (sin kx) 2.0)
0.3b	(* (/ 1 (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
2.9b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

42×	`*-un-lft-identity`
37×	`add-sqr-sqrt`
33×	`associate-l`
29×	`add-exp-log`
28×	`times-frac`
24×	`add-cube-cbrt`
22×	`sqrt-prod`
18×	`add-cbrt-cube`
13×	`pow1` `prod-exp`
11×	`unpow-prod-down`
8×	`distribute-lft-out`
7×	`cbrt-unprod`
5×	`unswap-sqr`
4×	`sqrt-div` `div-exp` `associate-r` `pow-prod-down` `add-log-exp`
3×	`pow-unpow`
2×	`cbrt-undiv` `rec-exp` `flip3-+` `1-exp` `associate-l/` `associate-/r/` `-commutative` `flip-+`
1×	`pow-to-exp` `rem-sqrt-square` `pow-pow` `sqrt-pow1` `pow1/2` `associate-*r/` `pow-exp` `div-inv` `sqr-pow`

Counts

4 → 111

Calls

4 calls:

15.0ms	(* (sin ky) (* (/ 1 (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th)))
2.0ms	(pow (sin kx) 2.0)
17.0ms	(* (/ 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)))

series130.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(* (sin ky) (* (/ 1 (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th)))
19.0ms	(pow (sin kx) 2.0)
45.0ms	(* (/ 1 (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
20.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify51.0ms

Algorithm

egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	443	1278
1	1781	1120
2	5002	1095

prune271.0ms

Filtered

81 candidates to 123 candidates (-51.9%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	118	5	123
Fresh	4	8	12
Picked	1	0	1
Done	0	0	0
Total	123	13	136

Merged error: 2.1b

Counts

136 → 13

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin ky) (/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
0.3b	(/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
0.3b	(pow (sin kx) 2.0)
2.9b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

72×	`*-un-lft-identity`
50×	`times-frac`
49×	`add-sqr-sqrt`
41×	`sqrt-prod`
40×	`add-cube-cbrt`
30×	`associate-r`
19×	`unpow-prod-down`
16×	`distribute-lft-out`
12×	`add-exp-log`
11×	`add-cbrt-cube`
8×	`pow1` `associate-/r*`
6×	`sqrt-div`
4×	`associate-/r/` `add-log-exp`
3×	`pow-unpow` `flip3-+` `associate-l` `flip-+` `associate-/l*` `unswap-sqr`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `div-inv`
1×	`pow-to-exp` `rem-sqrt-square` `pow-pow` `frac-2neg` `sqrt-pow1` `pow1/2` `associate-r/` `pow-prod-down` `pow-exp` `clear-num` `-commutative` `sqr-pow`

Counts

4 → 133

Calls

4 calls:

19.0ms	(* (sin ky) (/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
11.0ms	(/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (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)))

series128.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(* (sin ky) (/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
45.0ms	(/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
19.0ms	(pow (sin kx) 2.0)
19.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify56.0ms

Algorithm

egg-herbie

Counts

145 → 145

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	430	1588
1	1755	1442
2	5001	1432

prune278.0ms

Filtered

87 candidates to 145 candidates (-66.7%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	143	2	145
Fresh	2	10	12
Picked	0	1	1
Done	0	0	0
Total	145	13	158

Merged error: 2.1b

Counts

158 → 13

localize20.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (sin kx))
0.6b	(cbrt (sin kx))
0.6b	(cbrt (sin kx))
2.9b	(sqrt (+ (* (pow (* (cbrt (sin kx)) (cbrt (sin kx))) 2.0) (pow (cbrt (sin kx)) 2.0)) (pow (sin ky) 2.0)))

rewrite14.0ms

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

series77.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(cbrt (sin kx))
18.0ms	(cbrt (sin kx))
20.0ms	(cbrt (sin kx))
20.0ms	(sqrt (+ (* (pow (* (cbrt (sin kx)) (cbrt (sin kx))) 2.0) (pow (cbrt (sin kx)) 2.0)) (pow (sin ky) 2.0)))

simplify86.0ms

Algorithm

egg-herbie

Counts

60 → 60

Iterations

Useful iterations: 3 (79.0ms)

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

prune118.0ms

Filtered

47 candidates to 60 candidates (-27.7%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	60	0	60
Fresh	0	11	11
Picked	0	1	1
Done	0	1	1
Total	60	13	73

Merged error: 2.1b

Counts

73 → 13

regimes994.0ms

Accuracy

0% (1.6b remaining)

Error of 4.0b against oracle of 2.5b and baseline of 4.0b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	10
1	15	10

end0.0ms

sample10.3s

Algorithm

intervals

sampling

Space saved by range analysis: 0.146413%

Space saved by search: 0.146413%

Guaranteed chance to sample good point: 0%

Results

4.2s	3711×	body	1280	valid
1.4s	2028×	body	640	valid
355.0ms	716×	body	320	valid
181.0ms	1264×	body	80	valid
81.0ms	281×	body	160	valid

Details

sample4.1s

simplify50.0ms

prune5.0ms

localize15.0ms

rewrite34.0ms

series107.0ms

simplify44.0ms

prune287.0ms

localize16.0ms

rewrite46.0ms

series130.0ms

simplify51.0ms

prune271.0ms

localize15.0ms

rewrite44.0ms

series128.0ms

simplify56.0ms

prune278.0ms

localize20.0ms

rewrite14.0ms

series77.0ms

simplify86.0ms

prune118.0ms

regimes994.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample10.3s

Profiling