Details

sample190.0ms

Algorithm

intervals

Results

118.0ms	121×	body	1280	valid
33.0ms	56×	body	640	valid
10.0ms	43×	body	80	valid
9.0ms	22×	body	320	valid
4.0ms	14×	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: 6.1b

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))))
0.2b	(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
0.3b	(pow (sin kx) 2.0)
5.6b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite45.0ms

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-l`
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-r` `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` `pow-prod-down` `associate-l/` `pow-exp` `clear-num` `-commutative` `sqr-pow`

Counts

4 → 133

Calls

4 calls:

11.0ms	(/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
19.0ms	(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
2.0ms	(pow (sin kx) 2.0)
7.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series123.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
49.0ms	(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
19.0ms	(pow (sin kx) 2.0)
20.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify49.0ms

Algorithm

egg-herbie

Counts

145 → 145

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	418	1631
1	1508	1502
2	5001	1491

prune323.0ms

Filtered

95 candidates to 145 candidates (-52.6%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	134	11	145
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	135	11	146

Merged error: 4.1b

Counts

146 → 11

localize17.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sin ky) (/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
0.3b	(pow (sin kx) 2.0)
0.3b	(/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
5.6b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite42.0ms

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:

17.0ms	(* (sin ky) (/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
2.0ms	(pow (sin kx) 2.0)
11.0ms	(/ (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)))

series126.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(* (sin ky) (/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
18.0ms	(pow (sin kx) 2.0)
44.0ms	(/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
19.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify58.0ms

Algorithm

egg-herbie

Counts

145 → 145

Iterations

Useful iterations: 2 (42.0ms)

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

prune260.0ms

Filtered

86 candidates to 145 candidates (-68.6%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	145	0	145
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	145	11	156

Merged error: 4.1b

Counts

156 → 11

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	(* (sin ky) (/ 1 (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
5.6b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

42×	`*-un-lft-identity`
37×	`add-sqr-sqrt`
33×	`associate-r`
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-l` `pow-prod-down` `add-log-exp`
3×	`pow-unpow`
2×	`cbrt-undiv` `rec-exp` `flip3-+` `1-exp` `associate-r/` `associate-l/` `associate-/r/` `un-div-inv` `*-commutative` `flip-+`
1×	`pow-to-exp` `rem-sqrt-square` `pow-pow` `sqrt-pow1` `pow1/2` `pow-exp` `div-inv` `sqr-pow`

Counts

4 → 113

Calls

4 calls:

16.0ms	(* (* (sin ky) (/ 1 (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))) (sin th))
3.0ms	(pow (sin kx) 2.0)
20.0ms	(* (sin ky) (/ 1 (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
7.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series120.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(* (* (sin ky) (/ 1 (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))) (sin th))
18.0ms	(pow (sin kx) 2.0)
37.0ms	(* (sin ky) (/ 1 (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
19.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify62.0ms

Algorithm

egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	507	1234
1	2457	1064
2	5001	1023

prune213.0ms

Filtered

69 candidates to 125 candidates (-81.2%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	125	0	125
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	125	11	136

Merged error: 4.1b

Counts

136 → 11

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))
0.3b	(pow (sin kx) 2)
0.3b	(* (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin ky))
5.8b	(sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

78×	`*-un-lft-identity`
49×	`add-sqr-sqrt` `times-frac`
45×	`sqrt-prod`
36×	`add-cube-cbrt`
24×	`associate-l`
23×	`unpow-prod-down`
20×	`distribute-lft-out`
11×	`add-exp-log`
10×	`pow1`
8×	`add-cbrt-cube`
6×	`associate-/r/`
5×	`associate-/r*`
4×	`add-log-exp` `unswap-sqr`
3×	`rem-sqrt-square` `pow-unpow` `sqrt-pow1` `flip3-+` `associate-r` `flip-+` `div-inv` `associate-/l*`
2×	`pow-flip` `sqrt-div` `div-exp` `inv-pow`
1×	`cbrt-undiv` `pow-to-exp` `rec-exp` `pow-pow` `frac-2neg` `pow1/2` `1-exp` `pow-prod-down` `associate-l/` `pow-exp` `prod-exp` `clear-num` `-commutative` `cbrt-unprod` `unpow2` `sqr-pow`

Counts

4 → 138

Calls

4 calls:

10.0ms	(/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))
3.0ms	(pow (sin kx) 2)
18.0ms	(* (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin ky))
10.0ms	(sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))

series88.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))
7.0ms	(pow (sin kx) 2)
33.0ms	(* (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin ky))
28.0ms	(sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))

simplify47.0ms

Algorithm

egg-herbie

Counts

150 → 150

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	384	1400
1	1350	1277
2	5002	1219

prune200.0ms

Filtered

81 candidates to 150 candidates (-85.2%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	148	2	150
Fresh	2	6	8
Picked	0	1	1
Done	0	2	2
Total	150	11	161

Merged error: 4.1b

Counts

161 → 11

regimes1.1s

Accuracy

65.8% (0.5b remaining)

Error of 2.8b against oracle of 2.4b and baseline of 3.8b

bsearch2.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	23
1	30	23

end0.0ms

sample5.8s

Algorithm

intervals

Results

3.7s	3728×	body	1280	valid
1.2s	2022×	body	640	valid
293.0ms	703×	body	320	valid
142.0ms	1273×	body	80	valid
68.0ms	274×	body	160	valid

Details

sample190.0ms

simplify50.0ms

prune5.0ms

localize15.0ms

rewrite45.0ms

series123.0ms

simplify49.0ms

prune323.0ms

localize17.0ms

rewrite42.0ms

series126.0ms

simplify58.0ms

prune260.0ms

localize16.0ms

rewrite50.0ms

series120.0ms

simplify62.0ms

prune213.0ms

localize16.0ms

rewrite45.0ms

series88.0ms

simplify47.0ms

prune200.0ms

regimes1.1s

bsearch2.0ms

simplify1.0ms

end0.0ms

sample5.8s

Profiling