Details

sample203.0ms

Algorithm

intervals

Results

130.0ms	131×	body	1280	valid
46.0ms	69×	body	640	valid
8.0ms	21×	body	320	valid
3.0ms	29×	body	80	valid
2.0ms	6×	body	160	valid

simplify52.0ms

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: 3.8b

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)
3.4b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite36.0ms

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))
3.0ms	(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)))

series438.0ms

Counts

4 → 12

Calls

4 calls:

150.0ms	(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
104.0ms	(pow (sin ky) 2.0)
110.0ms	(pow (sin kx) 2.0)
73.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify51.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (34.0ms)

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

prune397.0ms

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: 2.8b

Counts

114 → 13

localize22.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (sin kx))
0.5b	(cbrt (sin kx))
0.5b	(cbrt (sin kx))
3.4b	(sqrt (+ (* (pow (* (cbrt (sin kx)) (cbrt (sin kx))) 2.0) (pow (cbrt (sin kx)) 2.0)) (pow (sin ky) 2.0)))

rewrite15.0ms

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))
9.0ms	(sqrt (+ (* (pow (* (cbrt (sin kx)) (cbrt (sin kx))) 2.0) (pow (cbrt (sin kx)) 2.0)) (pow (sin ky) 2.0)))

series384.0ms

Counts

4 → 12

Calls

4 calls:

106.0ms	(cbrt (sin kx))
99.0ms	(cbrt (sin kx))
99.0ms	(cbrt (sin kx))
79.0ms	(sqrt (+ (* (pow (* (cbrt (sin kx)) (cbrt (sin kx))) 2.0) (pow (cbrt (sin kx)) 2.0)) (pow (sin ky) 2.0)))

simplify78.0ms

Algorithm

egg-herbie

Counts

60 → 60

Iterations

Useful iterations: 3 (72.0ms)

Iter	Nodes	Cost
0	183	511
1	496	483
2	2171	477
3	5002	476

prune267.0ms

Filtered

60 candidates to 46 candidates (76.7%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	60	0	60
Fresh	0	12	12
Picked	0	1	1
Done	0	0	0
Total	60	13	73

Merged error: 2.8b

Counts

73 → 13

localize20.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (sin ky) (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
1.3b	(* (/ 1 (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))) (* (/ (sin ky) (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))) (sin th)))
3.4b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
3.4b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite74.0ms

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` `pow-prod-down` `associate-l/` `associate-/l`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `div-inv`
1×	`frac-times` `frac-2neg` `associate-r/` `associate-r` `clear-num` `-commutative`

Counts

4 → 166

Calls

4 calls:

17.0ms	(/ (sin ky) (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
33.0ms	(* (/ 1 (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))) (* (/ (sin ky) (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))) (sin th)))
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)))

series476.0ms

Counts

4 → 12

Calls

4 calls:

154.0ms	(/ (sin ky) (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
169.0ms	(* (/ 1 (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))) (* (/ (sin ky) (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))) (sin th)))
80.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
73.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify81.0ms

Algorithm

egg-herbie

Counts

178 → 178

Iterations

Useful iterations: 2 (58.0ms)

Iter	Nodes	Cost
0	577	3069
1	2934	2568
2	5001	2299

prune527.0ms

Filtered

178 candidates to 103 candidates (57.9%)

Pruning

14 alts after pruning (12 fresh and 2 done)

	Pruned	Kept	Total
New	177	1	178
Fresh	0	11	11
Picked	0	1	1
Done	0	1	1
Total	177	14	191

Merged error: 2.8b

Counts

191 → 14

localize26.0ms

Local error

Found 4 expressions with local error:

0.7b	(cbrt (sin ky))
3.4b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
3.4b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
3.4b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

20×	`*-un-lft-identity`
15×	`sqrt-prod`
11×	`add-sqr-sqrt`
8×	`add-cube-cbrt`
7×	`pow1`
6×	`unpow-prod-down` `sqrt-div` `distribute-lft-out`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`cbrt-prod` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`
1×	`pow1/3`

Counts

4 → 62

Calls

4 calls:

2.0ms	(cbrt (sin ky))
8.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
7.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
8.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series332.0ms

Counts

4 → 12

Calls

4 calls:

97.0ms	(cbrt (sin ky))
77.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
78.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
79.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify57.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 3 (50.0ms)

Iter	Nodes	Cost
0	171	583
1	424	554
2	1478	552
3	5002	551

prune282.0ms

Filtered

74 candidates to 53 candidates (71.6%)

Pruning

14 alts after pruning (11 fresh and 3 done)

	Pruned	Kept	Total
New	74	0	74
Fresh	0	11	11
Picked	0	1	1
Done	0	2	2
Total	74	14	88

Merged error: 2.8b

Counts

88 → 14

regimes800.0ms

Accuracy

0% (1.6b remaining)

Error of 4.3b against oracle of 2.8b and baseline of 4.3b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	20	18
1	20	18

end0.0ms

sample5.9s

Algorithm

intervals

Results

3.9s	3788×	body	1280	valid
1.2s	1995×	body	640	valid
298.0ms	711×	body	320	valid
139.0ms	1201×	body	80	valid
78.0ms	305×	body	160	valid