Details

sample152.0ms

Algorithm

intervals

Results

93.0ms	118×	body	1280	valid
30.0ms	61×	body	640	valid
8.0ms	24×	body	320	valid
4.0ms	43×	body	80	valid
2.0ms	10×	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

prune4.0ms

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: 5.4b

Counts

2 → 1

localize24.0ms

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)
5.0b	(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:

15.0ms	(* (/ (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)))

series434.0ms

Counts

4 → 12

Calls

4 calls:

150.0ms	(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
103.0ms	(pow (sin ky) 2.0)
104.0ms	(pow (sin kx) 2.0)
76.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify44.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (33.0ms)

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

prune382.0ms

Filtered

113 candidates to 78 candidates (69.0%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	102	11	113
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	103	11	114

Merged error: 4.0b

Counts

114 → 11

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(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)
5.0b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite35.0ms

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:

2.0ms	(pow (sin ky) 2.0)
16.0ms	(* (sin ky) (/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
3.0ms	(pow (sin kx) 2.0)
10.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series426.0ms

Counts

4 → 12

Calls

4 calls:

104.0ms	(pow (sin ky) 2.0)
139.0ms	(* (sin ky) (/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
104.0ms	(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

prune298.0ms

Filtered

113 candidates to 69 candidates (61.1%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	112	1	113
Fresh	1	9	10
Picked	0	1	1
Done	0	0	0
Total	113	11	124

Merged error: 4.0b

Counts

124 → 11

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)))))
5.0b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
5.0b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
5.0b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite34.0ms

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:

10.0ms	(cbrt (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
7.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
7.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
7.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series381.0ms

Counts

4 → 12

Calls

4 calls:

152.0ms	(cbrt (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
73.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
78.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
77.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify102.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 3 (85.0ms)

Iter	Nodes	Cost
0	282	1291
1	819	1231
2	3475	1224
3	5002	1219

prune364.0ms

Filtered

102 candidates to 68 candidates (66.7%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	102	0	102
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	102	11	113

Merged error: 4.0b

Counts

113 → 11

localize25.0ms

Local error

Found 4 expressions with local error:

1.0b	(sqrt (* (cbrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))) (cbrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
5.5b	(cbrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
5.5b	(cbrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
5.5b	(cbrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

19×	`*-un-lft-identity`
18×	`cbrt-div`
15×	`cbrt-prod`
12×	`pow1`
9×	`sqrt-pow1` `flip3-+` `pow1/3` `flip-+`
8×	`sqrt-div`
7×	`add-sqr-sqrt` `add-cube-cbrt`
6×	`unpow-prod-down` `distribute-lft-out`
4×	`add-exp-log` `frac-times` `add-cbrt-cube` `add-log-exp`
2×	`associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `pow-prod-up`
1×	`pow2` `rem-sqrt-square` `pow-plus` `pow1/2` `sqrt-prod`

Counts

4 → 72

Calls

4 calls:

23.0ms	(sqrt (* (cbrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))) (cbrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
13.0ms	(cbrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
8.0ms	(cbrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
10.0ms	(cbrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series393.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(sqrt (* (cbrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))) (cbrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
97.0ms	(cbrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
104.0ms	(cbrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
98.0ms	(cbrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify97.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 3 (87.0ms)

Iter	Nodes	Cost
0	197	1015
1	566	963
2	2309	957
3	5001	948

prune334.0ms

Filtered

84 candidates to 59 candidates (70.2%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	84	0	84
Fresh	0	8	8
Picked	0	1	1
Done	0	2	2
Total	84	11	95

Merged error: 4.0b

Counts

95 → 11

regimes502.0ms

Accuracy

0% (1.4b remaining)

Error of 4.1b against oracle of 2.7b and baseline of 4.1b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	10
1	15	10

end0.0ms

sample5.0s

Algorithm

intervals

Results

3.2s	3760×	body	1280	valid
1.2s	2008×	body	640	valid
258.0ms	730×	body	320	valid
128.0ms	1219×	body	80	valid
81.0ms	283×	body	160	valid

Details

sample152.0ms

simplify52.0ms

prune4.0ms

localize24.0ms

rewrite31.0ms

series434.0ms

simplify44.0ms

prune382.0ms

localize15.0ms

rewrite35.0ms

series426.0ms

simplify54.0ms

prune298.0ms

localize25.0ms

rewrite34.0ms

series381.0ms

simplify102.0ms

prune364.0ms

localize25.0ms

rewrite56.0ms

series393.0ms

simplify97.0ms

prune334.0ms

regimes502.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample5.0s

Profiling