Details

sample178.0ms

Algorithm

intervals

Results

112.0ms	118×	body	1280	valid
36.0ms	61×	body	640	valid
9.0ms	24×	body	320	valid
5.0ms	43×	body	80	valid
2.0ms	10×	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

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

localize21.0ms

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)))

rewrite30.0ms

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

series426.0ms

Counts

4 → 12

Calls

4 calls:

146.0ms	(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
101.0ms	(pow (sin ky) 2.0)
101.0ms	(pow (sin kx) 2.0)
77.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify42.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (32.0ms)

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

prune387.0ms

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)
17.0ms	(* (sin ky) (/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
5.0ms	(pow (sin kx) 2.0)
7.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series425.0ms

Counts

4 → 12

Calls

4 calls:

108.0ms	(pow (sin ky) 2.0)
138.0ms	(* (sin ky) (/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
102.0ms	(pow (sin kx) 2.0)
76.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify55.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 1 (11.0ms)

Iter	Nodes	Cost
0	437	948
1	1864	870
2	5002	870

prune309.0ms

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

localize24.0ms

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)))

rewrite33.0ms

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)))

series385.0ms

Counts

4 → 12

Calls

4 calls:

155.0ms	(cbrt (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
77.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
75.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
77.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify98.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 3 (86.0ms)

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

prune386.0ms

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)))

rewrite41.0ms

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:

16.0ms	(sqrt (* (cbrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))) (cbrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
7.0ms	(cbrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
9.0ms	(cbrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
7.0ms	(cbrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series382.0ms

Counts

4 → 12

Calls

4 calls:

96.0ms	(sqrt (* (cbrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))) (cbrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
95.0ms	(cbrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
95.0ms	(cbrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
96.0ms	(cbrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify95.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 3 (85.0ms)

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

prune342.0ms

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

regimes501.0ms

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

sample5.9s

Algorithm

intervals

Results

3.8s	3760×	body	1280	valid
1.3s	2008×	body	640	valid
303.0ms	730×	body	320	valid
139.0ms	1219×	body	80	valid
77.0ms	283×	body	160	valid