Details

sample148.0ms

Algorithm

intervals

Results

92.0ms	111×	body	1280	valid
28.0ms	63×	body	640	valid
7.0ms	22×	body	320	valid
5.0ms	49×	body	80	valid
2.0ms	11×	body	160	valid

simplify51.0ms

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: 4.9b

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 kx) 2.0)
0.3b	(pow (sin ky) 2.0)
4.5b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite32.0ms

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))
3.0ms	(pow (sin kx) 2.0)
3.0ms	(pow (sin ky) 2.0)
7.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series432.0ms

Counts

4 → 12

Calls

4 calls:

146.0ms	(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
102.0ms	(pow (sin kx) 2.0)
107.0ms	(pow (sin ky) 2.0)
77.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify48.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (33.0ms)

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

prune376.0ms

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: 3.6b

Counts

114 → 11

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (sin kx) 2.0)
0.3b	(pow (sin ky) 2.0)
0.3b	(* (sin ky) (/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
4.5b	(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-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:

3.0ms	(pow (sin kx) 2.0)
3.0ms	(pow (sin ky) 2.0)
17.0ms	(* (sin ky) (/ (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)))

series424.0ms

Counts

4 → 12

Calls

4 calls:

102.0ms	(pow (sin kx) 2.0)
107.0ms	(pow (sin ky) 2.0)
139.0ms	(* (sin ky) (/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 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

prune311.0ms

Filtered

113 candidates to 68 candidates (60.2%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	112	1	113
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	112	12	124

Merged error: 3.6b

Counts

124 → 12

localize19.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (sin ky) 2.0)
0.3b	(* (fabs (cbrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sqrt (cbrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
5.0b	(cbrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
5.0b	(cbrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

24×	`*-un-lft-identity`
18×	`add-sqr-sqrt`
16×	`cbrt-prod`
12×	`add-cube-cbrt`
11×	`associate-r`
10×	`sqrt-prod`
9×	`unpow-prod-down`
7×	`pow1` `add-exp-log`
6×	`cbrt-div` `add-cbrt-cube` `distribute-lft-out`
4×	`add-log-exp`
3×	`pow-unpow` `flip3-+` `associate-l` `flip-+` `unswap-sqr`
2×	`pow1/3` `sqrt-div` `associate-*r/`
1×	`pow-to-exp` `pow-pow` `pow-prod-down` `pow-exp` `prod-exp` `*-commutative` `cbrt-unprod` `sqr-pow`

Counts

4 → 77

Calls

4 calls:

3.0ms	(pow (sin ky) 2.0)
13.0ms	(* (fabs (cbrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sqrt (cbrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
7.0ms	(cbrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
7.0ms	(cbrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series416.0ms

Counts

4 → 12

Calls

4 calls:

106.0ms	(pow (sin ky) 2.0)
116.0ms	(* (fabs (cbrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sqrt (cbrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
97.0ms	(cbrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
97.0ms	(cbrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify147.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	338	1091
1	1137	1019
2	4670	1007
3	5001	1007

prune356.0ms

Filtered

89 candidates to 63 candidates (70.8%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	88	1	89
Fresh	1	9	10
Picked	1	0	1
Done	0	1	1
Total	90	11	101

Merged error: 3.6b

Counts

101 → 11

localize22.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (sin ky))
0.6b	(cbrt (sin ky))
4.5b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
4.5b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 56

Calls

4 calls:

1.0ms	(cbrt (sin ky))
1.0ms	(cbrt (sin ky))
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)))

series351.0ms

Counts

4 → 12

Calls

4 calls:

102.0ms	(cbrt (sin ky))
98.0ms	(cbrt (sin ky))
77.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
73.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify54.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 3 (48.0ms)

Iter	Nodes	Cost
0	171	470
1	424	444
2	1478	440
3	5002	438

prune253.0ms

Filtered

68 candidates to 50 candidates (73.5%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	67	1	68
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	67	12	79

Merged error: 3.6b

Counts

79 → 12

regimes437.0ms

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

sample4.8s

Algorithm

intervals

Results

3.1s	3708×	body	1280	valid
979.0ms	2028×	body	640	valid
250.0ms	700×	body	320	valid
128.0ms	1271×	body	80	valid
75.0ms	293×	body	160	valid