Details

sample193.0ms

Algorithm

intervals

Results

116.0ms	113×	body	1280	valid
38.0ms	64×	body	640	valid
13.0ms	35×	body	320	valid
4.0ms	37×	body	80	valid
2.0ms	7×	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

prune5.0ms

Filtered

1 candidates to 0 candidates (100.0%)

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: 3.0b

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)
2.7b	(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 kx) 2.0)
2.0ms	(pow (sin ky) 2.0)
6.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series530.0ms

Counts

4 → 12

Calls

4 calls:

174.0ms	(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
130.0ms	(pow (sin kx) 2.0)
128.0ms	(pow (sin ky) 2.0)
98.0ms	(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	991
1	1380	928
2	5001	927

prune800.0ms

Filtered

113 candidates to 78 candidates (31.0%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	104	9	113
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	104	10	114

Merged error: 2.4b

Counts

114 → 10

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin ky) (/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
0.2b	(pow (sin kx) 2.0)
0.3b	(pow (sin ky) 2.0)
2.7b	(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-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:

16.0ms	(* (sin ky) (/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
2.0ms	(pow (sin kx) 2.0)
2.0ms	(pow (sin ky) 2.0)
6.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series563.0ms

Counts

4 → 12

Calls

4 calls:

231.0ms	(* (sin ky) (/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
121.0ms	(pow (sin kx) 2.0)
121.0ms	(pow (sin ky) 2.0)
89.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify53.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 1 (11.0ms)

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

prune530.0ms

Filtered

113 candidates to 68 candidates (39.8%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	112	1	113
Fresh	1	7	8
Picked	1	0	1
Done	0	1	1
Total	114	9	123

Merged error: 2.4b

Counts

123 → 9

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)))))
2.7b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
2.7b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
2.7b	(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:

9.0ms	(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)))

series443.0ms

Counts

4 → 12

Calls

4 calls:

177.0ms	(cbrt (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
88.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
88.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
89.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify97.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 3 (82.0ms)

Iter	Nodes	Cost
0	282	1291
1	819	1231
2	3461	1223
3	5002	1218

prune482.0ms

Filtered

102 candidates to 68 candidates (33.3%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	102	0	102
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	102	9	111

Merged error: 2.4b

Counts

111 → 9

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)))))
3.2b	(cbrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
3.2b	(cbrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite32.0ms

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:

2.0ms	(pow (sin ky) 2.0)
12.0ms	(* (fabs (cbrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sqrt (cbrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
9.0ms	(cbrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
6.0ms	(cbrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series462.0ms

Counts

4 → 12

Calls

4 calls:

120.0ms	(pow (sin ky) 2.0)
125.0ms	(* (fabs (cbrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sqrt (cbrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
108.0ms	(cbrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
108.0ms	(cbrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify149.0ms

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

prune589.0ms

Filtered

89 candidates to 63 candidates (29.2%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	88	1	89
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	88	10	98

Merged error: 2.4b

Counts

98 → 10

regimes882.0ms

Accuracy

0% (1.4b remaining)

Error of 4.2b against oracle of 2.7b and baseline of 4.2b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	10
1	15	10

end0.0ms

sample5.8s

Algorithm

intervals

Results

3.7s	3723×	body	1280	valid
1.2s	2012×	body	640	valid
303.0ms	725×	body	320	valid
141.0ms	1250×	body	80	valid
78.0ms	290×	body	160	valid

Details

sample193.0ms

simplify51.0ms

prune5.0ms

localize15.0ms

rewrite30.0ms

series530.0ms

simplify44.0ms

prune800.0ms

localize15.0ms

rewrite31.0ms

series563.0ms

simplify53.0ms

prune530.0ms

localize24.0ms

rewrite33.0ms

series443.0ms

simplify97.0ms

prune482.0ms

localize19.0ms

rewrite32.0ms

series462.0ms

simplify149.0ms

prune589.0ms

regimes882.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample5.8s

Profiling