Details

sample156.0ms

Algorithm

intervals

Results

100.0ms	123×	body	1280	valid
29.0ms	58×	body	640	valid
6.0ms	48×	body	80	valid
5.0ms	16×	body	320	valid
2.0ms	11×	body	160	valid

simplify52.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	23	10
1	39	10
2	67	10
3	153	10
4	439	10
5	1830	10
6	5001	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: 4.8b

Counts

2 → 1

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sin ky) (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)
4.4b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

46×	`*-un-lft-identity`
39×	`add-sqr-sqrt`
26×	`add-cube-cbrt`
25×	`sqrt-prod`
24×	`times-frac`
22×	`unpow-prod-down`
10×	`distribute-lft-out`
9×	`hypot-def`
8×	`add-exp-log` `associate-/r*` `sqr-pow`
7×	`pow1`
6×	`pow-unpow` `add-cbrt-cube`
4×	`expm1-log1p-u` `sqrt-div` `log1p-expm1-u` `add-log-exp`
3×	`associate-/l*`
2×	`pow-to-exp` `pow-pow` `flip3-+` `pow-exp` `associate-/r/` `flip-+`
1×	`cbrt-undiv` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `clear-num` `div-inv`

Counts

4 → 117

Calls

4 calls:

11.0ms	(/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
3.0ms	(pow (sin kx) 2.0)
3.0ms	(pow (sin ky) 2.0)
8.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series418.0ms

Counts

4 → 12

Calls

4 calls:

132.0ms	(/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
105.0ms	(pow (sin kx) 2.0)
102.0ms	(pow (sin ky) 2.0)
78.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify42.0ms

Algorithm

egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	341	1065
1	1159	981
2	5001	976

prune401.0ms

Filtered

129 candidates to 87 candidates (67.4%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	120	9	129
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	121	9	130

Merged error: 0.1b

Counts

130 → 9

localize12.0ms

Local error

Found 3 expressions with local error:

0.1b	(hypot (sin ky) (sin kx))
0.1b	(* (/ (sin ky) (hypot (sin ky) (sin kx))) (sin th))
0.2b	(/ (sin ky) (hypot (sin ky) (sin kx)))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
19×	`add-cube-cbrt` `*-un-lft-identity` `times-frac`
13×	`associate-l`
10×	`add-exp-log` `add-cbrt-cube`
5×	`pow1`
3×	`expm1-log1p-u` `associate-r` `associate-/r` `log1p-expm1-u` `associate-/l` `add-log-exp`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `div-inv` `unswap-sqr`
1×	`hypot-udef` `frac-2neg` `pow-prod-down` `associate-l/` `clear-num` `-commutative`

Counts

3 → 73

Calls

3 calls:

1.0ms	(hypot (sin ky) (sin kx))
12.0ms	(* (/ (sin ky) (hypot (sin ky) (sin kx))) (sin th))
4.0ms	(/ (sin ky) (hypot (sin ky) (sin kx)))

series499.0ms

Counts

3 → 9

Calls

3 calls:

113.0ms	(hypot (sin ky) (sin kx))
226.0ms	(* (/ (sin ky) (hypot (sin ky) (sin kx))) (sin th))
160.0ms	(/ (sin ky) (hypot (sin ky) (sin kx)))

simplify140.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (28.0ms)

Iter	Nodes	Cost
0	287	725
1	1045	645
2	4962	644
3	5001	644

prune263.0ms

Filtered

82 candidates to 65 candidates (79.3%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	74	8	82
Fresh	6	2	8
Picked	1	0	1
Done	0	0	0
Total	81	10	91

Merged error: 0b

Counts

91 → 10

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b	(hypot (sin ky) (sin kx))
0.1b	(* (expm1 (log1p (/ (sin ky) (hypot (sin ky) (sin kx))))) (sin th))
0.2b	(/ (sin ky) (hypot (sin ky) (sin kx)))
1.0b	(log1p (/ (sin ky) (hypot (sin ky) (sin kx))))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
14×	`add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
8×	`add-exp-log` `add-cbrt-cube`
6×	`pow1`
5×	`expm1-log1p-u`
4×	`log1p-expm1-u` `add-log-exp`
3×	`associate-r` `associate-l` `associate-/r` `associate-/l`
1×	`cbrt-undiv` `log1p-udef` `hypot-udef` `frac-2neg` `log1p-expm1` `div-exp` `pow-prod-down` `prod-exp` `clear-num` `*-commutative` `cbrt-unprod` `div-inv` `unswap-sqr`

Counts

4 → 70

Calls

4 calls:

1.0ms	(hypot (sin ky) (sin kx))
4.0ms	(* (expm1 (log1p (/ (sin ky) (hypot (sin ky) (sin kx))))) (sin th))
4.0ms	(/ (sin ky) (hypot (sin ky) (sin kx)))
1.0ms	(log1p (/ (sin ky) (hypot (sin ky) (sin kx))))

series711.0ms

Counts

4 → 12

Calls

4 calls:

116.0ms	(hypot (sin ky) (sin kx))
210.0ms	(* (expm1 (log1p (/ (sin ky) (hypot (sin ky) (sin kx))))) (sin th))
167.0ms	(/ (sin ky) (hypot (sin ky) (sin kx)))
217.0ms	(log1p (/ (sin ky) (hypot (sin ky) (sin kx))))

simplify129.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 3 (115.0ms)

Iter	Nodes	Cost
0	269	738
1	880	648
2	4089	647
3	5002	645

prune262.0ms

Filtered

82 candidates to 67 candidates (81.7%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	82	0	82
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	82	10	92

Merged error: 0b

Counts

92 → 10

localize17.0ms

Local error

Found 3 expressions with local error:

0.1b	(hypot (sin ky) (sin kx))
0.3b	(* (sin ky) (/ (sin th) (hypot (sin ky) (sin kx))))
0.3b	(/ (sin th) (hypot (sin ky) (sin kx)))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
19×	`add-cube-cbrt` `*-un-lft-identity` `times-frac`
13×	`associate-r`
10×	`add-exp-log` `add-cbrt-cube`
5×	`pow1`
3×	`expm1-log1p-u` `associate-l` `associate-/r` `log1p-expm1-u` `associate-/l` `add-log-exp`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `div-inv` `unswap-sqr`
1×	`hypot-udef` `frac-2neg` `associate-r/` `pow-prod-down` `clear-num` `-commutative`

Counts

3 → 73

Calls

3 calls:

1.0ms	(hypot (sin ky) (sin kx))
7.0ms	(* (sin ky) (/ (sin th) (hypot (sin ky) (sin kx))))
4.0ms	(/ (sin th) (hypot (sin ky) (sin kx)))

series528.0ms

Counts

3 → 9

Calls

3 calls:

115.0ms	(hypot (sin ky) (sin kx))
216.0ms	(* (sin ky) (/ (sin th) (hypot (sin ky) (sin kx))))
197.0ms	(/ (sin th) (hypot (sin ky) (sin kx)))

simplify42.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 1 (8.0ms)

Iter	Nodes	Cost
0	258	719
1	1032	641
2	5001	641

prune193.0ms

Filtered

82 candidates to 65 candidates (79.3%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	80	2	82
Fresh	2	6	8
Picked	1	0	1
Done	1	0	1
Total	84	8	92

Merged error: 0b

Counts

92 → 8

regimes231.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	8
1	14	8

end0.0ms

sample5.1s

Algorithm

intervals

Results

3.2s	3727×	body	1280	valid
1.2s	2003×	body	640	valid
233.0ms	684×	body	320	valid
140.0ms	1280×	body	80	valid
67.0ms	306×	body	160	valid