Details

sample158.0ms

Algorithm

intervals

Results

93.0ms	115×	body	1280	valid
39.0ms	68×	body	640	valid
6.0ms	20×	body	320	valid
5.0ms	49×	body	80	valid
1.0ms	4×	body	160	valid

simplify54.0ms

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	1817	10
6	5001	10

prune4.0ms

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: 3.2b

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))))
0.3b	(pow (sin kx) 2.0)
0.3b	(pow (sin ky) 2.0)
3.0b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite27.0ms

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))))
2.0ms	(pow (sin kx) 2.0)
2.0ms	(pow (sin ky) 2.0)
8.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series439.0ms

Counts

4 → 12

Calls

4 calls:

135.0ms	(/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
106.0ms	(pow (sin kx) 2.0)
116.0ms	(pow (sin ky) 2.0)
82.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify44.0ms

Algorithm

egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	340	1065
1	1147	981
2	5002	976

prune341.0ms

Filtered

129 candidates to 87 candidates (32.6%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	121	8	129
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	122	8	130

Merged error: 0.1b

Counts

130 → 8

localize11.0ms

Local error

Found 3 expressions with local error:

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

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 81

Calls

3 calls:

1.0ms	(hypot (sin ky) (sin kx))
8.0ms	(* (/ (sin ky) (hypot (sin ky) (sin kx))) (sin th))
4.0ms	(/ (sin ky) (hypot (sin ky) (sin kx)))

series524.0ms

Counts

3 → 9

Calls

3 calls:

119.0ms	(hypot (sin ky) (sin kx))
233.0ms	(* (/ (sin ky) (hypot (sin ky) (sin kx))) (sin th))
172.0ms	(/ (sin ky) (hypot (sin ky) (sin kx)))

simplify41.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 1 (8.0ms)

Iter	Nodes	Cost
0	299	765
1	1286	685
2	5001	685

prune217.0ms

Filtered

90 candidates to 71 candidates (21.1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	82	8	90
Fresh	7	0	7
Picked	1	0	1
Done	0	0	0
Total	90	8	98

Merged error: 0.0b

Counts

98 → 8

localize11.0ms

Local error

Found 3 expressions with local error:

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

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

84×	`times-frac`
55×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
19×	`associate-/r*`
10×	`add-exp-log` `add-cbrt-cube`
9×	`associate-/r/` `associate-/l*`
6×	`div-inv`
4×	`cbrt-undiv` `div-exp`
3×	`pow1` `expm1-log1p-u` `frac-2neg` `clear-num` `log1p-expm1-u` `add-log-exp`
1×	`hypot-udef`

Counts

3 → 119

Calls

3 calls:

1.0ms	(hypot (sin ky) (sin kx))
3.0ms	(/ (hypot (sin ky) (sin kx)) (sin ky))
7.0ms	(/ (sin th) (/ (hypot (sin ky) (sin kx)) (sin ky)))

series521.0ms

Counts

3 → 9

Calls

3 calls:

124.0ms	(hypot (sin ky) (sin kx))
144.0ms	(/ (hypot (sin ky) (sin kx)) (sin ky))
253.0ms	(/ (sin th) (/ (hypot (sin ky) (sin kx)) (sin ky)))

simplify57.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	431	1463
1	1753	1371
2	5001	1369

prune310.0ms

Filtered

128 candidates to 103 candidates (19.5%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	124	4	128
Fresh	3	4	7
Picked	0	1	1
Done	0	0	0
Total	127	9	136

Merged error: 0b

Counts

136 → 9

localize12.0ms

Local error

Found 3 expressions with local error:

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

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 83

Calls

3 calls:

1.0ms	(hypot (sin ky) (sin kx))
8.0ms	(* (sin th) (/ (sin ky) (hypot (sin ky) (sin kx))))
4.0ms	(/ (sin ky) (hypot (sin ky) (sin kx)))

series700.0ms

Counts

3 → 9

Calls

3 calls:

267.0ms	(hypot (sin ky) (sin kx))
258.0ms	(* (sin th) (/ (sin ky) (hypot (sin ky) (sin kx))))
175.0ms	(/ (sin ky) (hypot (sin ky) (sin kx)))

simplify42.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 1 (9.0ms)

Iter	Nodes	Cost
0	298	769
1	1227	689
2	5001	689

prune191.0ms

Filtered

92 candidates to 70 candidates (23.9%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	90	2	92
Fresh	2	5	7
Picked	0	1	1
Done	0	1	1
Total	92	9	101

Merged error: 0b

Counts

101 → 9

regimes246.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	7
1	10	7

end0.0ms

sample4.7s

Algorithm

intervals

Results

3.1s	3676×	body	1280	valid
1.0s	2074×	body	640	valid
245.0ms	741×	body	320	valid
120.0ms	1237×	body	80	valid
57.0ms	272×	body	160	valid