Details

sample129.0ms

Algorithm

intervals

Results

63.0ms	80×	body	1280	valid
28.0ms	60×	body	640	valid
11.0ms	84×	body	80	valid
11.0ms	21×	body	320	valid
2.0ms	11×	body	160	valid

simplify50.0ms

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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.9b

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 ky) 2.0)
0.3b	(pow (sin kx) 2.0)
3.2b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

46×	`add-sqr-sqrt`
41×	`*-un-lft-identity`
30×	`associate-l`
26×	`times-frac`
25×	`add-cube-cbrt`
21×	`sqrt-prod`
20×	`unpow-prod-down`
11×	`add-exp-log`
9×	`pow1` `add-cbrt-cube` `hypot-def`
8×	`distribute-lft-out` `sqr-pow`
6×	`pow-unpow`
4×	`expm1-log1p-u` `sqrt-div` `log1p-expm1-u` `add-log-exp`
3×	`associate-r` `unswap-sqr`
2×	`pow-to-exp` `pow-pow` `flip3-+` `pow-exp` `prod-exp` `associate-/r/` `cbrt-unprod` `flip-+`
1×	`cbrt-undiv` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `div-exp` `pow-prod-down` `associate-l/` `-commutative` `div-inv`

Counts

4 → 118

Calls

4 calls:

44.0ms	(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
1.0ms	(pow (sin ky) 2.0)
2.0ms	(pow (sin kx) 2.0)
20.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series432.0ms

Counts

4 → 12

Calls

4 calls:

145.0ms	(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
108.0ms	(pow (sin ky) 2.0)
103.0ms	(pow (sin kx) 2.0)
75.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify43.0ms

Algorithm

egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	403	1038
1	1435	967
2	5002	965

prune479.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 9.5b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(hypot (sin ky) (sin kx))
0.1b	(/ (sin ky) (hypot (sin ky) (sin kx)))
0.2b	(* (/ (sin ky) (hypot (sin ky) (sin kx))) (sin th))

rewrite14.0ms

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:

0.0ms	(hypot (sin ky) (sin kx))
3.0ms	(/ (sin ky) (hypot (sin ky) (sin kx)))
9.0ms	(* (/ (sin ky) (hypot (sin ky) (sin kx))) (sin th))

series498.0ms

Counts

3 → 9

Calls

3 calls:

114.0ms	(hypot (sin ky) (sin kx))
164.0ms	(/ (sin ky) (hypot (sin ky) (sin kx)))
220.0ms	(* (/ (sin ky) (hypot (sin ky) (sin kx))) (sin th))

simplify140.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (27.0ms)

Iter	Nodes	Cost
0	287	725
1	1045	645
2	4965	644
3	5001	644

prune278.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 9.5b

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (hypot (sin ky) (sin kx)))
0.2b	(* (/ (/ (sin ky) (sqrt (hypot (sin ky) (sin kx)))) (sqrt (hypot (sin ky) (sin kx)))) (sin th))
0.2b	(/ (/ (sin ky) (sqrt (hypot (sin ky) (sin kx)))) (sqrt (hypot (sin ky) (sin kx))))
0.4b	(/ (sin ky) (sqrt (hypot (sin ky) (sin kx))))

rewrite89.0ms

Algorithm

rewrite-expression-head

Rules

526×	`times-frac`
306×	`add-sqr-sqrt`
281×	`add-cube-cbrt` `*-un-lft-identity`
272×	`sqrt-prod`
136×	`associate-l`
25×	`associate-/l*`
20×	`add-exp-log` `add-cbrt-cube`
16×	`div-inv`
12×	`associate-/r*`
7×	`pow1` `cbrt-undiv` `div-exp` `unswap-sqr`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`associate-r` `prod-exp` `cbrt-unprod`
2×	`frac-2neg` `clear-num`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow-prod-down` `associate-l/` `-commutative` `associate-/l/`

Counts

4 → 397

Calls

4 calls:

1.0ms	(sqrt (hypot (sin ky) (sin kx)))
50.0ms	(* (/ (/ (sin ky) (sqrt (hypot (sin ky) (sin kx)))) (sqrt (hypot (sin ky) (sin kx)))) (sin th))
11.0ms	(/ (/ (sin ky) (sqrt (hypot (sin ky) (sin kx)))) (sqrt (hypot (sin ky) (sin kx))))
4.0ms	(/ (sin ky) (sqrt (hypot (sin ky) (sin kx))))

series702.0ms

Counts

4 → 12

Calls

4 calls:

132.0ms	(sqrt (hypot (sin ky) (sin kx)))
219.0ms	(* (/ (/ (sin ky) (sqrt (hypot (sin ky) (sin kx)))) (sqrt (hypot (sin ky) (sin kx)))) (sin th))
166.0ms	(/ (/ (sin ky) (sqrt (hypot (sin ky) (sin kx)))) (sqrt (hypot (sin ky) (sin kx))))
184.0ms	(/ (sin ky) (sqrt (hypot (sin ky) (sin kx))))

simplify102.0ms

Algorithm

egg-herbie

Counts

409 → 409

Iterations

Useful iterations: 2 (58.0ms)

Iter	Nodes	Cost
0	961	6986
1	3484	6215
2	5001	6180

prune1.1s

Pruning

23 alts after pruning (22 fresh and 1 done)

Merged error: 9.5b

localize14.0ms

Local error

Found 3 expressions with local error:

0.0b	(hypot (sin ky) (sin kx))
0.2b	(/ (sin th) (hypot (sin ky) (sin kx)))
0.2b	(* (/ (sin ky) (sqrt 1)) (/ (sin th) (hypot (sin ky) (sin kx))))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 104

Calls

3 calls:

0.0ms	(hypot (sin ky) (sin kx))
3.0ms	(/ (sin th) (hypot (sin ky) (sin kx)))
18.0ms	(* (/ (sin ky) (sqrt 1)) (/ (sin th) (hypot (sin ky) (sin kx))))

series532.0ms

Counts

3 → 9

Calls

3 calls:

115.0ms	(hypot (sin ky) (sin kx))
198.0ms	(/ (sin th) (hypot (sin ky) (sin kx)))
219.0ms	(* (/ (sin ky) (sqrt 1)) (/ (sin th) (hypot (sin ky) (sin kx))))

simplify54.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	439	1231
1	1863	1108
2	5001	971

prune339.0ms

Pruning

25 alts after pruning (23 fresh and 2 done)

Merged error: 9.5b

regimes783.0ms

Accuracy

0% (0.2b remaining)

Error of 8.7b against oracle of 8.5b and baseline of 8.7b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	9
1	15	9

end0.0ms

sample4.2s

Algorithm

intervals

Results

2.2s	2714×	body	1280	valid
1.1s	1839×	body	640	valid
312.0ms	2389×	body	80	valid
244.0ms	700×	body	320	valid
87.0ms	358×	body	160	valid