Details

sample106.0ms

Algorithm

intervals

Results

49.0ms	71×	body	1280	valid
29.0ms	67×	body	640	valid
7.0ms	27×	body	320	valid
6.0ms	81×	body	80	valid
2.0ms	10×	body	160	valid

simplify51.0ms

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

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.0b

localize14.0ms

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)
5.1b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite73.0ms

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:

49.0ms	(* (/ (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)
17.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series423.0ms

Counts

4 → 12

Calls

4 calls:

147.0ms	(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
99.0ms	(pow (sin kx) 2.0)
101.0ms	(pow (sin ky) 2.0)
76.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify44.0ms

Algorithm

egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 2 (34.0ms)

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

prune468.0ms

Filtered

130 candidates to 95 candidates (73.1%)

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 10.6b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(hypot (sin ky) (sin kx))
0.2b	(/ (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))

series493.0ms

Counts

3 → 9

Calls

3 calls:

114.0ms	(hypot (sin ky) (sin kx))
162.0ms	(/ (sin ky) (hypot (sin ky) (sin kx)))
217.0ms	(* (/ (sin ky) (hypot (sin ky) (sin kx))) (sin th))

simplify139.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (28.0ms)

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

prune289.0ms

Filtered

82 candidates to 66 candidates (80.5%)

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 10.6b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(hypot (sin ky) (sin kx))
0.2b	(/ (sin th) (hypot (sin ky) (sin kx)))
0.3b	(* (sin ky) (/ (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:

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

series529.0ms

Counts

3 → 9

Calls

3 calls:

115.0ms	(hypot (sin ky) (sin kx))
196.0ms	(/ (sin th) (hypot (sin ky) (sin kx)))
218.0ms	(* (sin ky) (/ (sin th) (hypot (sin ky) (sin kx))))

simplify36.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 1 (7.0ms)

Iter	Nodes	Cost
0	258	719
1	1032	641
2	5002	641

prune294.0ms

Filtered

82 candidates to 65 candidates (79.3%)

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 10.6b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (hypot (sin ky) (sin kx)))
0.2b	(/ (sin th) (* (sqrt (hypot (sin ky) (sin kx))) (sqrt (hypot (sin ky) (sin kx)))))
0.3b	(* (sin ky) (/ (sin th) (* (sqrt (hypot (sin ky) (sin kx))) (sqrt (hypot (sin ky) (sin kx))))))
0.5b	(* (sqrt (hypot (sin ky) (sin kx))) (sqrt (hypot (sin ky) (sin kx))))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

35×	`add-sqr-sqrt`
22×	`pow1`
21×	`sqrt-prod`
20×	`add-exp-log` `add-cbrt-cube`
18×	`add-cube-cbrt` `*-un-lft-identity`
13×	`associate-r`
9×	`sqrt-pow1` `pow1/2` `associate-l`
8×	`swap-sqr`
7×	`times-frac`
6×	`prod-exp` `cbrt-unprod` `unswap-sqr`
5×	`pow-prod-up`
4×	`cbrt-undiv` `expm1-log1p-u` `div-exp` `pow-prod-down` `log1p-expm1-u` `add-log-exp`
3×	`pow-sqr` `associate-/l*`
2×	`*-commutative` `div-inv`
1×	`pow2` `rem-sqrt-square` `frac-2neg` `pow-plus` `sqrt-unprod` `associate-r/` `clear-num` `associate-/r` `rem-square-sqrt`

Counts

4 → 119

Calls

4 calls:

1.0ms	(sqrt (hypot (sin ky) (sin kx)))
6.0ms	(/ (sin th) (* (sqrt (hypot (sin ky) (sin kx))) (sqrt (hypot (sin ky) (sin kx)))))
20.0ms	(* (sin ky) (/ (sin th) (* (sqrt (hypot (sin ky) (sin kx))) (sqrt (hypot (sin ky) (sin kx))))))
7.0ms	(* (sqrt (hypot (sin ky) (sin kx))) (sqrt (hypot (sin ky) (sin kx))))

series658.0ms

Counts

4 → 12

Calls

4 calls:

129.0ms	(sqrt (hypot (sin ky) (sin kx)))
201.0ms	(/ (sin th) (* (sqrt (hypot (sin ky) (sin kx))) (sqrt (hypot (sin ky) (sin kx)))))
214.0ms	(* (sin ky) (/ (sin th) (* (sqrt (hypot (sin ky) (sin kx))) (sqrt (hypot (sin ky) (sin kx))))))
113.0ms	(* (sqrt (hypot (sin ky) (sin kx))) (sqrt (hypot (sin ky) (sin kx))))

simplify54.0ms

Algorithm

egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	350	1257
1	1529	1047
2	5001	1009

prune319.0ms

Filtered

131 candidates to 82 candidates (62.6%)

Pruning

22 alts after pruning (21 fresh and 1 done)

Merged error: 10.6b

regimes781.0ms

Accuracy

0% (0.4b remaining)

Error of 9.0b against oracle of 8.6b and baseline of 9.0b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	13
1	12	13

end0.0ms

sample3.4s

Algorithm

intervals

Results

1.9s	2684×	body	1280	valid
771.0ms	1843×	body	640	valid
204.0ms	760×	body	320	valid
201.0ms	2359×	body	80	valid
61.0ms	354×	body	160	valid