Details

sample123.0ms

Algorithm

intervals

Results

72.0ms	97×	body	1280	valid
22.0ms	54×	body	640	valid
6.0ms	23×	body	320	valid
6.0ms	67×	body	80	valid
3.0ms	15×	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

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.1b

localize16.0ms

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))
0.3b	(pow (sin kx) 2.0)
0.3b	(pow (sin ky) 2.0)
3.4b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite78.0ms

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:

52.0ms	(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
1.0ms	(pow (sin kx) 2.0)
2.0ms	(pow (sin ky) 2.0)
18.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series454.0ms

Counts

4 → 12

Calls

4 calls:

156.0ms	(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
108.0ms	(pow (sin kx) 2.0)
109.0ms	(pow (sin ky) 2.0)
81.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify45.0ms

Algorithm

egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 2 (35.0ms)

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

prune508.0ms

Filtered

130 candidates to 95 candidates (73.1%)

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 9.4b

localize17.0ms

Local error

Found 3 expressions with local error:

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

rewrite15.0ms

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))

series525.0ms

Counts

3 → 9

Calls

3 calls:

119.0ms	(hypot (sin ky) (sin kx))
174.0ms	(/ (sin ky) (hypot (sin ky) (sin kx)))
232.0ms	(* (/ (sin ky) (hypot (sin ky) (sin kx))) (sin th))

simplify142.0ms

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

prune291.0ms

Filtered

82 candidates to 65 candidates (79.3%)

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 9.4b

localize12.0ms

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:

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

series557.0ms

Counts

3 → 9

Calls

3 calls:

121.0ms	(hypot (sin ky) (sin kx))
225.0ms	(* (sin ky) (/ (sin th) (hypot (sin ky) (sin kx))))
210.0ms	(/ (sin th) (hypot (sin ky) (sin kx)))

simplify35.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 1 (7.0ms)

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

prune305.0ms

Filtered

82 candidates to 65 candidates (79.3%)

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 9.4b

localize17.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (cbrt (/ (sin ky) (hypot (sin ky) (sin kx)))) (cbrt (/ (sin ky) (hypot (sin ky) (sin kx)))))
0.4b	(cbrt (/ (sin ky) (hypot (sin ky) (sin kx))))
0.4b	(cbrt (/ (sin ky) (hypot (sin ky) (sin kx))))
0.4b	(cbrt (/ (sin ky) (hypot (sin ky) (sin kx))))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

103×	`cbrt-prod`
81×	`add-sqr-sqrt`
69×	`times-frac`
57×	`add-cube-cbrt` `*-un-lft-identity`
16×	`swap-sqr` `associate-r` `associate-l`
11×	`pow1`
9×	`pow1/3` `unswap-sqr`
7×	`cbrt-div` `div-inv`
6×	`add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `frac-times` `pow-plus` `associate-r/` `associate-l/` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 152

Calls

4 calls:

23.0ms	(* (cbrt (/ (sin ky) (hypot (sin ky) (sin kx)))) (cbrt (/ (sin ky) (hypot (sin ky) (sin kx)))))
2.0ms	(cbrt (/ (sin ky) (hypot (sin ky) (sin kx))))
2.0ms	(cbrt (/ (sin ky) (hypot (sin ky) (sin kx))))
2.0ms	(cbrt (/ (sin ky) (hypot (sin ky) (sin kx))))

series954.0ms

Counts

4 → 12

Calls

4 calls:

247.0ms	(* (cbrt (/ (sin ky) (hypot (sin ky) (sin kx)))) (cbrt (/ (sin ky) (hypot (sin ky) (sin kx)))))
235.0ms	(cbrt (/ (sin ky) (hypot (sin ky) (sin kx))))
252.0ms	(cbrt (/ (sin ky) (hypot (sin ky) (sin kx))))
220.0ms	(cbrt (/ (sin ky) (hypot (sin ky) (sin kx))))

simplify53.0ms

Algorithm

egg-herbie

Counts

164 → 164

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	291	2447
1	993	2341
2	5001	2212

prune610.0ms

Filtered

164 candidates to 130 candidates (79.3%)

Pruning

23 alts after pruning (23 fresh and 0 done)

Merged error: 9.4b

regimes765.0ms

Accuracy

0% (0.7b remaining)

Error of 9.2b against oracle of 8.6b and baseline of 9.2b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	60
1	25	60

end0.0ms

sample3.7s

Algorithm

intervals

Results

2.2s	2755×	body	1280	valid
789.0ms	1801×	body	640	valid
218.0ms	2337×	body	80	valid
211.0ms	753×	body	320	valid
94.0ms	354×	body	160	valid