Details

sample150.0ms

Algorithm

intervals

Results

97.0ms	126×	body	1280	valid
27.0ms	57×	body	640	valid
5.0ms	17×	body	320	valid
5.0ms	49×	body	80	valid
1.0ms	7×	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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 4.6b

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 ky) 2.0)
0.2b	(pow (sin kx) 2.0)
4.2b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite40.0ms

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:

16.0ms	(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
3.0ms	(pow (sin ky) 2.0)
3.0ms	(pow (sin kx) 2.0)
14.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series440.0ms

Counts

4 → 12

Calls

4 calls:

156.0ms	(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
103.0ms	(pow (sin ky) 2.0)
103.0ms	(pow (sin kx) 2.0)
78.0ms	(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	1039
1	1433	967
2	5002	965

prune464.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

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)))
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:

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

series517.0ms

Counts

3 → 9

Calls

3 calls:

121.0ms	(hypot (sin ky) (sin kx))
166.0ms	(/ (sin ky) (hypot (sin ky) (sin kx)))
229.0ms	(* (/ (sin ky) (hypot (sin ky) (sin kx))) (sin th))

simplify137.0ms

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

prune262.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize11.0ms

Local error

Found 3 expressions with local error:

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

rewrite18.0ms

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

series536.0ms

Counts

3 → 9

Calls

3 calls:

116.0ms	(hypot (sin ky) (sin kx))
201.0ms	(/ (sin th) (hypot (sin ky) (sin kx)))
219.0ms	(* (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

prune255.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sin ky) (expm1 (log1p (hypot (sin ky) (sin kx)))))
0.2b	(log1p (hypot (sin ky) (sin kx)))
0.2b	(* (/ (sin ky) (expm1 (log1p (hypot (sin ky) (sin kx))))) (sin th))
0.3b	(expm1 (log1p (hypot (sin ky) (sin kx))))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 85

Calls

4 calls:

4.0ms	(/ (sin ky) (expm1 (log1p (hypot (sin ky) (sin kx)))))
1.0ms	(log1p (hypot (sin ky) (sin kx)))
7.0ms	(* (/ (sin ky) (expm1 (log1p (hypot (sin ky) (sin kx))))) (sin th))
1.0ms	(expm1 (log1p (hypot (sin ky) (sin kx))))

series751.0ms

Counts

4 → 12

Calls

4 calls:

204.0ms	(/ (sin ky) (expm1 (log1p (hypot (sin ky) (sin kx)))))
139.0ms	(log1p (hypot (sin ky) (sin kx)))
252.0ms	(* (/ (sin ky) (expm1 (log1p (hypot (sin ky) (sin kx))))) (sin th))
154.0ms	(expm1 (log1p (hypot (sin ky) (sin kx))))

simplify36.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 2 (28.0ms)

Iter	Nodes	Cost
0	318	967
1	1131	835
2	5001	819

prune303.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0b

regimes289.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	7
1	10	7

end0.0ms

sample4.8s

Algorithm

intervals

Results

3.2s	3761×	body	1280	valid
964.0ms	1978×	body	640	valid
240.0ms	707×	body	320	valid
126.0ms	1274×	body	80	valid
59.0ms	280×	body	160	valid