Details

sample117.0ms

Algorithm

intervals

Results

64.0ms	81×	body	1280	valid
22.0ms	55×	body	640	valid
8.0ms	30×	body	320	valid
7.0ms	77×	body	80	valid
2.0ms	13×	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: 12.8b

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))))
0.2b	(pow (sin kx) 2.0)
0.2b	(pow (sin ky) 2.0)
4.8b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite45.0ms

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:

18.0ms	(/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
1.0ms	(pow (sin kx) 2.0)
1.0ms	(pow (sin ky) 2.0)
17.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series411.0ms

Counts

4 → 12

Calls

4 calls:

125.0ms	(/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
103.0ms	(pow (sin kx) 2.0)
111.0ms	(pow (sin ky) 2.0)
72.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify39.0ms

Algorithm

egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	341	1065
1	1159	981
2	5001	976

prune443.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 7.7b

localize11.0ms

Local error

Found 3 expressions with local error:

0.1b	(hypot (sin ky) (sin kx))
0.1b	(* (/ (sin ky) (hypot (sin ky) (sin kx))) (sin th))
0.2b	(/ (sin ky) (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-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))
8.0ms	(* (/ (sin ky) (hypot (sin ky) (sin kx))) (sin th))
3.0ms	(/ (sin ky) (hypot (sin ky) (sin kx)))

series508.0ms

Counts

3 → 9

Calls

3 calls:

116.0ms	(hypot (sin ky) (sin kx))
228.0ms	(* (/ (sin ky) (hypot (sin ky) (sin kx))) (sin th))
165.0ms	(/ (sin ky) (hypot (sin ky) (sin kx)))

simplify138.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (27.0ms)

Iter	Nodes	Cost
0	287	725
1	1045	645
2	4962	644
3	5001	644

prune321.0ms

Pruning

23 alts after pruning (23 fresh and 0 done)

Merged error: 7.7b

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))))

rewrite16.0ms

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))
6.0ms	(/ (sin th) (hypot (sin ky) (sin kx)))
8.0ms	(* (sin ky) (/ (sin th) (hypot (sin ky) (sin kx))))

series530.0ms

Counts

3 → 9

Calls

3 calls:

116.0ms	(hypot (sin ky) (sin kx))
196.0ms	(/ (sin th) (hypot (sin ky) (sin kx)))
217.0ms	(* (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

prune298.0ms

Pruning

23 alts after pruning (22 fresh and 1 done)

Merged error: 7.7b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ (sin ky) (expm1 (log1p (hypot (sin ky) (sin kx))))) (sin th))
0.2b	(/ (sin ky) (expm1 (log1p (hypot (sin ky) (sin kx)))))
0.2b	(log1p (hypot (sin ky) (sin kx)))
0.3b	(expm1 (log1p (hypot (sin ky) (sin kx))))

rewrite18.0ms

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:

9.0ms	(* (/ (sin ky) (expm1 (log1p (hypot (sin ky) (sin kx))))) (sin th))
6.0ms	(/ (sin ky) (expm1 (log1p (hypot (sin ky) (sin kx)))))
0.0ms	(log1p (hypot (sin ky) (sin kx)))
0.0ms	(expm1 (log1p (hypot (sin ky) (sin kx))))

series745.0ms

Counts

4 → 12

Calls

4 calls:

257.0ms	(* (/ (sin ky) (expm1 (log1p (hypot (sin ky) (sin kx))))) (sin th))
201.0ms	(/ (sin ky) (expm1 (log1p (hypot (sin ky) (sin kx)))))
136.0ms	(log1p (hypot (sin ky) (sin kx)))
150.0ms	(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

prune300.0ms

Pruning

23 alts after pruning (21 fresh and 2 done)

Merged error: 7.7b

regimes688.0ms

Accuracy

0% (0.2b remaining)

Error of 8.8b against oracle of 8.6b and baseline of 8.8b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	8
1	15	8

end0.0ms

sample3.7s

Algorithm

intervals

Results

2.1s	2769×	body	1280	valid
864.0ms	1737×	body	640	valid
230.0ms	2326×	body	80	valid
224.0ms	799×	body	320	valid
75.0ms	369×	body	160	valid