Details

sample139.0ms

Algorithm

intervals

Results

84.0ms	103×	body	1280	valid
24.0ms	52×	body	640	valid
9.0ms	75×	body	80	valid
6.0ms	17×	body	320	valid
2.0ms	9×	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: 9.6b

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)
2.2b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite72.0ms

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:

48.0ms	(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
1.0ms	(pow (sin ky) 2.0)
1.0ms	(pow (sin kx) 2.0)
17.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series429.0ms

Counts

4 → 12

Calls

4 calls:

144.0ms	(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
106.0ms	(pow (sin ky) 2.0)
103.0ms	(pow (sin kx) 2.0)
76.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify43.0ms

Algorithm

egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 2 (33.0ms)

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

prune497.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 7.2b

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)))
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))

series502.0ms

Counts

3 → 9

Calls

3 calls:

116.0ms	(hypot (sin ky) (sin kx))
165.0ms	(/ (sin ky) (hypot (sin ky) (sin kx)))
222.0ms	(* (/ (sin ky) (hypot (sin ky) (sin kx))) (sin th))

simplify142.0ms

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

prune317.0ms

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 7.2b

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 71

Calls

4 calls:

0.0ms	(log1p (expm1 (/ (sin ky) (hypot (sin ky) (sin kx)))))
3.0ms	(/ (sin ky) (hypot (sin ky) (sin kx)))
3.0ms	(* (log1p (expm1 (/ (sin ky) (hypot (sin ky) (sin kx))))) (sin th))
0.0ms	(expm1 (/ (sin ky) (hypot (sin ky) (sin kx))))

series796.0ms

Counts

4 → 12

Calls

4 calls:

207.0ms	(log1p (expm1 (/ (sin ky) (hypot (sin ky) (sin kx)))))
159.0ms	(/ (sin ky) (hypot (sin ky) (sin kx)))
221.0ms	(* (log1p (expm1 (/ (sin ky) (hypot (sin ky) (sin kx))))) (sin th))
208.0ms	(expm1 (/ (sin ky) (hypot (sin ky) (sin kx))))

simplify116.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 3 (109.0ms)

Iter	Nodes	Cost
0	253	765
1	833	670
2	3899	669
3	5001	668

prune336.0ms

Pruning

20 alts after pruning (19 fresh and 1 done)

Merged error: 7.2b

localize11.0ms

Local error

Found 3 expressions with local error:

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

rewrite17.0ms

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)))
12.0ms	(* (sin ky) (/ (sin th) (hypot (sin ky) (sin kx))))

series527.0ms

Counts

3 → 9

Calls

3 calls:

115.0ms	(hypot (sin ky) (sin kx))
196.0ms	(/ (sin th) (hypot (sin ky) (sin kx)))
216.0ms	(* (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

prune241.0ms

Pruning

20 alts after pruning (18 fresh and 2 done)

Merged error: 7.2b

regimes963.0ms

Accuracy

0% (0.2b remaining)

Error of 8.9b against oracle of 8.7b and baseline of 8.9b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	9
1	12	9

end0.0ms

sample4.1s

Algorithm

intervals

Results

2.3s	2755×	body	1280	valid
913.0ms	1804×	body	640	valid
319.0ms	2362×	body	80	valid
250.0ms	727×	body	320	valid
85.0ms	352×	body	160	valid