Details

sample104.0ms

Algorithm

intervals

Results

48.0ms	72×	body	1280	valid
21.0ms	56×	body	640	valid
11.0ms	90×	body	80	valid
7.0ms	26×	body	320	valid
2.0ms	12×	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: 14.5b

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 ky) 2.0)
0.3b	(pow (sin kx) 2.0)
3.3b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite81.0ms

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:

37.0ms	(/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
3.0ms	(pow (sin ky) 2.0)
4.0ms	(pow (sin kx) 2.0)
34.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series432.0ms

Counts

4 → 12

Calls

4 calls:

137.0ms	(/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
105.0ms	(pow (sin ky) 2.0)
112.0ms	(pow (sin kx) 2.0)
78.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify38.0ms

Algorithm

egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 2 (29.0ms)

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

prune441.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 11.0b

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

rewrite29.0ms

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))
18.0ms	(* (/ (sin ky) (hypot (sin ky) (sin kx))) (sin th))
8.0ms	(/ (sin ky) (hypot (sin ky) (sin kx)))

series541.0ms

Counts

3 → 9

Calls

3 calls:

122.0ms	(hypot (sin ky) (sin kx))
242.0ms	(* (/ (sin ky) (hypot (sin ky) (sin kx))) (sin th))
177.0ms	(/ (sin ky) (hypot (sin ky) (sin kx)))

simplify145.0ms

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

prune288.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 11.0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(hypot (sin ky) (sin kx))
0.1b	(/ (hypot (sin ky) (sin kx)) (sin ky))
0.2b	(* (/ 1 (/ (hypot (sin ky) (sin kx)) (sin ky))) (sin th))
0.2b	(/ 1 (/ (hypot (sin ky) (sin kx)) (sin ky)))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

156×	`times-frac`
104×	`add-sqr-sqrt`
92×	`*-un-lft-identity`
90×	`add-cube-cbrt`
44×	`associate-l`
36×	`add-exp-log`
20×	`add-cbrt-cube`
16×	`associate-/r*`
15×	`div-exp`
10×	`div-inv`
7×	`pow1` `cbrt-undiv` `prod-exp`
6×	`associate-/l*`
5×	`unswap-sqr`
4×	`expm1-log1p-u` `rec-exp` `1-exp` `log1p-expm1-u` `add-log-exp`
3×	`associate-r` `cbrt-unprod`
2×	`frac-2neg` `clear-num` `associate-/r/`
1×	`hypot-udef` `pow-flip` `pow-prod-down` `associate-l/` `-commutative` `inv-pow`

Counts

4 → 191

Calls

4 calls:

0.0ms	(hypot (sin ky) (sin kx))
8.0ms	(/ (hypot (sin ky) (sin kx)) (sin ky))
37.0ms	(* (/ 1 (/ (hypot (sin ky) (sin kx)) (sin ky))) (sin th))
11.0ms	(/ 1 (/ (hypot (sin ky) (sin kx)) (sin ky)))

series691.0ms

Counts

4 → 12

Calls

4 calls:

124.0ms	(hypot (sin ky) (sin kx))
150.0ms	(/ (hypot (sin ky) (sin kx)) (sin ky))
242.0ms	(* (/ 1 (/ (hypot (sin ky) (sin kx)) (sin ky))) (sin th))
174.0ms	(/ 1 (/ (hypot (sin ky) (sin kx)) (sin ky)))

simplify76.0ms

Algorithm

egg-herbie

Counts

203 → 203

Iterations

Useful iterations: 2 (55.0ms)

Iter	Nodes	Cost
0	637	2121
1	2915	1881
2	5001	1782

prune551.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 11.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(hypot (sin ky) (sin kx))
0.1b	(/ (* 1 (hypot (sin ky) (sin kx))) (sin ky))
0.2b	(* (/ 1 (/ (* 1 (hypot (sin ky) (sin kx))) (sin ky))) (sin th))
0.2b	(/ 1 (/ (* 1 (hypot (sin ky) (sin kx))) (sin ky)))

rewrite81.0ms

Algorithm

rewrite-expression-head

Rules

81×	`add-exp-log`
68×	`times-frac`
44×	`add-sqr-sqrt`
38×	`*-un-lft-identity`
37×	`add-cube-cbrt` `div-exp`
32×	`add-cbrt-cube`
27×	`prod-exp`
26×	`associate-l`
15×	`1-exp`
12×	`cbrt-undiv`
10×	`associate-/r*` `div-inv`
8×	`rec-exp`
7×	`pow1` `cbrt-unprod`
4×	`expm1-log1p-u` `log1p-expm1-u` `associate-/l*` `add-log-exp`
3×	`associate-r` `unswap-sqr`
2×	`frac-2neg` `clear-num` `associate-/r/`
1×	`hypot-udef` `pow-flip` `pow-prod-down` `associate-l/` `-commutative` `inv-pow`

Counts

4 → 156

Calls

4 calls:

0.0ms	(hypot (sin ky) (sin kx))
10.0ms	(/ (* 1 (hypot (sin ky) (sin kx))) (sin ky))
48.0ms	(* (/ 1 (/ (* 1 (hypot (sin ky) (sin kx))) (sin ky))) (sin th))
14.0ms	(/ 1 (/ (* 1 (hypot (sin ky) (sin kx))) (sin ky)))

series687.0ms

Counts

4 → 12

Calls

4 calls:

119.0ms	(hypot (sin ky) (sin kx))
148.0ms	(/ (* 1 (hypot (sin ky) (sin kx))) (sin ky))
243.0ms	(* (/ 1 (/ (* 1 (hypot (sin ky) (sin kx))) (sin ky))) (sin th))
176.0ms	(/ 1 (/ (* 1 (hypot (sin ky) (sin kx))) (sin ky)))

simplify59.0ms

Algorithm

egg-herbie

Counts

168 → 168

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	585	1625
1	2424	1340
2	5001	1269

prune368.0ms

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 11.0b

regimes551.0ms

Accuracy

0% (0.2b remaining)

Error of 9.0b against oracle of 8.8b and baseline of 9.0b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	9
1	18	9
2	18	9

end0.0ms

sample3.6s

Algorithm

intervals

Results

1.9s	2665×	body	1280	valid
756.0ms	1832×	body	640	valid
385.0ms	2388×	body	80	valid
204.0ms	747×	body	320	valid
65.0ms	368×	body	160	valid