Details

sample147.0ms

Algorithm

intervals

Results

88.0ms	115×	body	1280	valid
31.0ms	67×	body	640	valid
8.0ms	47×	body	80	valid
5.0ms	16×	body	320	valid
2.0ms	11×	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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 2.2b

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)
2.1b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite36.0ms

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:

12.0ms	(/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
3.0ms	(pow (sin ky) 2.0)
3.0ms	(pow (sin kx) 2.0)
15.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series419.0ms

Counts

4 → 12

Calls

4 calls:

130.0ms	(/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
104.0ms	(pow (sin ky) 2.0)
106.0ms	(pow (sin kx) 2.0)
78.0ms	(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

prune415.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(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)))

rewrite13.0ms

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

series507.0ms

Counts

3 → 9

Calls

3 calls:

115.0ms	(hypot (sin ky) (sin kx))
225.0ms	(* (/ (sin ky) (hypot (sin ky) (sin kx))) (sin th))
166.0ms	(/ (sin ky) (hypot (sin ky) (sin kx)))

simplify135.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (26.0ms)

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

prune266.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(hypot (sin ky) (sin kx))
0.1b	(* (sin th) (/ (sin ky) (hypot (sin ky) (sin kx))))
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-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))
7.0ms	(* (sin th) (/ (sin ky) (hypot (sin ky) (sin kx))))
4.0ms	(/ (sin ky) (hypot (sin ky) (sin kx)))

series531.0ms

Counts

3 → 9

Calls

3 calls:

121.0ms	(hypot (sin ky) (sin kx))
241.0ms	(* (sin th) (/ (sin ky) (hypot (sin ky) (sin kx))))
168.0ms	(/ (sin ky) (hypot (sin ky) (sin kx)))

simplify37.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 1 (7.0ms)

Iter	Nodes	Cost
0	284	728
1	1150	648
2	5002	648

prune257.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot (sin ky) (sin kx))
0.1b	(* (sin th) (/ 1 (/ (hypot (sin ky) (sin kx)) (sin ky))))
0.1b	(/ (hypot (sin ky) (sin kx)) (sin ky))
0.1b	(/ 1 (/ (hypot (sin ky) (sin kx)) (sin ky)))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

156×	`times-frac`
104×	`add-sqr-sqrt`
92×	`*-un-lft-identity`
90×	`add-cube-cbrt`
44×	`associate-r`
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-l` `cbrt-unprod`
2×	`frac-2neg` `clear-num` `associate-/r/`
1×	`hypot-udef` `pow-flip` `associate-r/` `pow-prod-down` `un-div-inv` `-commutative` `inv-pow`

Counts

4 → 192

Calls

4 calls:

1.0ms	(hypot (sin ky) (sin kx))
21.0ms	(* (sin th) (/ 1 (/ (hypot (sin ky) (sin kx)) (sin ky))))
4.0ms	(/ (hypot (sin ky) (sin kx)) (sin ky))
7.0ms	(/ 1 (/ (hypot (sin ky) (sin kx)) (sin ky)))

series673.0ms

Counts

4 → 12

Calls

4 calls:

117.0ms	(hypot (sin ky) (sin kx))
244.0ms	(* (sin th) (/ 1 (/ (hypot (sin ky) (sin kx)) (sin ky))))
142.0ms	(/ (hypot (sin ky) (sin kx)) (sin ky))
169.0ms	(/ 1 (/ (hypot (sin ky) (sin kx)) (sin ky)))

simplify75.0ms

Algorithm

egg-herbie

Counts

204 → 204

Iterations

Useful iterations: 2 (58.0ms)

Iter	Nodes	Cost
0	651	2171
1	3115	1931
2	5002	1806

prune504.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

regimes261.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	7
1	16	7
2	16	7

end0.0ms

sample4.8s

Algorithm

intervals

Results

3.2s	3680×	body	1280	valid
1.0s	2076×	body	640	valid
226.0ms	665×	body	320	valid
135.0ms	1276×	body	80	valid
63.0ms	303×	body	160	valid