Details

sample129.0ms

Algorithm

intervals

Results

72.0ms	86×	body	1280	valid
25.0ms	54×	body	640	valid
9.0ms	82×	body	80	valid
6.0ms	20×	body	320	valid
3.0ms	14×	body	160	valid

simplify52.0ms

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: 14.0b

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 kx) 2.0)
0.3b	(pow (sin ky) 2.0)
4.1b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite71.0ms

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:

43.0ms	(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
1.0ms	(pow (sin kx) 2.0)
6.0ms	(pow (sin ky) 2.0)
16.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series428.0ms

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 kx) 2.0)
101.0ms	(pow (sin ky) 2.0)
75.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify44.0ms

Algorithm

egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 2 (34.0ms)

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

prune492.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 9.6b

localize15.0ms

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

series493.0ms

Counts

3 → 9

Calls

3 calls:

113.0ms	(hypot (sin ky) (sin kx))
161.0ms	(/ (sin ky) (hypot (sin ky) (sin kx)))
218.0ms	(* (/ (sin ky) (hypot (sin ky) (sin kx))) (sin th))

simplify138.0ms

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

prune289.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 9.6b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(hypot (sin ky) (sin kx))
0.2b	(* (* (sin ky) (/ 1 (hypot (sin ky) (sin kx)))) (sin th))
0.2b	(/ 1 (hypot (sin ky) (sin kx)))
0.3b	(* (sin ky) (/ 1 (hypot (sin ky) (sin kx))))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-exp-log`
28×	`add-sqr-sqrt`
22×	`*-un-lft-identity`
21×	`add-cube-cbrt`
20×	`times-frac` `add-cbrt-cube`
16×	`associate-r`
13×	`prod-exp`
12×	`pow1`
7×	`cbrt-unprod`
6×	`div-exp`
4×	`expm1-log1p-u` `associate-l` `pow-prod-down` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `rec-exp` `1-exp` `associate-/r` `associate-/l` `unswap-sqr`
2×	`associate-r/` `associate-l/` `un-div-inv` `*-commutative` `div-inv`
1×	`hypot-udef` `pow-flip` `frac-2neg` `clear-num` `inv-pow`

Counts

4 → 107

Calls

4 calls:

0.0ms	(hypot (sin ky) (sin kx))
18.0ms	(* (* (sin ky) (/ 1 (hypot (sin ky) (sin kx)))) (sin th))
2.0ms	(/ 1 (hypot (sin ky) (sin kx)))
8.0ms	(* (sin ky) (/ 1 (hypot (sin ky) (sin kx))))

series631.0ms

Counts

4 → 12

Calls

4 calls:

113.0ms	(hypot (sin ky) (sin kx))
219.0ms	(* (* (sin ky) (/ 1 (hypot (sin ky) (sin kx)))) (sin th))
136.0ms	(/ 1 (hypot (sin ky) (sin kx)))
162.0ms	(* (sin ky) (/ 1 (hypot (sin ky) (sin kx))))

simplify49.0ms

Algorithm

egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	389	971
1	1695	810
2	5001	779

prune329.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 9.6b

localize17.0ms

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	(* (* 1 (/ (sin ky) (hypot (sin ky) (sin kx)))) (sin th))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 64

Calls

3 calls:

0.0ms	(hypot (sin ky) (sin kx))
3.0ms	(/ (sin ky) (hypot (sin ky) (sin kx)))
12.0ms	(* (* 1 (/ (sin ky) (hypot (sin ky) (sin kx)))) (sin th))

series497.0ms

Counts

3 → 9

Calls

3 calls:

113.0ms	(hypot (sin ky) (sin kx))
163.0ms	(/ (sin ky) (hypot (sin ky) (sin kx)))
220.0ms	(* (* 1 (/ (sin ky) (hypot (sin ky) (sin kx)))) (sin th))

simplify38.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 1 (8.0ms)

Iter	Nodes	Cost
0	312	659
1	1144	556
2	5001	556

prune209.0ms

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 9.6b

regimes558.0ms

Accuracy

0% (0.1b remaining)

Error of 8.7b against oracle of 8.6b and baseline of 8.7b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	7
1	17	7
2	17	7

end0.0ms

sample4.2s

Algorithm

intervals

Results

2.5s	2809×	body	1280	valid
919.0ms	1822×	body	640	valid
255.0ms	2289×	body	80	valid
240.0ms	706×	body	320	valid
88.0ms	374×	body	160	valid