Details

sample113.0ms

Algorithm

intervals

Results

60.0ms	88×	body	1280	valid
18.0ms	46×	body	640	valid
11.0ms	83×	body	80	valid
7.0ms	25×	body	320	valid
2.0ms	14×	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

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.2b

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)))) (sin th))
0.2b	(pow (sin ky) 2.0)
0.3b	(pow (sin kx) 2.0)
3.9b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite74.0ms

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:

49.0ms	(* (/ (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)))

series422.0ms

Counts

4 → 12

Calls

4 calls:

144.0ms	(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
102.0ms	(pow (sin ky) 2.0)
100.0ms	(pow (sin kx) 2.0)
75.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify45.0ms

Algorithm

egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 2 (35.0ms)

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

prune482.0ms

Filtered

130 candidates to 95 candidates (73.1%)

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 8.0b

localize15.0ms

Local error

Found 3 expressions with local error:

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

series501.0ms

Counts

3 → 9

Calls

3 calls:

114.0ms	(hypot (sin ky) (sin kx))
164.0ms	(/ (sin ky) (hypot (sin ky) (sin kx)))
223.0ms	(* (/ (sin ky) (hypot (sin ky) (sin kx))) (sin th))

simplify143.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (28.0ms)

Iter	Nodes	Cost
0	287	725
1	1045	645
2	4965	644
3	5001	644

prune288.0ms

Filtered

82 candidates to 65 candidates (79.3%)

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 8.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (/ 1 (sqrt (hypot (sin ky) (sin kx)))) (/ (sin ky) (sqrt (hypot (sin ky) (sin kx))))) (sin th))
0.3b	(/ 1 (sqrt (hypot (sin ky) (sin kx))))
0.4b	(* (/ 1 (sqrt (hypot (sin ky) (sin kx)))) (/ (sin ky) (sqrt (hypot (sin ky) (sin kx)))))
0.4b	(/ (sin ky) (sqrt (hypot (sin ky) (sin kx))))

rewrite79.0ms

Algorithm

rewrite-expression-head

Rules

107×	`add-sqr-sqrt`
94×	`times-frac`
67×	`*-un-lft-identity`
64×	`add-exp-log`
61×	`add-cube-cbrt`
53×	`sqrt-prod`
38×	`add-cbrt-cube`
25×	`associate-r` `prod-exp`
23×	`associate-l`
19×	`div-exp`
15×	`unswap-sqr`
13×	`pow1` `cbrt-unprod`
12×	`associate-/r*`
10×	`cbrt-undiv`
6×	`associate-/l*`
5×	`rec-exp` `1-exp` `associate-*l/`
4×	`expm1-log1p-u` `pow-prod-down` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`pow-flip`
2×	`frac-times` `frac-2neg` `associate-r/` `clear-num` `-commutative`
1×	`sqrt-pow1` `pow1/2` `inv-pow`

Counts

4 → 206

Calls

4 calls:

35.0ms	(* (* (/ 1 (sqrt (hypot (sin ky) (sin kx)))) (/ (sin ky) (sqrt (hypot (sin ky) (sin kx))))) (sin th))
3.0ms	(/ 1 (sqrt (hypot (sin ky) (sin kx))))
28.0ms	(* (/ 1 (sqrt (hypot (sin ky) (sin kx)))) (/ (sin ky) (sqrt (hypot (sin ky) (sin kx)))))
4.0ms	(/ (sin ky) (sqrt (hypot (sin ky) (sin kx))))

series725.0ms

Counts

4 → 12

Calls

4 calls:

228.0ms	(* (* (/ 1 (sqrt (hypot (sin ky) (sin kx)))) (/ (sin ky) (sqrt (hypot (sin ky) (sin kx))))) (sin th))
151.0ms	(/ 1 (sqrt (hypot (sin ky) (sin kx))))
166.0ms	(* (/ 1 (sqrt (hypot (sin ky) (sin kx)))) (/ (sin ky) (sqrt (hypot (sin ky) (sin kx)))))
179.0ms	(/ (sin ky) (sqrt (hypot (sin ky) (sin kx))))

simplify90.0ms

Algorithm

egg-herbie

Counts

218 → 218

Iterations

Useful iterations: 2 (65.0ms)

Iter	Nodes	Cost
0	683	3002
1	3312	2563
2	5001	2352

prune556.0ms

Filtered

218 candidates to 119 candidates (54.6%)

Pruning

22 alts after pruning (21 fresh and 1 done)

Merged error: 8.0b

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)))
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))

series492.0ms

Counts

3 → 9

Calls

3 calls:

115.0ms	(hypot (sin ky) (sin kx))
160.0ms	(/ (sin ky) (hypot (sin ky) (sin kx)))
216.0ms	(* (/ (sin ky) (hypot (sin ky) (sin kx))) (sin th))

simplify129.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (26.0ms)

Iter	Nodes	Cost
0	287	725
1	1045	645
2	4965	644
3	5001	644

prune205.0ms

Filtered

82 candidates to 54 candidates (65.9%)

Pruning

21 alts after pruning (19 fresh and 2 done)

Merged error: 8.0b

regimes527.0ms

Accuracy

0% (0.1b remaining)

Error of 8.9b against oracle of 8.8b and baseline of 8.9b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	7
1	10	7

end0.0ms

sample3.6s

Algorithm

intervals

Results

2.1s	2684×	body	1280	valid
800.0ms	1906×	body	640	valid
211.0ms	767×	body	320	valid
206.0ms	2275×	body	80	valid
71.0ms	368×	body	160	valid