Details

sample133.0ms

Algorithm

intervals

Results

75.0ms	95×	body	1280	valid
28.0ms	63×	body	640	valid
8.0ms	64×	body	80	valid
8.0ms	26×	body	320	valid
2.0ms	8×	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: 11.4b

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))
0.3b	(pow (sin ky) 2.0)
0.3b	(pow (sin kx) 2.0)
2.5b	(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:

44.0ms	(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
1.0ms	(pow (sin ky) 2.0)
2.0ms	(pow (sin kx) 2.0)
20.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series425.0ms

Counts

4 → 12

Calls

4 calls:

143.0ms	(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
103.0ms	(pow (sin ky) 2.0)
102.0ms	(pow (sin kx) 2.0)
76.0ms	(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

prune472.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 8.7b

localize12.0ms

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

series497.0ms

Counts

3 → 9

Calls

3 calls:

113.0ms	(hypot (sin ky) (sin kx))
165.0ms	(/ (sin ky) (hypot (sin ky) (sin kx)))
220.0ms	(* (/ (sin ky) (hypot (sin ky) (sin kx))) (sin th))

simplify136.0ms

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

prune280.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 8.7b

localize11.0ms

Local error

Found 3 expressions with local error:

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

rewrite16.0ms

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))
6.0ms	(/ (sin th) (hypot (sin ky) (sin kx)))
8.0ms	(* (sin ky) (/ (sin th) (hypot (sin ky) (sin kx))))

series525.0ms

Counts

3 → 9

Calls

3 calls:

114.0ms	(hypot (sin ky) (sin kx))
197.0ms	(/ (sin th) (hypot (sin ky) (sin kx)))
214.0ms	(* (sin ky) (/ (sin th) (hypot (sin ky) (sin kx))))

simplify35.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 1 (7.0ms)

Iter	Nodes	Cost
0	258	719
1	1032	641
2	5002	641

prune290.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 8.7b

localize13.0ms

Local error

Found 4 expressions with local error:

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

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:

0.0ms	(hypot (sin ky) (sin kx))
2.0ms	(/ (hypot (sin ky) (sin kx)) (sin th))
24.0ms	(* (sin ky) (/ 1 (/ (hypot (sin ky) (sin kx)) (sin th))))
5.0ms	(/ 1 (/ (hypot (sin ky) (sin kx)) (sin th)))

series727.0ms

Counts

4 → 12

Calls

4 calls:

120.0ms	(hypot (sin ky) (sin kx))
190.0ms	(/ (hypot (sin ky) (sin kx)) (sin th))
225.0ms	(* (sin ky) (/ 1 (/ (hypot (sin ky) (sin kx)) (sin th))))
192.0ms	(/ 1 (/ (hypot (sin ky) (sin kx)) (sin th)))

simplify73.0ms

Algorithm

egg-herbie

Counts

204 → 204

Iterations

Useful iterations: 2 (56.0ms)

Iter	Nodes	Cost
0	627	2164
1	3002	1925
2	5002	1801

prune496.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 8.7b

regimes565.0ms

Accuracy

0% (0.2b remaining)

Error of 9.1b against oracle of 8.9b and baseline of 9.1b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	7

end0.0ms

sample3.8s

Algorithm

intervals

Results

2.1s	2755×	body	1280	valid
852.0ms	1854×	body	640	valid
285.0ms	2290×	body	80	valid
239.0ms	743×	body	320	valid
80.0ms	358×	body	160	valid