Details

sample120.0ms

Algorithm

intervals

Results

69.0ms	96×	body	1280	valid
23.0ms	59×	body	640	valid
6.0ms	75×	body	80	valid
4.0ms	15×	body	320	valid
2.0ms	11×	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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.2b

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
0.3b	(pow (sin kx) 2.0)
0.3b	(pow (sin ky) 2.0)
3.4b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite83.0ms

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))))
4.0ms	(pow (sin kx) 2.0)
4.0ms	(pow (sin ky) 2.0)
35.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series388.0ms

Counts

4 → 12

Calls

4 calls:

119.0ms	(/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
97.0ms	(pow (sin kx) 2.0)
105.0ms	(pow (sin ky) 2.0)
67.0ms	(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

prune466.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 8.6b

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

rewrite30.0ms

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))
19.0ms	(* (/ (sin ky) (hypot (sin ky) (sin kx))) (sin th))
9.0ms	(/ (sin ky) (hypot (sin ky) (sin kx)))

series463.0ms

Counts

3 → 9

Calls

3 calls:

106.0ms	(hypot (sin ky) (sin kx))
204.0ms	(* (/ (sin ky) (hypot (sin ky) (sin kx))) (sin th))
153.0ms	(/ (sin ky) (hypot (sin ky) (sin kx)))

simplify139.0ms

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

prune296.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 8.6b

localize12.0ms

Local error

Found 3 expressions with local error:

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

rewrite31.0ms

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))
20.0ms	(* (sin ky) (/ (sin th) (hypot (sin ky) (sin kx))))
9.0ms	(/ (sin th) (hypot (sin ky) (sin kx)))

series495.0ms

Counts

3 → 9

Calls

3 calls:

108.0ms	(hypot (sin ky) (sin kx))
207.0ms	(* (sin ky) (/ (sin th) (hypot (sin ky) (sin kx))))
180.0ms	(/ (sin th) (hypot (sin ky) (sin kx)))

simplify34.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 1 (7.0ms)

Iter	Nodes	Cost
0	258	719
1	1032	641
2	5001	641

prune307.0ms

Pruning

19 alts after pruning (18 fresh and 1 done)

Merged error: 8.6b

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (cbrt (/ (sin ky) (hypot (sin ky) (sin kx)))) (cbrt (/ (sin ky) (hypot (sin ky) (sin kx)))))
0.4b	(cbrt (/ (sin ky) (hypot (sin ky) (sin kx))))
0.4b	(cbrt (/ (sin ky) (hypot (sin ky) (sin kx))))
0.4b	(cbrt (/ (sin ky) (hypot (sin ky) (sin kx))))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

103×	`cbrt-prod`
81×	`add-sqr-sqrt`
69×	`times-frac`
57×	`add-cube-cbrt` `*-un-lft-identity`
16×	`swap-sqr` `associate-r` `associate-l`
11×	`pow1`
9×	`pow1/3` `unswap-sqr`
7×	`cbrt-div` `div-inv`
6×	`add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `frac-times` `pow-plus` `associate-r/` `associate-l/` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 152

Calls

4 calls:

26.0ms	(* (cbrt (/ (sin ky) (hypot (sin ky) (sin kx)))) (cbrt (/ (sin ky) (hypot (sin ky) (sin kx)))))
2.0ms	(cbrt (/ (sin ky) (hypot (sin ky) (sin kx))))
2.0ms	(cbrt (/ (sin ky) (hypot (sin ky) (sin kx))))
3.0ms	(cbrt (/ (sin ky) (hypot (sin ky) (sin kx))))

series841.0ms

Counts

4 → 12

Calls

4 calls:

224.0ms	(* (cbrt (/ (sin ky) (hypot (sin ky) (sin kx)))) (cbrt (/ (sin ky) (hypot (sin ky) (sin kx)))))
203.0ms	(cbrt (/ (sin ky) (hypot (sin ky) (sin kx))))
203.0ms	(cbrt (/ (sin ky) (hypot (sin ky) (sin kx))))
211.0ms	(cbrt (/ (sin ky) (hypot (sin ky) (sin kx))))

simplify52.0ms

Algorithm

egg-herbie

Counts

164 → 164

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	291	2447
1	993	2341
2	5001	2212

prune646.0ms

Pruning

26 alts after pruning (25 fresh and 1 done)

Merged error: 8.6b

regimes886.0ms

Accuracy

0% (0.2b remaining)

Error of 8.8b against oracle of 8.7b and baseline of 8.8b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	7
1	10	7

end0.0ms

sample3.7s

Algorithm

intervals

Results

2.0s	2698×	body	1280	valid
774.0ms	1845×	body	640	valid
362.0ms	751×	body	320	valid
222.0ms	2377×	body	80	valid
58.0ms	329×	body	160	valid