Details

sample327.0ms

Algorithm

intervals

Results

113.0ms	84×	body	1280	valid
68.0ms	71×	body	80	valid
49.0ms	62×	body	640	valid
15.0ms	29×	body	320	valid
4.0ms	10×	body	160	valid

simplify5.2s

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	13	16
1	23	16
2	39	16
3	68	16
4	152	16
5	333	16
6	1049	16
7	4305	16
done	5001	16

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.3b

localize34.0ms

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 kx) 2.0)
0.3b	(pow (sin ky) 2.0)
2.4b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite135.0ms

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:

63.0ms	(/ (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)
58.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series697.0ms

Counts

4 → 12

Calls

4 calls:

234.0ms	(/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
163.0ms	(pow (sin kx) 2.0)
148.0ms	(pow (sin ky) 2.0)
152.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify2.0s

Counts

129 → 129

Iterations

Useful iterations: 3 (771.0ms)

Iter	Nodes	Cost
0	178	1808
1	340	1625
2	850	1557
3	2640	1556
done	5000	1556

prune585.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 9.8b

localize18.0ms

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)))

rewrite64.0ms

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))
36.0ms	(* (/ (sin ky) (hypot (sin ky) (sin kx))) (sin th))
26.0ms	(/ (sin ky) (hypot (sin ky) (sin kx)))

series741.0ms

Counts

3 → 9

Calls

3 calls:

164.0ms	(hypot (sin ky) (sin kx))
330.0ms	(* (/ (sin ky) (hypot (sin ky) (sin kx))) (sin th))
247.0ms	(/ (sin ky) (hypot (sin ky) (sin kx)))

simplify2.2s

Counts

82 → 82

Iterations

Useful iterations: 3 (893.0ms)

Iter	Nodes	Cost
0	130	1126
1	284	1106
2	790	987
3	2333	984
done	5000	984

prune530.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 9.8b

localize27.0ms

Local error

Found 3 expressions with local error:

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

rewrite67.0ms

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))
25.0ms	(/ (sin th) (hypot (sin ky) (sin kx)))
37.0ms	(* (sin ky) (/ (sin th) (hypot (sin ky) (sin kx))))

series797.0ms

Counts

3 → 9

Calls

3 calls:

178.0ms	(hypot (sin ky) (sin kx))
317.0ms	(/ (sin th) (hypot (sin ky) (sin kx)))
302.0ms	(* (sin ky) (/ (sin th) (hypot (sin ky) (sin kx))))

simplify2.3s

Counts

82 → 82

Iterations

Useful iterations: 3 (928.0ms)

Iter	Nodes	Cost
0	121	1123
1	252	1091
2	782	976
3	2471	975
done	5000	975

prune449.0ms

Pruning

20 alts after pruning (19 fresh and 1 done)

Merged error: 9.8b

localize33.0ms

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))))

rewrite55.0ms

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:

35.0ms	(* (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))))

series1.3s

Counts

4 → 12

Calls

4 calls:

348.0ms	(* (cbrt (/ (sin ky) (hypot (sin ky) (sin kx)))) (cbrt (/ (sin ky) (hypot (sin ky) (sin kx)))))
322.0ms	(cbrt (/ (sin ky) (hypot (sin ky) (sin kx))))
320.0ms	(cbrt (/ (sin ky) (hypot (sin ky) (sin kx))))
336.0ms	(cbrt (/ (sin ky) (hypot (sin ky) (sin kx))))

simplify3.8s

Counts

164 → 164

Iterations

Useful iterations: done (3.8s)

Iter	Nodes	Cost
0	171	3641
1	290	3469
2	755	3314
3	1550	3076
4	4046	3045
done	5000	2977

prune952.0ms

Pruning

21 alts after pruning (20 fresh and 1 done)

Merged error: 9.8b

regimes989.0ms

Accuracy

0% (0.2b remaining)

Error of 8.9b against oracle of 8.7b and baseline of 8.9b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	11
1	10	11
done	10	11

end0.0ms

sample8.7s

Algorithm

intervals

Results

4.8s	2639×	body	1280	valid
1.8s	1890×	body	640	valid
969.0ms	834×	body	320	valid
656.0ms	2351×	body	80	valid
94.0ms	286×	body	160	valid