Details

sample121.0ms

Algorithm

intervals

Results

69.0ms	90×	body	1280	valid
25.0ms	66×	body	640	valid
7.0ms	25×	body	320	valid
5.0ms	62×	body	80	valid
2.0ms	13×	body	160	valid

simplify2.9s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	13	16
1	23	16
2	38	16
3	67	16
4	134	16
5	308	16
6	1011	16
7	3997	16
done	5000	16

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.7b

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))))
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)))

rewrite46.0ms

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:

23.0ms	(/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
1.0ms	(pow (sin kx) 2.0)
1.0ms	(pow (sin ky) 2.0)
17.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series398.0ms

Counts

4 → 12

Calls

4 calls:

126.0ms	(/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
99.0ms	(pow (sin kx) 2.0)
99.0ms	(pow (sin ky) 2.0)
74.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify2.1s

Counts

129 → 129

Iterations

Useful iterations: 3 (739.0ms)

Iter	Nodes	Cost
0	178	1808
1	342	1619
2	987	1557
3	4643	1556
done	5000	1556

prune452.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 7.3b

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

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))
9.0ms	(* (/ (sin ky) (hypot (sin ky) (sin kx))) (sin th))
3.0ms	(/ (sin ky) (hypot (sin ky) (sin kx)))

series485.0ms

Counts

3 → 9

Calls

3 calls:

110.0ms	(hypot (sin ky) (sin kx))
213.0ms	(* (/ (sin ky) (hypot (sin ky) (sin kx))) (sin th))
162.0ms	(/ (sin ky) (hypot (sin ky) (sin kx)))

simplify1.8s

Counts

82 → 82

Iterations

Useful iterations: 3 (689.0ms)

Iter	Nodes	Cost
0	130	1126
1	287	1106
2	828	987
3	3860	984
done	5000	984

prune292.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 7.3b

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))))

rewrite14.0ms

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))
3.0ms	(/ (sin th) (hypot (sin ky) (sin kx)))
9.0ms	(* (sin ky) (/ (sin th) (hypot (sin ky) (sin kx))))

series503.0ms

Counts

3 → 9

Calls

3 calls:

108.0ms	(hypot (sin ky) (sin kx))
185.0ms	(/ (sin th) (hypot (sin ky) (sin kx)))
209.0ms	(* (sin ky) (/ (sin th) (hypot (sin ky) (sin kx))))

simplify2.0s

Counts

82 → 82

Iterations

Useful iterations: 3 (637.0ms)

Iter	Nodes	Cost
0	121	1123
1	258	1091
2	830	976
3	4429	975
done	5000	975

prune291.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 7.3b

localize15.0ms

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

rewrite32.0ms

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:

20.0ms	(* (cbrt (/ (sin ky) (hypot (sin ky) (sin kx)))) (cbrt (/ (sin ky) (hypot (sin ky) (sin kx)))))
1.0ms	(cbrt (/ (sin ky) (hypot (sin ky) (sin kx))))
1.0ms	(cbrt (/ (sin ky) (hypot (sin ky) (sin kx))))
2.0ms	(cbrt (/ (sin ky) (hypot (sin ky) (sin kx))))

series854.0ms

Counts

4 → 12

Calls

4 calls:

226.0ms	(* (cbrt (/ (sin ky) (hypot (sin ky) (sin kx)))) (cbrt (/ (sin ky) (hypot (sin ky) (sin kx)))))
211.0ms	(cbrt (/ (sin ky) (hypot (sin ky) (sin kx))))
208.0ms	(cbrt (/ (sin ky) (hypot (sin ky) (sin kx))))
208.0ms	(cbrt (/ (sin ky) (hypot (sin ky) (sin kx))))

simplify2.2s

Counts

164 → 164

Iterations

Useful iterations: 3 (798.0ms)

Iter	Nodes	Cost
0	171	3641
1	291	3469
2	874	3314
3	3956	3076
done	5001	3076

prune628.0ms

Pruning

19 alts after pruning (18 fresh and 1 done)

Merged error: 7.3b

regimes643.0ms

Accuracy

0% (0.2b remaining)

Error of 8.6b against oracle of 8.4b and baseline of 8.6b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

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

end0.0ms

sample3.6s

Algorithm

intervals

Results

2.1s	2763×	body	1280	valid
786.0ms	1892×	body	640	valid
214.0ms	2267×	body	80	valid
206.0ms	757×	body	320	valid
59.0ms	321×	body	160	valid