Details

sample339.0ms

Algorithm

intervals

Results

112.0ms	88×	body	1280	valid
105.0ms	59×	body	640	valid
19.0ms	33×	body	320	valid
12.0ms	68×	body	80	valid
3.0ms	8×	body	160	valid

simplify4.9s

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

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 9.7b

localize45.0ms

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)
2.5b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite140.0ms

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:

53.0ms	(/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
11.0ms	(pow (sin kx) 2.0)
4.0ms	(pow (sin ky) 2.0)
63.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series732.0ms

Counts

4 → 12

Calls

4 calls:

232.0ms	(/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
184.0ms	(pow (sin kx) 2.0)
146.0ms	(pow (sin ky) 2.0)
170.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify2.1s

Counts

129 → 129

Iterations

Useful iterations: 3 (784.0ms)

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

prune697.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 7.0b

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

rewrite50.0ms

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:

1.0ms	(hypot (sin ky) (sin kx))
36.0ms	(* (/ (sin ky) (hypot (sin ky) (sin kx))) (sin th))
9.0ms	(/ (sin ky) (hypot (sin ky) (sin kx)))

series823.0ms

Counts

3 → 9

Calls

3 calls:

216.0ms	(hypot (sin ky) (sin kx))
340.0ms	(* (/ (sin ky) (hypot (sin ky) (sin kx))) (sin th))
267.0ms	(/ (sin ky) (hypot (sin ky) (sin kx)))

simplify2.0s

Counts

82 → 82

Iterations

Useful iterations: 3 (779.0ms)

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

prune456.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 6.9b

localize26.0ms

Local error

Found 3 expressions with local error:

0.1b	(hypot (sin ky) (sin kx))
0.2b	(/ (sin th) (hypot (sin ky) (sin kx)))
0.3b	(* (sin ky) (/ (sin th) (hypot (sin ky) (sin kx))))

rewrite62.0ms

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))
17.0ms	(/ (sin th) (hypot (sin ky) (sin kx)))
40.0ms	(* (sin ky) (/ (sin th) (hypot (sin ky) (sin kx))))

series819.0ms

Counts

3 → 9

Calls

3 calls:

168.0ms	(hypot (sin ky) (sin kx))
311.0ms	(/ (sin th) (hypot (sin ky) (sin kx)))
340.0ms	(* (sin ky) (/ (sin th) (hypot (sin ky) (sin kx))))

simplify2.4s

Counts

82 → 82

Iterations

Useful iterations: 3 (870.0ms)

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

prune852.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 6.9b

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b	(hypot (sin ky) (sin kx))
0.2b	(/ (hypot (sin ky) (sin kx)) (sin th))
0.3b	(/ 1 (/ (hypot (sin ky) (sin kx)) (sin th)))
0.3b	(* (sin ky) (/ 1 (/ (hypot (sin ky) (sin kx)) (sin th))))

rewrite138.0ms

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:

1.0ms	(hypot (sin ky) (sin kx))
12.0ms	(/ (hypot (sin ky) (sin kx)) (sin th))
23.0ms	(/ 1 (/ (hypot (sin ky) (sin kx)) (sin th)))
84.0ms	(* (sin ky) (/ 1 (/ (hypot (sin ky) (sin kx)) (sin th))))

series1.2s

Counts

4 → 12

Calls

4 calls:

174.0ms	(hypot (sin ky) (sin kx))
292.0ms	(/ (hypot (sin ky) (sin kx)) (sin th))
323.0ms	(/ 1 (/ (hypot (sin ky) (sin kx)) (sin th)))
395.0ms	(* (sin ky) (/ 1 (/ (hypot (sin ky) (sin kx)) (sin th))))

simplify3.4s

Counts

204 → 204

Iterations

Useful iterations: done (3.4s)

Iter	Nodes	Cost
0	267	3490
1	594	3012
2	1339	2664
3	4099	2644
done	5000	2628

prune731.0ms

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 6.9b

regimes951.0ms

Accuracy

0% (0.1b remaining)

Error of 8.6b against oracle of 8.5b and baseline of 8.6b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

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

end0.0ms

sample9.2s

Algorithm

intervals

Results

5.6s	2737×	body	1280	valid
1.8s	1809×	body	640	valid
581.0ms	2326×	body	80	valid
579.0ms	776×	body	320	valid
125.0ms	352×	body	160	valid