Details

sample1.2s

Algorithm

intervals

Results

401.0ms	22×	body	320	valid
347.0ms	90×	body	1280	valid
123.0ms	64×	body	640	valid
35.0ms	66×	body	80	valid
6.0ms	14×	body	160	valid

simplify12.5s

Counts

1 → 1

Iterations

Iter	Nodes
done	5034
7	4708
6	1067
5	304
4	132
3	66
2	39
1	23
0	13

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.2b

localize65.0ms

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 kx) 2.0)
0.3b	(pow (sin ky) 2.0)
3.0b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite278.0ms

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:

180.0ms	(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
7.0ms	(pow (sin kx) 2.0)
8.0ms	(pow (sin ky) 2.0)
72.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series869.0ms

Counts

4 → 12

Calls

4 calls:

312.0ms	(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
191.0ms	(pow (sin kx) 2.0)
203.0ms	(pow (sin ky) 2.0)
163.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify4.5s

Counts

130 → 130

Iterations

Iter	Nodes
done	5001
3	4158
2	1310
1	453
0	188

prune1.5s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 11.0b

localize41.0ms

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))

rewrite73.0ms

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))
18.0ms	(/ (sin ky) (hypot (sin ky) (sin kx)))
50.0ms	(* (/ (sin ky) (hypot (sin ky) (sin kx))) (sin th))

series992.0ms

Counts

3 → 9

Calls

3 calls:

214.0ms	(hypot (sin ky) (sin kx))
328.0ms	(/ (sin ky) (hypot (sin ky) (sin kx)))
450.0ms	(* (/ (sin ky) (hypot (sin ky) (sin kx))) (sin th))

simplify4.1s

Counts

82 → 82

Iterations

Iter	Nodes
done	5115
3	2826
2	968
1	301
0	130

prune971.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 11.0b

localize40.0ms

Local error

Found 3 expressions with local error:

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

rewrite72.0ms

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))
37.0ms	(* (sin ky) (/ (sin th) (hypot (sin ky) (sin kx))))
30.0ms	(/ (sin th) (hypot (sin ky) (sin kx)))

series1.0s

Counts

3 → 9

Calls

3 calls:

233.0ms	(hypot (sin ky) (sin kx))
406.0ms	(* (sin ky) (/ (sin th) (hypot (sin ky) (sin kx))))
403.0ms	(/ (sin th) (hypot (sin ky) (sin kx)))

simplify3.4s

Counts

82 → 82

Iterations

Iter	Nodes
done	5004
3	2551
2	872
1	275
0	121

prune937.0ms

Pruning

21 alts after pruning (20 fresh and 1 done)

Merged error: 11.0b

localize75.0ms

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))))

rewrite97.0ms

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:

69.0ms	(* (cbrt (/ (sin ky) (hypot (sin ky) (sin kx)))) (cbrt (/ (sin ky) (hypot (sin ky) (sin kx)))))
5.0ms	(cbrt (/ (sin ky) (hypot (sin ky) (sin kx))))
5.0ms	(cbrt (/ (sin ky) (hypot (sin ky) (sin kx))))
5.0ms	(cbrt (/ (sin ky) (hypot (sin ky) (sin kx))))

series1.8s

Counts

4 → 12

Calls

4 calls:

519.0ms	(* (cbrt (/ (sin ky) (hypot (sin ky) (sin kx)))) (cbrt (/ (sin ky) (hypot (sin ky) (sin kx)))))
419.0ms	(cbrt (/ (sin ky) (hypot (sin ky) (sin kx))))
454.0ms	(cbrt (/ (sin ky) (hypot (sin ky) (sin kx))))
437.0ms	(cbrt (/ (sin ky) (hypot (sin ky) (sin kx))))

simplify5.7s

Counts

164 → 164

Iterations

Iter	Nodes
done	5000
4	4725
3	1682
2	751
1	322
0	171

prune1.9s

Pruning

24 alts after pruning (24 fresh and 0 done)

Merged error: 11.0b

regimes2.8s

Accuracy

0% (0.5b remaining)

Error of 9.7b against oracle of 9.1b and baseline of 9.7b

bsearch0.0ms

simplify8.0ms

Iterations

Iter	Nodes
done	22
1	22
0	19

end0.0ms

sample11.9s

Algorithm

intervals

Results

6.1s	2668×	body	1280	valid
3.8s	1867×	body	640	valid
754.0ms	753×	body	320	valid
598.0ms	2370×	body	80	valid
150.0ms	342×	body	160	valid