Details

sample434.0ms

Algorithm

intervals

Results

126.0ms	79×	body	1280	valid
122.0ms	62×	body	640	valid
18.0ms	27×	body	320	valid
16.0ms	82×	body	80	valid
2.0ms	6×	body	160	valid

simplify1.2s

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	13	16
1	23	16
2	39	16
3	68	16
4	156	16
5	653	16
done	5000	16

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.6b

localize32.0ms

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 ky) 2.0)
0.3b	(pow (sin kx) 2.0)
3.7b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite277.0ms

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:

176.0ms	(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
7.0ms	(pow (sin ky) 2.0)
8.0ms	(pow (sin kx) 2.0)
74.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series625.0ms

Counts

4 → 12

Calls

4 calls:

255.0ms	(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
111.0ms	(pow (sin ky) 2.0)
138.0ms	(pow (sin kx) 2.0)
120.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify1.3s

Counts

130 → 130

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	188	1736
1	462	1637
2	1906	1529
done	5001	1528

prune1.0s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 10.7b

localize26.0ms

Local error

Found 3 expressions with local error:

0.0b	(hypot (sin kx) (sin ky))
0.2b	(/ (sin ky) (hypot (sin kx) (sin ky)))
0.2b	(* (/ (sin ky) (hypot (sin kx) (sin ky))) (sin th))

rewrite67.0ms

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 kx) (sin ky))
24.0ms	(/ (sin ky) (hypot (sin kx) (sin ky)))
40.0ms	(* (/ (sin ky) (hypot (sin kx) (sin ky))) (sin th))

series752.0ms

Counts

3 → 9

Calls

3 calls:

193.0ms	(hypot (sin kx) (sin ky))
245.0ms	(/ (sin ky) (hypot (sin kx) (sin ky)))
314.0ms	(* (/ (sin ky) (hypot (sin kx) (sin ky))) (sin th))

simplify1.1s

Counts

82 → 82

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	130	1126
1	301	1107
2	1346	995
done	5000	984

prune680.0ms

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 10.7b

localize49.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot (sin kx) (sin ky))
0.2b	(/ (hypot (sin kx) (sin ky)) (sin ky))
0.2b	(/ 1 (/ (hypot (sin kx) (sin ky)) (sin ky)))
0.2b	(* (/ 1 (/ (hypot (sin kx) (sin ky)) (sin ky))) (sin th))

rewrite109.0ms

Algorithm

rewrite-expression-head

Rules

156×	`times-frac`
104×	`add-sqr-sqrt`
92×	`*-un-lft-identity`
90×	`add-cube-cbrt`
44×	`associate-l`
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-r` `cbrt-unprod`
2×	`frac-2neg` `clear-num` `associate-/r/`
1×	`hypot-udef` `pow-flip` `pow-prod-down` `associate-l/` `-commutative` `inv-pow`

Counts

4 → 191

Calls

4 calls:

1.0ms	(hypot (sin kx) (sin ky))
11.0ms	(/ (hypot (sin kx) (sin ky)) (sin ky))
11.0ms	(/ 1 (/ (hypot (sin kx) (sin ky)) (sin ky)))
66.0ms	(* (/ 1 (/ (hypot (sin kx) (sin ky)) (sin ky))) (sin th))

series1.0s

Counts

4 → 12

Calls

4 calls:

179.0ms	(hypot (sin kx) (sin ky))
298.0ms	(/ (hypot (sin kx) (sin ky)) (sin ky))
227.0ms	(/ 1 (/ (hypot (sin kx) (sin ky)) (sin ky)))
313.0ms	(* (/ 1 (/ (hypot (sin kx) (sin ky)) (sin ky))) (sin th))

simplify3.5s

Counts

203 → 203

Iterations

Useful iterations: done (3.5s)

Iter	Nodes	Cost
0	255	3365
1	682	3081
2	4662	2733
done	5000	2732

prune1.0s

Pruning

17 alts after pruning (15 fresh and 2 done)

Merged error: 10.7b

localize28.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (cbrt (/ (sin ky) (hypot (sin kx) (sin ky)))) (cbrt (/ (sin ky) (hypot (sin kx) (sin ky)))))
0.5b	(cbrt (/ (sin ky) (hypot (sin kx) (sin ky))))
0.5b	(cbrt (/ (sin ky) (hypot (sin kx) (sin ky))))
0.5b	(cbrt (/ (sin ky) (hypot (sin kx) (sin ky))))

rewrite77.0ms

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:

46.0ms	(* (cbrt (/ (sin ky) (hypot (sin kx) (sin ky)))) (cbrt (/ (sin ky) (hypot (sin kx) (sin ky)))))
5.0ms	(cbrt (/ (sin ky) (hypot (sin kx) (sin ky))))
5.0ms	(cbrt (/ (sin ky) (hypot (sin kx) (sin ky))))
15.0ms	(cbrt (/ (sin ky) (hypot (sin kx) (sin ky))))

series1.4s

Counts

4 → 12

Calls

4 calls:

348.0ms	(* (cbrt (/ (sin ky) (hypot (sin kx) (sin ky)))) (cbrt (/ (sin ky) (hypot (sin kx) (sin ky)))))
363.0ms	(cbrt (/ (sin ky) (hypot (sin kx) (sin ky))))
324.0ms	(cbrt (/ (sin ky) (hypot (sin kx) (sin ky))))
323.0ms	(cbrt (/ (sin ky) (hypot (sin kx) (sin ky))))

simplify1.6s

Counts

164 → 164

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	171	3641
1	326	3469
2	1372	3316
done	5000	3137

prune1.6s

Pruning

27 alts after pruning (25 fresh and 2 done)

Merged error: 10.7b

regimes1.9s

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

sample9.1s

Algorithm

intervals

Results

4.7s	2726×	body	1280	valid
2.4s	1825×	body	640	valid
565.0ms	750×	body	320	valid
483.0ms	2382×	body	80	valid
480.0ms	317×	body	160	valid