Details

sample797.0ms

Algorithm

intervals

Results

443.0ms	75×	body	80	valid
136.0ms	84×	body	1280	valid
76.0ms	48×	body	640	valid
21.0ms	35×	body	320	valid
6.0ms	14×	body	160	valid

simplify4.9s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
7	4952
6	1182
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: 10.6b

localize60.0ms

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))
0.2b	(pow (sin kx) 2.0)
0.2b	(pow (sin ky) 2.0)
3.0b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite165.0ms

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:

83.0ms	(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
6.0ms	(pow (sin kx) 2.0)
6.0ms	(pow (sin ky) 2.0)
65.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series678.0ms

Counts

4 → 12

Calls

4 calls:

236.0ms	(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
143.0ms	(pow (sin kx) 2.0)
176.0ms	(pow (sin ky) 2.0)
122.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify3.3s

Counts

130 → 130

Iterations

Iter	Nodes
done	5000
3	4224
2	1321
1	456
0	189

prune1.1s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 7.4b

localize29.0ms

Local error

Found 3 expressions with local error:

0.0b	(hypot (sin ky) (sin kx))
0.1b	(/ (sin ky) (hypot (sin ky) (sin kx)))
0.2b	(* (/ (sin ky) (hypot (sin ky) (sin kx))) (sin th))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
19×	`*-un-lft-identity` `times-frac` `add-cube-cbrt`
13×	`associate-l`
10×	`add-cbrt-cube` `add-exp-log`
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` `clear-num` `frac-2neg` `pow-prod-down` `associate-l/` `-commutative`

Counts

3 → 73

Calls

3 calls:

0.0ms	(hypot (sin ky) (sin kx))
9.0ms	(/ (sin ky) (hypot (sin ky) (sin kx)))
19.0ms	(* (/ (sin ky) (hypot (sin ky) (sin kx))) (sin th))

series807.0ms

Counts

3 → 9

Calls

3 calls:

169.0ms	(hypot (sin ky) (sin kx))
268.0ms	(/ (sin ky) (hypot (sin ky) (sin kx)))
371.0ms	(* (/ (sin ky) (hypot (sin ky) (sin kx))) (sin th))

simplify2.1s

Counts

82 → 82

Iterations

Iter	Nodes
done	5007
3	2899
2	970
1	304
0	132

prune686.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 7.4b

localize32.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot (sin ky) (sin kx))
0.1b	(/ (hypot (sin ky) (sin kx)) (sin ky))
0.2b	(* (/ 1 (/ (hypot (sin ky) (sin kx)) (sin ky))) (sin th))
0.2b	(/ 1 (/ (hypot (sin ky) (sin kx)) (sin ky)))

rewrite108.0ms

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×	`clear-num` `frac-2neg` `associate-/r/`
1×	`hypot-udef` `pow-prod-down` `associate-l/` `-commutative` `pow-flip` `inv-pow`

Counts

4 → 191

Calls

4 calls:

0.0ms	(hypot (sin ky) (sin kx))
9.0ms	(/ (hypot (sin ky) (sin kx)) (sin ky))
62.0ms	(* (/ 1 (/ (hypot (sin ky) (sin kx)) (sin ky))) (sin th))
23.0ms	(/ 1 (/ (hypot (sin ky) (sin kx)) (sin ky)))

series1.0s

Counts

4 → 12

Calls

4 calls:

187.0ms	(hypot (sin ky) (sin kx))
226.0ms	(/ (hypot (sin ky) (sin kx)) (sin ky))
374.0ms	(* (/ 1 (/ (hypot (sin ky) (sin kx)) (sin ky))) (sin th))
240.0ms	(/ 1 (/ (hypot (sin ky) (sin kx)) (sin ky)))

simplify2.4s

Counts

203 → 203

Iterations

Iter	Nodes
done	5000
2	2010
1	723
0	275

prune1.5s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 7.4b

localize19.0ms

Local error

Found 3 expressions with local error:

0.0b	(hypot (sin ky) (sin kx))
0.1b	(/ (hypot (sin ky) (sin kx)) (sin ky))
0.2b	(/ (sin th) (/ (hypot (sin ky) (sin kx)) (sin ky)))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

84×	`times-frac`
53×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
16×	`associate-/r*`
10×	`add-cbrt-cube` `add-exp-log`
6×	`div-inv` `associate-/l*`
4×	`cbrt-undiv` `div-exp`
3×	`expm1-log1p-u` `pow1` `log1p-expm1-u` `add-log-exp`
2×	`clear-num` `frac-2neg`
1×	`hypot-udef` `associate-/r/`

Counts

3 → 111

Calls

3 calls:

0.0ms	(hypot (sin ky) (sin kx))
5.0ms	(/ (hypot (sin ky) (sin kx)) (sin ky))
16.0ms	(/ (sin th) (/ (hypot (sin ky) (sin kx)) (sin ky)))

series778.0ms

Counts

3 → 9

Calls

3 calls:

166.0ms	(hypot (sin ky) (sin kx))
201.0ms	(/ (hypot (sin ky) (sin kx)) (sin ky))
410.0ms	(/ (sin th) (/ (hypot (sin ky) (sin kx)) (sin ky)))

simplify1.7s

Counts

120 → 120

Iterations

Iter	Nodes
done	5001
2	1451
1	480
0	200

prune938.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 7.4b

regimes1.5s

Accuracy

0% (0.2b remaining)

Error of 9.3b against oracle of 9.2b and baseline of 9.3b

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	13
1	13
0	11

end0.0ms

sample9.3s

Algorithm

intervals

Results

6.0s	2684×	body	1280	valid
1.7s	1806×	body	640	valid
597.0ms	2364×	body	80	valid
460.0ms	788×	body	320	valid
123.0ms	358×	body	160	valid