Details

sample359.0ms

Algorithm

intervals

Results

191.0ms	88×	body	1280	valid
44.0ms	54×	body	640	valid
16.0ms	23×	body	320	valid
14.0ms	80×	body	80	valid
5.0ms	11×	body	160	valid

simplify10.8s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
7	4952
6	1182
5	304
4	132
3	66
2	39
1	23
0	13

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.5b

localize53.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
0.2b	(pow (sin ky) 2.0)
0.2b	(pow (sin kx) 2.0)
3.6b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite298.0ms

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` `insert-posit16` `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 → 122

Calls

4 calls:

174.0ms	(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
11.0ms	(pow (sin ky) 2.0)
11.0ms	(pow (sin kx) 2.0)
93.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series1.2s

Counts

4 → 12

Calls

4 calls:

480.0ms	(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
255.0ms	(pow (sin ky) 2.0)
213.0ms	(pow (sin kx) 2.0)
260.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify6.3s

Counts

134 → 134

Iterations

Iter	Nodes
done	5199
3	3789
2	1290
1	459
0	193

prune1.9s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 7.7b

localize58.0ms

Local error

Found 3 expressions with local error:

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

rewrite91.0ms

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` `insert-posit16` `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 → 76

Calls

3 calls:

2.0ms	(hypot (sin ky) (sin kx))
23.0ms	(/ (sin ky) (hypot (sin ky) (sin kx)))
58.0ms	(* (/ (sin ky) (hypot (sin ky) (sin kx))) (sin th))

series1.4s

Counts

3 → 9

Calls

3 calls:

306.0ms	(hypot (sin ky) (sin kx))
453.0ms	(/ (sin ky) (hypot (sin ky) (sin kx)))
616.0ms	(* (/ (sin ky) (hypot (sin ky) (sin kx))) (sin th))

simplify4.9s

Counts

85 → 85

Iterations

Iter	Nodes
done	5004
3	2674
2	948
1	307
0	135

prune1.4s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 7.7b

localize42.0ms

Local error

Found 4 expressions with local error:

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

rewrite123.0ms

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` `insert-posit16` `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 → 195

Calls

4 calls:

1.0ms	(hypot (sin ky) (sin kx))
8.0ms	(/ (hypot (sin ky) (sin kx)) (sin ky))
82.0ms	(* (/ 1 (/ (hypot (sin ky) (sin kx)) (sin ky))) (sin th))
14.0ms	(/ 1 (/ (hypot (sin ky) (sin kx)) (sin ky)))

series1.8s

Counts

4 → 12

Calls

4 calls:

298.0ms	(hypot (sin ky) (sin kx))
369.0ms	(/ (hypot (sin ky) (sin kx)) (sin ky))
700.0ms	(* (/ 1 (/ (hypot (sin ky) (sin kx)) (sin ky))) (sin th))
460.0ms	(/ 1 (/ (hypot (sin ky) (sin kx)) (sin ky)))

simplify4.7s

Counts

207 → 207

Iterations

Iter	Nodes
done	5000
2	2056
1	725
0	279

prune2.7s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 7.7b

localize45.0ms

Local error

Found 3 expressions with local error:

0.0b	(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))))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
19×	`*-un-lft-identity` `times-frac` `add-cube-cbrt`
13×	`associate-r`
10×	`add-cbrt-cube` `add-exp-log`
5×	`pow1`
3×	`expm1-log1p-u` `associate-/r` `associate-l` `insert-posit16` `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-r/` `-commutative`

Counts

3 → 76

Calls

3 calls:

1.0ms	(hypot (sin ky) (sin kx))
12.0ms	(/ (sin th) (hypot (sin ky) (sin kx)))
31.0ms	(* (sin ky) (/ (sin th) (hypot (sin ky) (sin kx))))

series1.5s

Counts

3 → 9

Calls

3 calls:

309.0ms	(hypot (sin ky) (sin kx))
667.0ms	(/ (sin th) (hypot (sin ky) (sin kx)))
562.0ms	(* (sin ky) (/ (sin th) (hypot (sin ky) (sin kx))))

simplify4.9s

Counts

85 → 85

Iterations

Iter	Nodes
done	5000
3	2583
2	884
1	281
0	125

prune1.0s

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 7.7b

regimes3.1s

Accuracy

0% (0.2b remaining)

Error of 8.9b against oracle of 8.7b and baseline of 8.9b

bsearch0.0ms

simplify6.0ms

Iterations

Iter	Nodes
done	10
1	10
0	9

end0.0ms

sample8.8s

Algorithm

intervals

Results

4.8s	2716×	body	1280	valid
1.9s	1885×	body	640	valid
910.0ms	2301×	body	80	valid
588.0ms	751×	body	320	valid
132.0ms	347×	body	160	valid