Details

sample365.0ms

Algorithm

intervals

Results

135.0ms	91×	body	1280	valid
56.0ms	24×	body	320	valid
50.0ms	58×	body	640	valid
14.0ms	71×	body	80	valid
5.0ms	12×	body	160	valid

simplify1.1s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
5	654
4	156
3	68
2	39
1	23
0	13

prune16.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 9.7b

localize26.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
0.2b	(pow (sin kx) 2.0)
0.3b	(pow (sin ky) 2.0)
2.7b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite126.0ms

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×	`associate-/r*` `add-exp-log` `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` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `div-inv`

Counts

4 → 117

Calls

4 calls:

57.0ms	(/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
6.0ms	(pow (sin kx) 2.0)
5.0ms	(pow (sin ky) 2.0)
49.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series631.0ms

Counts

4 → 12

Calls

4 calls:

191.0ms	(/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
135.0ms	(pow (sin kx) 2.0)
165.0ms	(pow (sin ky) 2.0)
140.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify921.0ms

Counts

129 → 129

Iterations

Iter	Nodes
done	5001
2	1650
1	395
0	178

prune1.0s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 6.8b

localize43.0ms

Local error

Found 3 expressions with local error:

0.1b

(hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))

0.1b

(* (/ (sin ky) (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))) (sin th))

0.1b

(/ (sin ky) (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2))))

rewrite47.0ms

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 (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))

29.0ms

(* (/ (sin ky) (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))) (sin th))

13.0ms

(/ (sin ky) (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2))))

series1.3s

Counts

3 → 9

Calls

3 calls:

298.0ms

(hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))

469.0ms

(* (/ (sin ky) (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))) (sin th))

555.0ms

(/ (sin ky) (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2))))

simplify923.0ms

Counts

82 → 82

Iterations

Iter	Nodes
done	5000
2	1352
1	314
0	135

prune688.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 6.8b

localize34.0ms

Local error

Found 4 expressions with local error:

0.1b	(hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))
0.1b	(/ (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2))) (sin ky))
0.1b	(* (/ 1 (/ (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2))) (sin ky))) (sin th))
0.2b	(/ 1 (/ (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2))) (sin ky)))

rewrite68.0ms

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 (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))
9.0ms	(/ (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2))) (sin ky))
42.0ms	(* (/ 1 (/ (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2))) (sin ky))) (sin th))
9.0ms	(/ 1 (/ (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2))) (sin ky)))

series1.8s

Counts

4 → 12

Calls

4 calls:

426.0ms	(hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))
449.0ms	(/ (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2))) (sin ky))
538.0ms	(* (/ 1 (/ (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2))) (sin ky))) (sin th))
409.0ms	(/ 1 (/ (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2))) (sin ky)))

simplify2.4s

Counts

203 → 203

Iterations

Iter	Nodes
done	5001
2	4519
1	793
0	291

prune1.5s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 6.8b

localize23.0ms

Local error

Found 3 expressions with local error:

0.1b

(hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))

0.1b

(/ (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2))) (sin ky))

0.2b

(/ (sin th) (/ (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2))) (sin ky)))

rewrite35.0ms

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 (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))

10.0ms

(/ (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2))) (sin ky))

21.0ms

(/ (sin th) (/ (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2))) (sin ky)))

series1.3s

Counts

3 → 9

Calls

3 calls:

390.0ms

(hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))

459.0ms

(/ (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2))) (sin ky))

475.0ms

(/ (sin th) (/ (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2))) (sin ky)))

simplify1.4s

Counts

120 → 120

Iterations

Iter	Nodes
done	5001
2	2466
1	496
0	206

prune992.0ms

Pruning

20 alts after pruning (19 fresh and 1 done)

Merged error: 6.8b

regimes1.6s

Accuracy

0% (0.2b remaining)

Error of 8.7b against oracle of 8.5b and baseline of 8.7b

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	14
0	14

end0.0ms

sample9.0s

Algorithm

intervals

Results

5.1s	2672×	body	1280	valid
2.2s	1912×	body	640	valid
567.0ms	761×	body	320	valid
520.0ms	2276×	body	80	valid
135.0ms	379×	body	160	valid