Details

sample358.0ms

Algorithm

intervals

Results

133.0ms	91×	body	1280	valid
90.0ms	58×	body	640	valid
20.0ms	28×	body	320	valid
12.0ms	64×	body	80	valid
6.0ms	15×	body	160	valid

simplify12.3s

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	13	16
1	28	16
2	71	16
3	250	16
done	5000	16

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 9.8b

localize41.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (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)
2.5b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite170.0ms

Algorithm

rewrite-expression-head

Rules

46×	`*-un-lft-identity`
27×	`add-sqr-sqrt`
26×	`add-cube-cbrt`
25×	`sqrt-prod`
24×	`times-frac`
16×	`unpow-prod-down`
10×	`distribute-lft-out`
8×	`add-exp-log` `associate-/r*`
7×	`pow1`
6×	`pow-unpow` `add-cbrt-cube`
4×	`sqrt-div` `add-log-exp`
3×	`associate-/l*`
2×	`pow-to-exp` `pow-pow` `flip3-+` `pow-exp` `associate-/r/` `flip-+` `sqr-pow`
1×	`cbrt-undiv` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `clear-num` `div-inv`

Counts

4 → 100

Calls

4 calls:

86.0ms	(/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
7.0ms	(pow (sin kx) 2.0)
8.0ms	(pow (sin ky) 2.0)
60.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series713.0ms

Counts

4 → 12

Calls

4 calls:

229.0ms	(/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
164.0ms	(pow (sin kx) 2.0)
148.0ms	(pow (sin ky) 2.0)
170.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify5.2s

Counts

112 → 112

Iterations

Useful iterations: done (5.2s)

Iter	Nodes	Cost
0	170	1738
1	1193	1550
done	5000	1503

prune616.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 9.2b

localize21.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))
0.3b	(* (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin ky))
0.3b	(pow (sin ky) 2)
2.5b	(sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))

rewrite264.0ms

Algorithm

rewrite-expression-head

Rules

78×	`*-un-lft-identity`
49×	`add-sqr-sqrt` `times-frac`
45×	`sqrt-prod`
36×	`add-cube-cbrt`
24×	`associate-l`
23×	`unpow-prod-down`
20×	`distribute-lft-out`
11×	`add-exp-log`
10×	`pow1`
8×	`add-cbrt-cube`
6×	`associate-/r/`
5×	`associate-/r*`
4×	`add-log-exp` `unswap-sqr`
3×	`rem-sqrt-square` `pow-unpow` `sqrt-pow1` `flip3-+` `associate-r` `flip-+` `div-inv` `associate-/l*`
2×	`pow-flip` `sqrt-div` `div-exp` `inv-pow`
1×	`cbrt-undiv` `pow-to-exp` `rec-exp` `pow-pow` `frac-2neg` `pow1/2` `1-exp` `pow-prod-down` `associate-l/` `pow-exp` `prod-exp` `clear-num` `-commutative` `cbrt-unprod` `unpow2` `sqr-pow`

Counts

4 → 138

Calls

4 calls:

65.0ms	(/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))
118.0ms	(* (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin ky))
4.0ms	(pow (sin ky) 2)
69.0ms	(sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))

series466.0ms

Counts

4 → 12

Calls

4 calls:

125.0ms	(/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))
162.0ms	(* (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin ky))
33.0ms	(pow (sin ky) 2)
146.0ms	(sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))

simplify1.8s

Counts

150 → 150

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	191	2472
done	5001	2214

prune774.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 9.2b

localize38.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ 1 (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))) (/ (sin ky) (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
0.4b	(/ (sin ky) (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
2.5b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
2.5b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite417.0ms

Algorithm

rewrite-expression-head

Rules

185×	`sqrt-prod`
163×	`add-sqr-sqrt`
144×	`times-frac`
132×	`*-un-lft-identity`
72×	`add-cube-cbrt`
39×	`associate-r` `associate-l`
28×	`add-exp-log` `unswap-sqr`
24×	`unpow-prod-down` `distribute-lft-out`
18×	`add-cbrt-cube`
16×	`sqrt-div`
11×	`associate-/r*`
9×	`div-exp`
8×	`pow1` `prod-exp`
6×	`associate-/r/`
5×	`cbrt-undiv` `flip3-+` `flip-+`
4×	`cbrt-unprod` `add-log-exp`
3×	`div-inv` `associate-/l*`
2×	`rem-sqrt-square` `rec-exp` `sqrt-pow1` `pow1/2` `1-exp`
1×	`frac-times` `frac-2neg` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `*-commutative`

Counts

4 → 225

Calls

4 calls:

253.0ms	(* (/ 1 (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))) (/ (sin ky) (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
63.0ms	(/ (sin ky) (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
41.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
31.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series653.0ms

Counts

4 → 12

Calls

4 calls:

183.0ms	(* (/ 1 (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))) (/ (sin ky) (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
249.0ms	(/ (sin ky) (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
107.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
114.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify708.0ms

Counts

237 → 237

Iterations

Useful iterations: done (695.0ms)

Iter	Nodes	Cost
0	259	7250
done	5001	6290

prune1.3s

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 9.2b

localize24.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))
0.3b	(* (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin ky))
0.3b	(pow (sin ky) 2)
2.5b	(sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))

rewrite214.0ms

Algorithm

rewrite-expression-head

Rules

78×	`*-un-lft-identity`
49×	`add-sqr-sqrt` `times-frac`
45×	`sqrt-prod`
36×	`add-cube-cbrt`
24×	`associate-l`
23×	`unpow-prod-down`
20×	`distribute-lft-out`
11×	`add-exp-log`
10×	`pow1`
8×	`add-cbrt-cube`
6×	`associate-/r/`
5×	`associate-/r*`
4×	`add-log-exp` `unswap-sqr`
3×	`rem-sqrt-square` `pow-unpow` `sqrt-pow1` `flip3-+` `associate-r` `flip-+` `div-inv` `associate-/l*`
2×	`pow-flip` `sqrt-div` `div-exp` `inv-pow`
1×	`cbrt-undiv` `pow-to-exp` `rec-exp` `pow-pow` `frac-2neg` `pow1/2` `1-exp` `pow-prod-down` `associate-l/` `pow-exp` `prod-exp` `clear-num` `-commutative` `cbrt-unprod` `unpow2` `sqr-pow`

Counts

4 → 138

Calls

4 calls:

37.0ms	(/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))
126.0ms	(* (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin ky))
4.0ms	(pow (sin ky) 2)
41.0ms	(sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))

series528.0ms

Counts

4 → 12

Calls

4 calls:

151.0ms	(/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))
190.0ms	(* (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin ky))
34.0ms	(pow (sin ky) 2)
153.0ms	(sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))

simplify1.8s

Counts

150 → 150

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	191	2472
done	5001	2214

prune734.0ms

Pruning

19 alts after pruning (18 fresh and 1 done)

Merged error: 9.2b

regimes1.4s

Accuracy

0% (1.4b remaining)

Error of 12.5b against oracle of 11.1b and baseline of 12.5b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	15	18
1	20	18
done	20	18

end0.0ms

sample8.8s

Algorithm

intervals

Results

4.6s	2751×	body	1280	valid
2.0s	1789×	body	640	valid
1.1s	2310×	body	80	valid
479.0ms	806×	body	320	valid
111.0ms	344×	body	160	valid