Details

sample317.0ms

Algorithm

intervals

Results

166.0ms	86×	body	1280	valid
55.0ms	65×	body	640	valid
14.0ms	75×	body	80	valid
13.0ms	21×	body	320	valid
4.0ms	9×	body	160	valid

simplify67.0ms

Counts: 1 → 1

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 10.7b

localize42.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
0.3b	(pow (sin kx) 2.0)
0.3b	(pow (sin ky) 2.0)
4.1b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite146.0ms

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:

64.0ms	(/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
4.0ms	(pow (sin kx) 2.0)
5.0ms	(pow (sin ky) 2.0)
67.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series618.0ms

Counts

4 → 12

Calls

4 calls:

180.0ms	(/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
142.0ms	(pow (sin kx) 2.0)
174.0ms	(pow (sin ky) 2.0)
121.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify86.0ms

Counts: 112 → 112

prune604.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 9.2b

localize52.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin ky))
0.3b	(pow (sin kx) 2)
0.3b	(pow (sin ky) 2)
4.3b	(sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))

rewrite231.0ms

Algorithm

rewrite-expression-head

Rules

54×	`*-un-lft-identity`
45×	`sqrt-prod`
41×	`add-sqr-sqrt`
34×	`times-frac`
28×	`add-cube-cbrt`
24×	`associate-l`
18×	`unpow-prod-down`
12×	`distribute-lft-out`
10×	`pow1`
8×	`add-exp-log`
6×	`pow-unpow` `add-cbrt-cube`
4×	`associate-/r/` `add-log-exp` `unswap-sqr`
3×	`rem-sqrt-square` `sqrt-pow1` `associate-r`
2×	`pow-to-exp` `pow-pow` `flip3-+` `sqrt-div` `pow-exp` `flip-+` `div-inv` `unpow2` `sqr-pow`
1×	`pow-flip` `pow1/2` `pow-prod-down` `associate-l/` `prod-exp` `-commutative` `cbrt-unprod` `inv-pow`

Counts

4 → 115

Calls

4 calls:

159.0ms	(* (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin ky))
8.0ms	(pow (sin kx) 2)
8.0ms	(pow (sin ky) 2)
46.0ms	(sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))

series441.0ms

Counts

4 → 12

Calls

4 calls:

210.0ms	(* (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin ky))
27.0ms	(pow (sin kx) 2)
36.0ms	(pow (sin ky) 2)
168.0ms	(sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))

simplify125.0ms

Counts: 127 → 127

prune703.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 9.2b

localize29.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* (sqrt 1) (sin ky)) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))
0.3b	(pow (sin kx) 2)
0.3b	(pow (sin ky) 2)
4.1b	(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))

rewrite154.0ms

Algorithm

rewrite-expression-head

Rules

25×	`*-un-lft-identity`
15×	`sqrt-prod`
14×	`add-sqr-sqrt`
13×	`add-cube-cbrt`
12×	`unpow-prod-down`
11×	`add-exp-log`
9×	`add-cbrt-cube`
8×	`times-frac` `associate-/r*`
7×	`pow1`
6×	`pow-unpow` `distribute-lft-out`
4×	`sqrt-div` `add-log-exp`
2×	`cbrt-undiv` `pow-to-exp` `pow-pow` `flip3-+` `div-exp` `pow-exp` `associate-/r/` `flip-+` `unpow2` `sqr-pow`
1×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `prod-exp` `clear-num` `cbrt-unprod` `div-inv` `associate-/l*`

Counts

4 → 86

Calls

4 calls:

85.0ms	(/ (* (sqrt 1) (sin ky)) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))
4.0ms	(pow (sin kx) 2)
4.0ms	(pow (sin ky) 2)
56.0ms	(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))

series398.0ms

Counts

4 → 12

Calls

4 calls:

207.0ms	(/ (* (sqrt 1) (sin ky)) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))
21.0ms	(pow (sin kx) 2)
34.0ms	(pow (sin ky) 2)
137.0ms	(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))

simplify50.0ms

Counts: 98 → 98

prune645.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 9.2b

localize51.0ms

Local error

Found 4 expressions with local error:

0.4b	(cbrt (/ (* (sqrt 1) (sin ky)) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
4.1b	(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
4.1b	(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
4.1b	(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))

rewrite182.0ms

Algorithm

rewrite-expression-head

Rules

26×	`*-un-lft-identity`
20×	`sqrt-prod`
14×	`cbrt-prod`
13×	`add-sqr-sqrt`
10×	`add-cube-cbrt`
8×	`unpow-prod-down` `times-frac` `sqrt-div` `distribute-lft-out`
7×	`pow1`
4×	`add-exp-log` `flip3-+` `add-cbrt-cube` `flip-+` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
2×	`associate-/r/`
1×	`cbrt-div` `pow1/3` `div-inv`

Counts

4 → 74

Calls

4 calls:

45.0ms	(cbrt (/ (* (sqrt 1) (sin ky)) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
33.0ms	(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
61.0ms	(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
36.0ms	(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))

series664.0ms

Counts

4 → 12

Calls

4 calls:

287.0ms	(cbrt (/ (* (sqrt 1) (sin ky)) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
150.0ms	(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
117.0ms	(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
109.0ms	(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))

simplify80.0ms

Counts: 86 → 86

prune657.0ms

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 9.2b

regimes1.2s

Accuracy

72.5% (0.4b remaining)

Error of 11.8b against oracle of 11.4b and baseline of 12.7b

bsearch4.0ms

simplify49.0ms

end0.0ms

sample9.5s

Algorithm

intervals

Results

5.1s	2755×	body	1280	valid
2.0s	1829×	body	640	valid
1.0s	2284×	body	80	valid
646.0ms	771×	body	320	valid
126.0ms	361×	body	160	valid