Details

sample646.0ms

Algorithm

intervals

Results

292.0ms	88×	body	1280	valid
93.0ms	59×	body	640	valid
80.0ms	8×	body	160	valid
25.0ms	33×	body	320	valid
17.0ms	68×	body	80	valid

simplify1.1s

Counts: 1 → 1

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 9.7b

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))))
0.3b	(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:

74.0ms	(/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
8.0ms	(pow (sin kx) 2.0)
8.0ms	(pow (sin ky) 2.0)
64.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series614.0ms

Counts

4 → 12

Calls

4 calls:

206.0ms	(/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
168.0ms	(pow (sin kx) 2.0)
122.0ms	(pow (sin ky) 2.0)
118.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify1.9s

Counts: 112 → 112

prune645.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 9.1b

localize42.0ms

Local error

Found 4 expressions with local error:

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

rewrite187.0ms

Algorithm

rewrite-expression-head

Rules

180×	`times-frac`
150×	`*-un-lft-identity`
99×	`add-sqr-sqrt`
98×	`add-cube-cbrt`
65×	`sqrt-prod`
32×	`unpow-prod-down`
28×	`associate-/r*`
26×	`distribute-lft-out`
17×	`add-exp-log`
9×	`add-cbrt-cube`
8×	`pow1`
7×	`div-exp`
6×	`pow-unpow`
5×	`div-inv`
4×	`add-log-exp`
3×	`cbrt-undiv` `associate-/l*`
2×	`pow-to-exp` `rec-exp` `pow-pow` `sqrt-div` `1-exp` `pow-exp` `sqr-pow`
1×	`rem-sqrt-square` `pow-flip` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `clear-num` `associate-/r/` `flip-+` `inv-pow`

Counts

4 → 187

Calls

4 calls:

7.0ms	(pow (sin kx) 2.0)
85.0ms	(/ 1 (/ (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))) (sin ky)))
7.0ms	(pow (sin ky) 2.0)
64.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series627.0ms

Counts

4 → 12

Calls

4 calls:

167.0ms	(pow (sin kx) 2.0)
185.0ms	(/ 1 (/ (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))) (sin ky)))
129.0ms	(pow (sin ky) 2.0)
147.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify1.2s

Counts: 199 → 199

prune828.0ms

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 9.1b

localize22.0ms

Local error

Found 4 expressions with local error:

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

rewrite232.0ms

Algorithm

rewrite-expression-head

Rules

1005×	`times-frac`
608×	`*-un-lft-identity`
437×	`add-sqr-sqrt`
436×	`add-cube-cbrt`
215×	`sqrt-prod`
92×	`unpow-prod-down`
86×	`distribute-lft-out`
46×	`add-exp-log` `div-inv`
32×	`div-exp`
30×	`sqrt-div` `associate-/l*`
29×	`associate-/r/`
16×	`add-cbrt-cube`
15×	`flip3-+` `flip-+`
13×	`associate-/r*`
8×	`cbrt-undiv` `rec-exp` `1-exp`
7×	`pow1`
6×	`pow-unpow`
4×	`add-log-exp`
2×	`pow-to-exp` `pow-pow` `pow-exp` `sqr-pow`
1×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `associate-/l/`

Counts

4 → 516

Calls

4 calls:

97.0ms	(/ (/ 1 (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (/ 1 (sin ky)))
4.0ms	(pow (sin kx) 2.0)
4.0ms	(pow (sin ky) 2.0)
58.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series636.0ms

Counts

4 → 12

Calls

4 calls:

190.0ms	(/ (/ 1 (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (/ 1 (sin ky)))
173.0ms	(pow (sin kx) 2.0)
129.0ms	(pow (sin ky) 2.0)
144.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify1.2s

Counts: 528 → 528

prune2.5s

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 9.1b

localize69.0ms

Local error

Found 4 expressions with local error:

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

rewrite3.9s

Algorithm

rewrite-expression-head

Rules

44158×	`times-frac`
18865×	`*-un-lft-identity`
14182×	`add-sqr-sqrt`
14181×	`add-cube-cbrt`
10811×	`sqrt-prod`
4680×	`cbrt-prod`
4472×	`unpow-prod-down`
2342×	`distribute-lft-out`
1729×	`div-inv`
710×	`sqr-pow`
707×	`associate-/r*`
406×	`associate-/r/`
392×	`sqrt-div`
196×	`flip3-+` `flip-+`
129×	`add-exp-log`
93×	`div-exp`
57×	`add-cbrt-cube`
49×	`cbrt-undiv`
14×	`associate-/l*`
9×	`prod-exp`
7×	`pow1`
6×	`rec-exp` `pow-unpow` `1-exp`
5×	`cbrt-unprod`
4×	`add-log-exp`
2×	`pow-to-exp` `pow-pow` `pow-exp`
1×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `associate-/l/`

Counts

4 → 10724

Calls

4 calls:

7.0ms	(pow (sin kx) 2.0)
603.0ms	(/ (/ (* (cbrt 1) (cbrt 1)) (sqrt (pow 1 2.0))) (/ (/ 1 (sin ky)) (/ (cbrt 1) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
4.0ms	(pow (sin ky) 2.0)
31.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series661.0ms

Counts

4 → 12

Calls

4 calls:

182.0ms	(pow (sin kx) 2.0)
207.0ms	(/ (/ (* (cbrt 1) (cbrt 1)) (sqrt (pow 1 2.0))) (/ (/ 1 (sin ky)) (/ (cbrt 1) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
135.0ms	(pow (sin ky) 2.0)
137.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify15.5s

Counts: 10736 → 10736

prune1.4m

Pruning

23 alts after pruning (23 fresh and 0 done)

Merged error: 9.1b

regimes1.6s

Accuracy

-10.1% (1.5b remaining)

Error of 12.4b against oracle of 10.9b and baseline of 12.2b

bsearch0.0ms

simplify666.0ms

end0.0ms

sample7.8s

Algorithm

intervals

Results

4.6s	2737×	body	1280	valid
1.8s	1809×	body	640	valid
532.0ms	776×	body	320	valid
400.0ms	2326×	body	80	valid
102.0ms	352×	body	160	valid