Details

sample470.0ms

Algorithm

intervals

Results

204.0ms	83×	body	1280	valid
72.0ms	58×	body	640	valid
24.0ms	77×	body	80	valid
22.0ms	26×	body	320	valid
6.0ms	12×	body	160	valid

simplify1.0s

Counts: 1 → 1

prune32.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.4b

localize58.0ms

Local error

Found 4 expressions with local error:

2.5b	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
0.3b	(* (sin kx) (sin kx))
0.2b	(* (sin ky) (sin ky))
0.2b	(/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))

rewrite92.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
28×	`*-un-lft-identity` `add-cube-cbrt`
19×	`pow1`
18×	`times-frac`
15×	`sqrt-prod`
10×	`add-cbrt-cube` `add-exp-log`
6×	`associate-/r` `sqrt-div` `swap-sqr` `associate-r` `associate-l*` `sin-mult`
4×	`insert-posit16` `add-log-exp`
3×	`associate-/r/` `associate-/l*`
2×	`pow2` `flip3-+` `pow-plus` `pow-prod-down` `frac-add` `prod-exp` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `flip-+` `sqr-sin` `unswap-sqr`
1×	`cbrt-undiv` `rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `div-inv`

Counts

4 → 116

Calls

4 calls:

Slowest

26.0ms	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
26.0ms	(/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))
21.0ms	(* (sin kx) (sin kx))
14.0ms	(* (sin ky) (sin ky))

series354.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

178.0ms	(/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))
126.0ms	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
29.0ms	(* (sin ky) (sin ky))
20.0ms	(* (sin kx) (sin kx))

simplify618.0ms

Counts: 128 → 128

prune1.8s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 10.9b

localize60.0ms

Local error

Found 4 expressions with local error:

2.5b	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
0.3b	(* (sin kx) (sin kx))
0.2b	(* (sin ky) (sin ky))
0.2b	(/ 1 (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin ky)))

rewrite89.0ms

Algorithm

rewrite-expression-head

Rules

138×	`times-frac`
93×	`add-sqr-sqrt`
88×	`*-un-lft-identity` `add-cube-cbrt`
39×	`sqrt-prod`
22×	`associate-/r*`
20×	`pow1`
19×	`add-exp-log`
13×	`add-cbrt-cube`
7×	`div-exp`
6×	`swap-sqr` `associate-r` `associate-l`
5×	`div-inv`
4×	`insert-posit16` `sin-mult` `add-log-exp`
3×	`cbrt-undiv` `sqrt-div` `associate-/l*`
2×	`pow2` `rec-exp` `pow-plus` `1-exp` `pow-prod-down` `prod-exp` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `sqr-sin` `unswap-sqr`
1×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `frac-add` `associate-/r/` `flip-+` `pow-flip` `inv-pow`

Counts

4 → 186

Calls

4 calls:

Slowest

32.0ms	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
21.0ms	(* (sin kx) (sin kx))
20.0ms	(* (sin ky) (sin ky))
12.0ms	(/ 1 (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin ky)))

series328.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

186.0ms	(/ 1 (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin ky)))
98.0ms	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
25.0ms	(* (sin ky) (sin ky))
20.0ms	(* (sin kx) (sin kx))

simplify1.2s

Counts: 198 → 198

prune3.3s

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 10.9b

localize32.0ms

Local error

Found 4 expressions with local error:

2.5b	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
0.3b	(* (sin kx) (sin kx))
0.2b	(/ (/ 1 (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (/ 1 (sin ky)))
0.2b	(* (sin ky) (sin ky))

rewrite175.0ms

Algorithm

rewrite-expression-head

Rules

811×	`times-frac`
382×	`add-sqr-sqrt`
377×	`*-un-lft-identity` `add-cube-cbrt`
129×	`sqrt-prod`
48×	`add-exp-log`
45×	`sqrt-div`
43×	`associate-/r/`
41×	`div-inv`
32×	`div-exp` `sin-mult`
25×	`associate-/l*`
20×	`add-cbrt-cube`
19×	`pow1`
15×	`flip3-+` `frac-add` `flip-+`
13×	`associate-/r*`
8×	`cbrt-undiv` `rec-exp` `1-exp`
6×	`swap-sqr` `associate-r` `associate-l`
4×	`insert-posit16` `add-log-exp`
2×	`pow2` `pow-plus` `pow-prod-down` `prod-exp` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `sqr-sin` `unswap-sqr`
1×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `associate-/l/`

Counts

4 → 469

Calls

4 calls:

Slowest

76.0ms	(/ (/ 1 (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (/ 1 (sin ky)))
30.0ms	(* (sin kx) (sin kx))
22.0ms	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
22.0ms	(* (sin ky) (sin ky))

series327.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

172.0ms	(/ (/ 1 (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (/ 1 (sin ky)))
116.0ms	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
20.0ms	(* (sin kx) (sin kx))
20.0ms	(* (sin ky) (sin ky))

simplify1.3s

Counts: 481 → 481

prune7.5s

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 10.9b

localize55.0ms

Local error

Found 4 expressions with local error:

2.5b	(sqrt (+ (* (* (sin kx) (* (cbrt (sin kx)) (cbrt (sin kx)))) (cbrt (sin kx))) (* (sin ky) (sin ky))))
0.6b	(cbrt (sin kx))
0.6b	(cbrt (sin kx))
0.6b	(cbrt (sin kx))

rewrite161.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod` `add-sqr-sqrt`
8×	`*-un-lft-identity` `add-cube-cbrt`
5×	`pow1`
4×	`add-cbrt-cube` `add-exp-log` `insert-posit16` `add-log-exp`
3×	`pow1/3` `sqrt-prod`
2×	`sqrt-div`
1×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`

Counts

4 → 52

Calls

4 calls:

Slowest

157.0ms	(sqrt (+ (* (* (sin kx) (* (cbrt (sin kx)) (cbrt (sin kx)))) (cbrt (sin kx))) (* (sin ky) (sin ky))))
1.0ms	(cbrt (sin kx))
1.0ms	(cbrt (sin kx))
1.0ms	(cbrt (sin kx))

series566.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

161.0ms	(cbrt (sin kx))
156.0ms	(cbrt (sin kx))
140.0ms	(cbrt (sin kx))
109.0ms	(sqrt (+ (* (* (sin kx) (* (cbrt (sin kx)) (cbrt (sin kx)))) (cbrt (sin kx))) (* (sin ky) (sin ky))))

simplify963.0ms

Counts: 64 → 64

prune961.0ms

Pruning

16 alts after pruning (14 fresh and 2 done)

Merged error: 10.8b

regimes995.0ms

Accuracy

0% (1.2b remaining)

Error of 12.2b against oracle of 11.0b and baseline of 12.2b

bsearch5.0ms

end0.0ms

sample12.3s

Algorithm

intervals

Results

6.4s	2771×	body	1280	valid
3.9s	1783×	body	640	valid
805.0ms	2285×	body	80	valid
758.0ms	790×	body	320	valid
239.0ms	371×	body	160	valid