Details

sample1.5s

Algorithm

intervals

Results

1.0s	96×	body	1280	valid
191.0ms	47×	body	640	valid
40.0ms	10×	body	160	valid
25.0ms	25×	body	320	valid
21.0ms	78×	body	80	valid

simplify552.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	2000
6	850
5	327
4	155
3	80
2	49
1	25
0	13

prune28.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.4b

localize56.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin th) (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))
0.2b	(* (sin kx) (sin kx))
0.3b	(* (sin ky) (sin ky))
5.8b	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))

rewrite188.0ms

Algorithm

rewrite-expression-head

Rules

40×	`add-sqr-sqrt`
31×	`associate-r`
27×	`*-un-lft-identity` `add-cube-cbrt`
21×	`pow1`
20×	`times-frac`
13×	`add-cbrt-cube` `add-exp-log` `sqrt-prod`
9×	`associate-l`
6×	`sqrt-div` `swap-sqr` `sin-mult`
5×	`unswap-sqr`
4×	`prod-exp` `cbrt-unprod` `insert-posit16` `add-log-exp`
3×	`pow-prod-down` `associate-/r/` `*-commutative`
2×	`pow2` `flip3-+` `pow-plus` `frac-add` `pow-sqr` `pow-prod-up` `flip-+` `sqr-sin`
1×	`cbrt-undiv` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `div-exp` `associate-*r/` `div-inv`

Counts

4 → 119

Calls

4 calls:

112.0ms	(* (sin th) (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))
22.0ms	(* (sin kx) (sin kx))
22.0ms	(* (sin ky) (sin ky))
27.0ms	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))

series434.0ms

Counts

4 → 12

Calls

4 calls:

229.0ms	(* (sin th) (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))
32.0ms	(* (sin kx) (sin kx))
36.0ms	(* (sin ky) (sin ky))
137.0ms	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))

simplify483.0ms

Counts

131 → 131

Iterations

Iter	Nodes
done	2001
1	563
0	214

prune850.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 12.7b

localize51.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin th) (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))))
0.2b	(* (sin kx) (sin kx))
0.3b	(* (sin ky) (sin ky))
5.8b	(sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))

rewrite159.0ms

Algorithm

rewrite-expression-head

Rules

40×	`add-sqr-sqrt`
31×	`associate-r`
27×	`*-un-lft-identity` `add-cube-cbrt`
21×	`pow1`
20×	`times-frac`
13×	`add-cbrt-cube` `add-exp-log` `sqrt-prod`
9×	`associate-l`
6×	`sqrt-div` `swap-sqr` `sin-mult`
5×	`unswap-sqr`
4×	`prod-exp` `cbrt-unprod` `insert-posit16` `add-log-exp`
3×	`pow-prod-down` `associate-/r/` `*-commutative`
2×	`pow2` `flip3-+` `pow-plus` `frac-add` `pow-sqr` `pow-prod-up` `flip-+` `sqr-sin`
1×	`cbrt-undiv` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `div-exp` `associate-*r/` `div-inv`

Counts

4 → 119

Calls

4 calls:

107.0ms	(* (sin th) (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))))
20.0ms	(* (sin kx) (sin kx))
12.0ms	(* (sin ky) (sin ky))
17.0ms	(sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))

series376.0ms

Counts

4 → 12

Calls

4 calls:

206.0ms	(* (sin th) (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))))
28.0ms	(* (sin kx) (sin kx))
21.0ms	(* (sin ky) (sin ky))
120.0ms	(sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))

simplify537.0ms

Counts

131 → 131

Iterations

Iter	Nodes
done	2000
1	565
0	214

prune777.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 11.2b

localize40.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ (sin th) (sqrt (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))))) (/ (sin ky) (sqrt (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))))))
0.4b	(/ (sin ky) (sqrt (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))))
5.8b	(sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))
5.8b	(sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))

rewrite267.0ms

Algorithm

rewrite-expression-head

Rules

124×	`add-sqr-sqrt`
120×	`sqrt-prod`
105×	`times-frac`
66×	`*-un-lft-identity` `add-cube-cbrt`
34×	`associate-r` `associate-l`
24×	`sqrt-div`
18×	`add-cbrt-cube` `add-exp-log`
16×	`unswap-sqr`
10×	`sin-mult`
9×	`associate-/r*` `associate-/r/`
8×	`pow1`
5×	`cbrt-undiv` `flip3-+` `div-exp` `frac-add` `flip-+`
4×	`prod-exp` `cbrt-unprod` `insert-posit16` `add-log-exp`
3×	`div-inv` `associate-/l*`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`frac-times` `clear-num` `frac-2neg` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative`

Counts

4 → 194

Calls

4 calls:

190.0ms	(* (/ (sin th) (sqrt (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))))) (/ (sin ky) (sqrt (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))))))
41.0ms	(/ (sin ky) (sqrt (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))))
15.0ms	(sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))
17.0ms	(sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))

series669.0ms

Counts

4 → 12

Calls

4 calls:

220.0ms	(* (/ (sin th) (sqrt (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))))) (/ (sin ky) (sqrt (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))))))
228.0ms	(/ (sin ky) (sqrt (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))))
106.0ms	(sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))
115.0ms	(sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))

simplify1.0s

Counts

206 → 206

Iterations

Iter	Nodes
done	2002
1	727
0	268

prune1.2s

Pruning

16 alts after pruning (14 fresh and 2 done)

Merged error: 11.2b

localize75.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))))
5.8b	(sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))
5.8b	(sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))
5.8b	(sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 69

Calls

4 calls:

10.0ms	(cbrt (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))))
21.0ms	(sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))
17.0ms	(sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))
12.0ms	(sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))

series504.0ms

Counts

4 → 12

Calls

4 calls:

174.0ms	(cbrt (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))))
111.0ms	(sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))
112.0ms	(sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))
107.0ms	(sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))

simplify842.0ms

Counts

81 → 81

Iterations

Iter	Nodes
done	2036
3	1550
2	537
1	221
0	103

prune611.0ms

Pruning

15 alts after pruning (12 fresh and 3 done)

Merged error: 11.2b

regimes1.1s

Accuracy

-14% (2.2b remaining)

Error of 12.5b against oracle of 10.3b and baseline of 12.2b

bsearch2.0ms

simplify8.0ms

Iterations

Iter	Nodes
done	41
1	41
0	30

end0.0ms

sample12.5s

Algorithm

intervals

Results

6.9s	2755×	body	1280	valid
3.4s	1826×	body	640	valid
973.0ms	781×	body	320	valid
697.0ms	2295×	body	80	valid
207.0ms	343×	body	160	valid