Details

sample501.0ms

Algorithm

intervals

Results

198.0ms	98×	body	1280	valid
109.0ms	43×	body	640	valid
25.0ms	28×	body	320	valid
23.0ms	75×	body	80	valid
7.0ms	12×	body	160	valid

simplify1.2s

Counts

1 → 1

Iterations

Iter	Nodes
done	2001
7	2001
6	850
5	327
4	155
3	80
2	49
1	25
0	13

prune22.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.3b

localize58.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin th) (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))
0.3b	(* (sin ky) (sin ky))
0.3b	(* (sin kx) (sin kx))
3.9b	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))

rewrite154.0ms

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:

80.0ms	(* (sin th) (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))
19.0ms	(* (sin ky) (sin ky))
20.0ms	(* (sin kx) (sin kx))
32.0ms	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))

series449.0ms

Counts

4 → 12

Calls

4 calls:

233.0ms	(* (sin th) (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))
34.0ms	(* (sin ky) (sin ky))
34.0ms	(* (sin kx) (sin kx))
148.0ms	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))

simplify1.2s

Counts

131 → 131

Iterations

Iter	Nodes
done	2002
2	2002
1	563
0	214

prune869.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 10.7b

localize54.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin th) (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))))
0.3b	(* (sin ky) (sin ky))
0.3b	(* (sin kx) (sin kx))
3.9b	(sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))

rewrite112.0ms

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:

71.0ms	(* (sin th) (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))))
16.0ms	(* (sin ky) (sin ky))
11.0ms	(* (sin kx) (sin kx))
12.0ms	(sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))

series355.0ms

Counts

4 → 12

Calls

4 calls:

198.0ms	(* (sin th) (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))))
30.0ms	(* (sin ky) (sin ky))
31.0ms	(* (sin kx) (sin kx))
96.0ms	(sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))

simplify1.3s

Counts

131 → 131

Iterations

Iter	Nodes
done	2000
2	2000
1	565
0	214

prune880.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 9.5b

localize79.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (sin kx))
0.6b	(cbrt (sin kx))
0.6b	(cbrt (sin kx))
3.9b	(sqrt (+ (* (* (sin kx) (* (cbrt (sin kx)) (cbrt (sin kx)))) (cbrt (sin kx))) (* (sin ky) (sin ky))))

rewrite144.0ms

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:

3.0ms	(cbrt (sin kx))
3.0ms	(cbrt (sin kx))
3.0ms	(cbrt (sin kx))
135.0ms	(sqrt (+ (* (* (sin kx) (* (cbrt (sin kx)) (cbrt (sin kx)))) (cbrt (sin kx))) (* (sin ky) (sin ky))))

series529.0ms

Counts

4 → 12

Calls

4 calls:

123.0ms	(cbrt (sin kx))
123.0ms	(cbrt (sin kx))
179.0ms	(cbrt (sin kx))
104.0ms	(sqrt (+ (* (* (sin kx) (* (cbrt (sin kx)) (cbrt (sin kx)))) (cbrt (sin kx))) (* (sin ky) (sin ky))))

simplify1.7s

Counts

64 → 64

Iterations

Iter	Nodes
done	2000
4	2000
3	1735
2	550
1	189
0	81

prune566.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 9.5b

localize96.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))
3.9b	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
3.9b	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
3.9b	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
20×	`*-un-lft-identity` `add-cube-cbrt`
18×	`times-frac` `sqrt-prod`
12×	`sqrt-div`
8×	`sin-mult`
7×	`pow1`
4×	`flip3-+` `add-cbrt-cube` `frac-add` `add-exp-log` `flip-+` `insert-posit16` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-/r/`
1×	`cbrt-div` `pow1/3` `div-inv`

Counts

4 → 86

Calls

4 calls:

11.0ms	(cbrt (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))
12.0ms	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
16.0ms	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
24.0ms	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))

series617.0ms

Counts

4 → 12

Calls

4 calls:

268.0ms	(cbrt (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))
131.0ms	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
117.0ms	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
101.0ms	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))

simplify1.4s

Counts

98 → 98

Iterations

Iter	Nodes
done	2001
3	2001
2	731
1	314
0	172

prune811.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 9.5b

regimes1.2s

Accuracy

0% (2.2b remaining)

Error of 12.7b against oracle of 10.6b and baseline of 12.7b

bsearch0.0ms

simplify6.0ms

Iterations

Iter	Nodes
done	19
1	19
0	15

end0.0ms

sample13.3s

Algorithm

intervals

Results

7.0s	2759×	body	1280	valid
3.7s	1835×	body	640	valid
1.2s	772×	body	320	valid
803.0ms	2296×	body	80	valid
204.0ms	338×	body	160	valid