Details

sample630.0ms

Algorithm

intervals

Results

396.0ms	87×	body	1280	valid
90.0ms	57×	body	640	valid
20.0ms	81×	body	80	valid
15.0ms	21×	body	320	valid
5.0ms	10×	body	160	valid

simplify1.9s

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	13	16
1	23	16
2	35	16
3	64	16
4	140	16
5	632	16
done	5000	16

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.6b

localize64.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
0.3b	(pow (sin kx) 2.0)
0.3b	(pow (sin ky) 2.0)
3.4b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite171.0ms

Algorithm

rewrite-expression-head

Rules

41×	`*-un-lft-identity`
34×	`add-sqr-sqrt`
30×	`associate-l`
26×	`times-frac`
25×	`add-cube-cbrt`
21×	`sqrt-prod`
14×	`unpow-prod-down`
11×	`add-exp-log`
9×	`pow1` `add-cbrt-cube`
8×	`distribute-lft-out`
6×	`pow-unpow`
4×	`sqrt-div` `add-log-exp`
3×	`associate-r` `unswap-sqr`
2×	`pow-to-exp` `pow-pow` `flip3-+` `pow-exp` `prod-exp` `associate-/r/` `cbrt-unprod` `flip-+` `sqr-pow`
1×	`cbrt-undiv` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `div-exp` `pow-prod-down` `associate-l/` `-commutative` `div-inv`

Counts

4 → 101

Calls

4 calls:

103.0ms	(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
6.0ms	(pow (sin kx) 2.0)
6.0ms	(pow (sin ky) 2.0)
48.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series691.0ms

Counts

4 → 12

Calls

4 calls:

255.0ms	(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
135.0ms	(pow (sin kx) 2.0)
166.0ms	(pow (sin ky) 2.0)
135.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify1.0s

Counts

113 → 113

Iterations

Useful iterations: 2 (359.0ms)

Iter	Nodes	Cost
0	181	1660
1	451	1562
2	1861	1469
done	5000	1469

prune1.0s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 11.5b

localize69.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (sin kx))
0.6b	(cbrt (sin kx))
0.6b	(cbrt (sin kx))
3.4b	(sqrt (+ (* (pow (* (cbrt (sin kx)) (cbrt (sin kx))) 2.0) (pow (cbrt (sin kx)) 2.0)) (pow (sin ky) 2.0)))

rewrite49.0ms

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` `add-log-exp`
3×	`pow1/3` `sqrt-prod`
2×	`sqrt-div`
1×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`

Counts

4 → 48

Calls

4 calls:

1.0ms	(cbrt (sin kx))
1.0ms	(cbrt (sin kx))
1.0ms	(cbrt (sin kx))
45.0ms	(sqrt (+ (* (pow (* (cbrt (sin kx)) (cbrt (sin kx))) 2.0) (pow (cbrt (sin kx)) 2.0)) (pow (sin ky) 2.0)))

series555.0ms

Counts

4 → 12

Calls

4 calls:

124.0ms	(cbrt (sin kx))
140.0ms	(cbrt (sin kx))
161.0ms	(cbrt (sin kx))
131.0ms	(sqrt (+ (* (pow (* (cbrt (sin kx)) (cbrt (sin kx))) 2.0) (pow (cbrt (sin kx)) 2.0)) (pow (sin ky) 2.0)))

simplify1.6s

Counts

60 → 60

Iterations

Useful iterations: 3 (493.0ms)

Iter	Nodes	Cost
0	81	818
1	191	744
2	573	620
3	2801	609
done	5002	609

prune603.0ms

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 11.5b

localize84.0ms

Local error

Found 4 expressions with local error:

0.7b	(cbrt (cbrt (sin kx)))
0.7b	(cbrt (cbrt (sin kx)))
0.7b	(cbrt (cbrt (sin kx)))
3.4b	(sqrt (+ (* (pow (* (cbrt (sin kx)) (cbrt (sin kx))) 2.0) (pow (* (* (cbrt (cbrt (sin kx))) (cbrt (cbrt (sin kx)))) (cbrt (cbrt (sin kx)))) 2.0)) (pow (sin ky) 2.0)))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 57

Calls

4 calls:

2.0ms	(cbrt (cbrt (sin kx)))
2.0ms	(cbrt (cbrt (sin kx)))
2.0ms	(cbrt (cbrt (sin kx)))
43.0ms	(sqrt (+ (* (pow (* (cbrt (sin kx)) (cbrt (sin kx))) 2.0) (pow (* (* (cbrt (cbrt (sin kx))) (cbrt (cbrt (sin kx)))) (cbrt (cbrt (sin kx)))) 2.0)) (pow (sin ky) 2.0)))

series516.0ms

Counts

4 → 12

Calls

4 calls:

125.0ms	(cbrt (cbrt (sin kx)))
136.0ms	(cbrt (cbrt (sin kx)))
145.0ms	(cbrt (cbrt (sin kx)))
111.0ms	(sqrt (+ (* (pow (* (cbrt (sin kx)) (cbrt (sin kx))) 2.0) (pow (* (* (cbrt (cbrt (sin kx))) (cbrt (cbrt (sin kx)))) (cbrt (cbrt (sin kx)))) 2.0)) (pow (sin ky) 2.0)))

simplify1.2s

Counts

69 → 69

Iterations

Useful iterations: 3 (415.0ms)

Iter	Nodes	Cost
0	89	1212
1	193	1125
2	534	881
3	2381	816
done	5001	816

prune805.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 11.5b

localize77.0ms

Local error

Found 4 expressions with local error:

0.7b	(cbrt (cbrt (sin kx)))
0.7b	(cbrt (cbrt (sin kx)))
0.7b	(cbrt (cbrt (sin kx)))
3.4b	(sqrt (+ (* (pow (* (cbrt (sin kx)) (cbrt (sin kx))) 2.0) (pow (* (* (cbrt (cbrt (sin kx))) (cbrt (cbrt (sin kx)))) (* (cbrt (* (cbrt (cbrt (sin kx))) (cbrt (cbrt (sin kx))))) (cbrt (cbrt (cbrt (sin kx)))))) 2.0)) (pow (sin ky) 2.0)))

rewrite98.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 57

Calls

4 calls:

2.0ms	(cbrt (cbrt (sin kx)))
2.0ms	(cbrt (cbrt (sin kx)))
2.0ms	(cbrt (cbrt (sin kx)))
92.0ms	(sqrt (+ (* (pow (* (cbrt (sin kx)) (cbrt (sin kx))) 2.0) (pow (* (* (cbrt (cbrt (sin kx))) (cbrt (cbrt (sin kx)))) (* (cbrt (* (cbrt (cbrt (sin kx))) (cbrt (cbrt (sin kx))))) (cbrt (cbrt (cbrt (sin kx)))))) 2.0)) (pow (sin ky) 2.0)))

series552.0ms

Counts

4 → 12

Calls

4 calls:

135.0ms	(cbrt (cbrt (sin kx)))
140.0ms	(cbrt (cbrt (sin kx)))
177.0ms	(cbrt (cbrt (sin kx)))
100.0ms	(sqrt (+ (* (pow (* (cbrt (sin kx)) (cbrt (sin kx))) 2.0) (pow (* (* (cbrt (cbrt (sin kx))) (cbrt (cbrt (sin kx)))) (* (cbrt (* (cbrt (cbrt (sin kx))) (cbrt (cbrt (sin kx))))) (cbrt (cbrt (cbrt (sin kx)))))) 2.0)) (pow (sin ky) 2.0)))

simplify1.3s

Counts

69 → 69

Iterations

Useful iterations: 3 (498.0ms)

Iter	Nodes	Cost
0	91	1488
1	201	1377
2	556	1241
3	2400	1230
done	5001	1230

prune689.0ms

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 11.5b

regimes2.9s

Accuracy

0% (1.6b remaining)

Error of 12.7b against oracle of 11.1b and baseline of 12.7b

bsearch0.0ms

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	25	62
1	31	62
done	31	62

end0.0ms

sample8.9s

Algorithm

intervals

Results

5.2s	2742×	body	1280	valid
1.9s	1814×	body	640	valid
680.0ms	2358×	body	80	valid
484.0ms	723×	body	320	valid
181.0ms	363×	body	160	valid