Details

sample230.0ms

Algorithm

intervals

Results

78.0ms	64×	body	640	valid
74.0ms	83×	body	1280	valid
9.0ms	26×	body	320	valid
9.0ms	76×	body	80	valid
2.0ms	7×	body	160	valid

simplify1.2s

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	13	16
1	23	16
2	39	16
3	68	16
4	156	16
5	653	16
done	5000	16

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 10.4b

localize42.0ms

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))
0.2b	(pow (sin kx) 2.0)
0.2b	(pow (sin ky) 2.0)
2.9b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite236.0ms

Algorithm

rewrite-expression-head

Rules

46×	`add-sqr-sqrt`
41×	`*-un-lft-identity`
30×	`associate-l`
26×	`times-frac`
25×	`add-cube-cbrt`
21×	`sqrt-prod`
20×	`unpow-prod-down`
11×	`add-exp-log`
9×	`pow1` `add-cbrt-cube` `hypot-def`
8×	`distribute-lft-out` `sqr-pow`
6×	`pow-unpow`
4×	`expm1-log1p-u` `sqrt-div` `log1p-expm1-u` `add-log-exp`
3×	`associate-r` `unswap-sqr`
2×	`pow-to-exp` `pow-pow` `flip3-+` `pow-exp` `prod-exp` `associate-/r/` `cbrt-unprod` `flip-+`
1×	`cbrt-undiv` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `div-exp` `pow-prod-down` `associate-l/` `-commutative` `div-inv`

Counts

4 → 118

Calls

4 calls:

152.0ms	(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
11.0ms	(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)))

series696.0ms

Counts

4 → 12

Calls

4 calls:

241.0ms	(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
152.0ms	(pow (sin kx) 2.0)
160.0ms	(pow (sin ky) 2.0)
143.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify1.2s

Counts

130 → 130

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	188	1736
1	462	1637
2	1905	1529
done	5000	1528

prune842.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 7.3b

localize33.0ms

Local error

Found 3 expressions with local error:

0.0b	(hypot (sin ky) (sin kx))
0.2b	(/ (sin ky) (hypot (sin ky) (sin kx)))
0.2b	(* (/ (sin ky) (hypot (sin ky) (sin kx))) (sin th))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
19×	`add-cube-cbrt` `*-un-lft-identity` `times-frac`
13×	`associate-l`
10×	`add-exp-log` `add-cbrt-cube`
5×	`pow1`
3×	`expm1-log1p-u` `associate-r` `associate-/r` `log1p-expm1-u` `associate-/l` `add-log-exp`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `div-inv` `unswap-sqr`
1×	`hypot-udef` `frac-2neg` `pow-prod-down` `associate-l/` `clear-num` `-commutative`

Counts

3 → 73

Calls

3 calls:

0.0ms	(hypot (sin ky) (sin kx))
9.0ms	(/ (sin ky) (hypot (sin ky) (sin kx)))
22.0ms	(* (/ (sin ky) (hypot (sin ky) (sin kx))) (sin th))

series875.0ms

Counts

3 → 9

Calls

3 calls:

190.0ms	(hypot (sin ky) (sin kx))
289.0ms	(/ (sin ky) (hypot (sin ky) (sin kx)))
396.0ms	(* (/ (sin ky) (hypot (sin ky) (sin kx))) (sin th))

simplify1.0s

Counts

82 → 82

Iterations

Useful iterations: done (1.0s)

Iter	Nodes	Cost
0	130	1126
1	301	1106
2	1343	993
done	5001	984

prune484.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 7.3b

localize31.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot (sin ky) (sin kx))
0.1b	(/ (hypot (sin ky) (sin kx)) (sin ky))
0.2b	(* (/ 1 (/ (hypot (sin ky) (sin kx)) (sin ky))) (sin th))
0.2b	(/ 1 (/ (hypot (sin ky) (sin kx)) (sin ky)))

rewrite89.0ms

Algorithm

rewrite-expression-head

Rules

156×	`times-frac`
104×	`add-sqr-sqrt`
92×	`*-un-lft-identity`
90×	`add-cube-cbrt`
44×	`associate-l`
36×	`add-exp-log`
20×	`add-cbrt-cube`
16×	`associate-/r*`
15×	`div-exp`
10×	`div-inv`
7×	`pow1` `cbrt-undiv` `prod-exp`
6×	`associate-/l*`
5×	`unswap-sqr`
4×	`expm1-log1p-u` `rec-exp` `1-exp` `log1p-expm1-u` `add-log-exp`
3×	`associate-r` `cbrt-unprod`
2×	`frac-2neg` `clear-num` `associate-/r/`
1×	`hypot-udef` `pow-flip` `pow-prod-down` `associate-l/` `-commutative` `inv-pow`

Counts

4 → 191

Calls

4 calls:

0.0ms	(hypot (sin ky) (sin kx))
6.0ms	(/ (hypot (sin ky) (sin kx)) (sin ky))
53.0ms	(* (/ 1 (/ (hypot (sin ky) (sin kx)) (sin ky))) (sin th))
19.0ms	(/ 1 (/ (hypot (sin ky) (sin kx)) (sin ky)))

series1.0s

Counts

4 → 12

Calls

4 calls:

198.0ms	(hypot (sin ky) (sin kx))
201.0ms	(/ (hypot (sin ky) (sin kx)) (sin ky))
311.0ms	(* (/ 1 (/ (hypot (sin ky) (sin kx)) (sin ky))) (sin th))
298.0ms	(/ 1 (/ (hypot (sin ky) (sin kx)) (sin ky)))

simplify3.4s

Counts

203 → 203

Iterations

Useful iterations: done (3.4s)

Iter	Nodes	Cost
0	273	3401
1	733	3116
2	4402	2712
done	5000	2708

prune951.0ms

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 7.3b

localize30.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (/ (hypot (sin ky) (sin kx)) (sin ky)))
0.3b	(cbrt (/ (hypot (sin ky) (sin kx)) (sin ky)))
0.3b	(cbrt (/ (hypot (sin ky) (sin kx)) (sin ky)))
0.4b	(* (cbrt (/ (hypot (sin ky) (sin kx)) (sin ky))) (cbrt (/ (hypot (sin ky) (sin kx)) (sin ky))))

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

103×	`cbrt-prod`
81×	`add-sqr-sqrt`
69×	`times-frac`
57×	`add-cube-cbrt` `*-un-lft-identity`
16×	`swap-sqr` `associate-r` `associate-l`
11×	`pow1`
9×	`pow1/3` `unswap-sqr`
7×	`cbrt-div` `div-inv`
6×	`add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `frac-times` `pow-plus` `associate-r/` `associate-l/` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 152

Calls

4 calls:

3.0ms	(cbrt (/ (hypot (sin ky) (sin kx)) (sin ky)))
3.0ms	(cbrt (/ (hypot (sin ky) (sin kx)) (sin ky)))
3.0ms	(cbrt (/ (hypot (sin ky) (sin kx)) (sin ky)))
47.0ms	(* (cbrt (/ (hypot (sin ky) (sin kx)) (sin ky))) (cbrt (/ (hypot (sin ky) (sin kx)) (sin ky))))

series1.4s

Counts

4 → 12

Calls

4 calls:

353.0ms	(cbrt (/ (hypot (sin ky) (sin kx)) (sin ky)))
333.0ms	(cbrt (/ (hypot (sin ky) (sin kx)) (sin ky)))
333.0ms	(cbrt (/ (hypot (sin ky) (sin kx)) (sin ky)))
373.0ms	(* (cbrt (/ (hypot (sin ky) (sin kx)) (sin ky))) (cbrt (/ (hypot (sin ky) (sin kx)) (sin ky))))

simplify1.9s

Counts

164 → 164

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	170	3647
1	328	3474
2	1375	3298
done	5000	3078

prune1.1s

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 7.3b

regimes828.0ms

Accuracy

0% (0.5b remaining)

Error of 8.9b against oracle of 8.4b and baseline of 8.9b

bsearch0.0ms

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	14	34
1	18	34
done	18	34

end0.0ms

sample9.1s

Algorithm

intervals

Results

4.7s	2689×	body	1280	valid
2.8s	1844×	body	640	valid
558.0ms	2387×	body	80	valid
517.0ms	737×	body	320	valid
114.0ms	343×	body	160	valid