Details

sample462.0ms

Algorithm

intervals

Results

136.0ms	68×	body	640	valid
133.0ms	78×	body	1280	valid
20.0ms	31×	body	320	valid
17.0ms	68×	body	80	valid
5.0ms	11×	body	160	valid

simplify1.6s

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

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

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.7b

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))
0.2b	(pow (sin ky) 2.0)
0.2b	(pow (sin kx) 2.0)
2.2b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite276.0ms

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:

187.0ms	(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
7.0ms	(pow (sin ky) 2.0)
7.0ms	(pow (sin kx) 2.0)
63.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series962.0ms

Counts

4 → 12

Calls

4 calls:

336.0ms	(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
218.0ms	(pow (sin ky) 2.0)
216.0ms	(pow (sin kx) 2.0)
192.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify1.7s

Counts

130 → 130

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	188	1736
1	462	1637
2	1906	1529
done	5001	1528

prune1.4s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 10.5b

localize49.0ms

Local error

Found 3 expressions with local error:

0.1b

(hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))

0.1b

(/ (sin ky) (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2))))

0.2b

(* (/ (sin ky) (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))) (sin th))

rewrite61.0ms

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:

1.0ms

(hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))

18.0ms

(/ (sin ky) (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2))))

38.0ms

(* (/ (sin ky) (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))) (sin th))

series2.0s

Counts

3 → 9

Calls

3 calls:

531.0ms

(hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))

771.0ms

(/ (sin ky) (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2))))

694.0ms

(* (/ (sin ky) (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))) (sin th))

simplify1.6s

Counts

82 → 82

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	134	1912
1	311	1885
2	1347	1670
done	5000	1669

prune1.0s

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 10.4b

localize62.0ms

Local error

Found 4 expressions with local error:

0.1b	(log1p (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2))))
0.1b	(/ (sin ky) (expm1 (log1p (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2))))))
0.2b	(* (/ (sin ky) (expm1 (log1p (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))))) (sin th))
0.3b	(expm1 (log1p (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))))

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 85

Calls

4 calls:

1.0ms	(log1p (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2))))
17.0ms	(/ (sin ky) (expm1 (log1p (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2))))))
47.0ms	(* (/ (sin ky) (expm1 (log1p (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))))) (sin th))
1.0ms	(expm1 (log1p (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))))

series2.5s

Counts

4 → 12

Calls

4 calls:

507.0ms	(log1p (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2))))
833.0ms	(/ (sin ky) (expm1 (log1p (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2))))))
683.0ms	(* (/ (sin ky) (expm1 (log1p (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))))) (sin th))
516.0ms	(expm1 (log1p (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))))

simplify1.4s

Counts

97 → 97

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	168	2365
1	385	2152
2	1608	1899
done	5000	1889

prune1.1s

Pruning

20 alts after pruning (19 fresh and 1 done)

Merged error: 10.4b

localize92.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (cbrt (/ (sin ky) (expm1 (log1p (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2))))))) (cbrt (/ (sin ky) (expm1 (log1p (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2))))))))
0.4b	(cbrt (/ (sin ky) (expm1 (log1p (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))))))
0.4b	(cbrt (/ (sin ky) (expm1 (log1p (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))))))
0.4b	(cbrt (/ (sin ky) (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))))

rewrite102.0ms

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:

74.0ms	(* (cbrt (/ (sin ky) (expm1 (log1p (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2))))))) (cbrt (/ (sin ky) (expm1 (log1p (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2))))))))
5.0ms	(cbrt (/ (sin ky) (expm1 (log1p (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))))))
5.0ms	(cbrt (/ (sin ky) (expm1 (log1p (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))))))
5.0ms	(cbrt (/ (sin ky) (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))))

series4.6s

Counts

4 → 12

Calls

4 calls:

1.3s	(* (cbrt (/ (sin ky) (expm1 (log1p (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2))))))) (cbrt (/ (sin ky) (expm1 (log1p (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2))))))))
1.1s	(cbrt (/ (sin ky) (expm1 (log1p (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))))))
1.2s	(cbrt (/ (sin ky) (expm1 (log1p (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))))))
985.0ms	(cbrt (/ (sin ky) (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))))

simplify2.1s

Counts

164 → 164

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	250	6832
1	473	6032
2	1676	5765
done	5001	5532

prune2.3s

Pruning

21 alts after pruning (20 fresh and 1 done)

Merged error: 10.4b

regimes2.4s

Accuracy

0% (0.3b remaining)

Error of 8.9b against oracle of 8.6b and baseline of 8.9b

bsearch0.0ms

simplify8.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	16	21
1	17	21
done	17	21

end0.0ms

sample11.6s

Algorithm

intervals

Results

6.2s	2747×	body	1280	valid
2.7s	1826×	body	640	valid
1.2s	2321×	body	80	valid
656.0ms	760×	body	320	valid
146.0ms	346×	body	160	valid