Details

sample97.0ms

Algorithm

intervals

Results

39.0ms	313×	body	80	valid
13.0ms	36×	body	640	valid
11.0ms	25×	body	1280	valid
4.0ms	15×	body	320	valid
1.0ms	6×	body	160	valid

simplify8.2s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
5	4217
4	728
3	160
2	57
1	26
0	12

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.4b

localize54.0ms

Local error

Found 4 expressions with local error:

0.6b	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
5.8b	(* (* x (pow sin 2.0)) x)
8.1b	(* x (pow sin 2.0))
19.1b	(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

rewrite278.0ms

Algorithm

rewrite-expression-head

Rules

122×	`add-exp-log`
82×	`prod-exp`
34×	`add-cbrt-cube`
18×	`pow-to-exp` `pow-exp`
17×	`add-sqr-sqrt`
16×	`div-exp` `cbrt-unprod`
12×	`*-un-lft-identity` `add-cube-cbrt`
11×	`associate-r` `associate-l`
7×	`unpow-prod-down`
6×	`pow1`
4×	`expm1-log1p-u` `cbrt-undiv` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`times-frac` `-commutative` `associate-/l` `unswap-sqr` `sqr-pow`
1×	`clear-num` `associate-/r*` `frac-2neg` `pow-prod-down` `div-inv`

Counts

4 → 127

Calls

4 calls:

111.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
29.0ms	(* (* x (pow sin 2.0)) x)
26.0ms	(* x (pow sin 2.0))
101.0ms	(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

series2.0s

Counts

4 → 12

Calls

4 calls:

827.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
294.0ms	(* (* x (pow sin 2.0)) x)
301.0ms	(* x (pow sin 2.0))
610.0ms	(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

simplify3.0s

Counts

139 → 139

Iterations

Iter	Nodes
done	5004
2	1482
1	434
0	178

prune1.4s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 13.7b

localize71.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))
0.6b	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
5.8b	(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
19.1b	(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

rewrite1.1s

Algorithm

rewrite-expression-head

Rules

416×	`add-exp-log`
343×	`prod-exp`
84×	`pow-to-exp` `pow-exp`
52×	`add-cbrt-cube`
43×	`div-exp`
29×	`cbrt-unprod`
11×	`add-sqr-sqrt` `-un-lft-identity` `associate-r*` `add-cube-cbrt`
9×	`associate-l`
6×	`pow1` `unpow-prod-down`
5×	`cbrt-undiv`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`times-frac` `-commutative` `associate-/l`
2×	`sqr-pow`
1×	`clear-num` `associate-/r*` `frac-2neg` `pow-prod-down` `div-inv`

Counts

4 → 198

Calls

4 calls:

48.0ms	(* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))
429.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
168.0ms	(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
391.0ms	(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

series2.4s

Counts

4 → 12

Calls

4 calls:

357.0ms	(* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))
1.0s	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
346.0ms	(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
735.0ms	(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

simplify4.4s

Counts

210 → 210

Iterations

Iter	Nodes
done	5004
2	2136
1	566
0	210

prune1.5s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 9.6b

localize69.0ms

Local error

Found 4 expressions with local error:

0.6b	(/ (cos (* 2.0 x)) (* (pow cos (/ 2.0 2)) (* (* (pow cos (/ 2.0 2)) x) (* x (pow sin 2.0)))))
5.5b	(* (pow cos (/ 2.0 2)) (* (* (pow cos (/ 2.0 2)) x) (* x (pow sin 2.0))))
8.1b	(* x (pow sin 2.0))
10.8b	(* (* (pow cos (/ 2.0 2)) x) (* x (pow sin 2.0)))

rewrite490.0ms

Algorithm

rewrite-expression-head

Rules

472×	`add-exp-log`
385×	`prod-exp`
91×	`pow-to-exp` `pow-exp`
61×	`add-cbrt-cube`
52×	`div-exp`
35×	`cbrt-unprod`
16×	`add-sqr-sqrt`
11×	`-un-lft-identity` `associate-l*` `add-cube-cbrt`
9×	`associate-r`
7×	`unpow-prod-down`
6×	`pow1` `cbrt-undiv`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`times-frac` `-commutative` `associate-/l` `unswap-sqr` `sqr-pow`
1×	`clear-num` `associate-/r*` `frac-2neg` `pow-prod-down` `div-inv`

Counts

4 → 215

Calls

4 calls:

157.0ms	(/ (cos (* 2.0 x)) (* (pow cos (/ 2.0 2)) (* (* (pow cos (/ 2.0 2)) x) (* x (pow sin 2.0)))))
201.0ms	(* (pow cos (/ 2.0 2)) (* (* (pow cos (/ 2.0 2)) x) (* x (pow sin 2.0))))
16.0ms	(* x (pow sin 2.0))
68.0ms	(* (* (pow cos (/ 2.0 2)) x) (* x (pow sin 2.0)))

series3.0s

Counts

4 → 12

Calls

4 calls:

1.0s	(/ (cos (* 2.0 x)) (* (pow cos (/ 2.0 2)) (* (* (pow cos (/ 2.0 2)) x) (* x (pow sin 2.0)))))
723.0ms	(* (pow cos (/ 2.0 2)) (* (* (pow cos (/ 2.0 2)) x) (* x (pow sin 2.0))))
356.0ms	(* x (pow sin 2.0))
840.0ms	(* (* (pow cos (/ 2.0 2)) x) (* x (pow sin 2.0)))

simplify4.4s

Counts

227 → 227

Iterations

Iter	Nodes
done	5046
2	2031
1	581
0	223

prune1.8s

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 8.8b

localize59.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))
0.6b	(/ (cos (* 2.0 x)) (* (pow cos (/ 2.0 2)) (* (* (pow cos (/ 2.0 2)) x) (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))))))
5.5b	(* (pow cos (/ 2.0 2)) (* (* (pow cos (/ 2.0 2)) x) (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))))
10.8b	(* (* (pow cos (/ 2.0 2)) x) (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))))

rewrite1.3s

Algorithm

rewrite-expression-head

Rules

1711×	`add-exp-log`
1564×	`prod-exp`
400×	`pow-to-exp` `pow-exp`
160×	`div-exp`
97×	`add-cbrt-cube`
62×	`cbrt-unprod`
10×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
9×	`associate-r` `associate-l`
8×	`cbrt-undiv`
6×	`pow1` `unpow-prod-down`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`times-frac` `-commutative` `associate-/l`
2×	`sqr-pow`
1×	`clear-num` `associate-/r*` `frac-2neg` `pow-prod-down` `div-inv`

Counts

4 → 478

Calls

4 calls:

75.0ms	(* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))
428.0ms	(/ (cos (* 2.0 x)) (* (pow cos (/ 2.0 2)) (* (* (pow cos (/ 2.0 2)) x) (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))))))
483.0ms	(* (pow cos (/ 2.0 2)) (* (* (pow cos (/ 2.0 2)) x) (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))))
168.0ms	(* (* (pow cos (/ 2.0 2)) x) (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))))

series2.9s

Counts

4 → 12

Calls

4 calls:

330.0ms	(* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))
1.0s	(/ (cos (* 2.0 x)) (* (pow cos (/ 2.0 2)) (* (* (pow cos (/ 2.0 2)) x) (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))))))
809.0ms	(* (pow cos (/ 2.0 2)) (* (* (pow cos (/ 2.0 2)) x) (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))))
750.0ms	(* (* (pow cos (/ 2.0 2)) x) (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))))

simplify5.2s

Counts

490 → 490

Iterations

Iter	Nodes
done	5018
2	2791
1	856
0	295

prune1.3s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 6.2b

regimes2.5s

Accuracy

15.7% (3.7b remaining)

Error of 9.1b against oracle of 5.4b and baseline of 9.8b

bsearch5.0ms

simplify13.0ms

Iterations

Iter	Nodes
done	37
1	37
0	27

end0.0ms

sample4.0s

Algorithm

intervals

Results

1.5s	8918×	body	80	valid
653.0ms	848×	body	1280	valid
522.0ms	300×	body	160	valid
459.0ms	944×	body	640	valid
296.0ms	563×	body	320	valid