Details

sample104.0ms

Algorithm

intervals

Results

42.0ms	304×	body	80	valid
14.0ms	32×	body	640	valid
12.0ms	23×	body	1280	valid
7.0ms	23×	body	320	valid
2.0ms	9×	body	160	valid

simplify3.4s

Counts

1 → 1

Iterations

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

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.6b

localize31.0ms

Local error

Found 4 expressions with local error:

0.7b	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
3.0b	(* (* x (pow sin 2.0)) x)
7.0b	(* x (pow sin 2.0))
20.7b	(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

rewrite186.0ms

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` `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 → 123

Calls

4 calls:

72.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
26.0ms	(* (* x (pow sin 2.0)) x)
14.0ms	(* x (pow sin 2.0))
66.0ms	(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

series1.2s

Counts

4 → 12

Calls

4 calls:

429.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
202.0ms	(* (* x (pow sin 2.0)) x)
194.0ms	(* x (pow sin 2.0))
376.0ms	(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

simplify1.6s

Counts

135 → 135

Iterations

Iter	Nodes
done	5000
2	1436
1	432
0	174

prune790.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 14.2b

localize49.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))
0.7b	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
3.0b	(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
20.7b	(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

rewrite551.0ms

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` `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 → 194

Calls

4 calls:

23.0ms	(* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))
211.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
77.0ms	(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
228.0ms	(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

series1.1s

Counts

4 → 12

Calls

4 calls:

209.0ms	(* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))
412.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
188.0ms	(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
330.0ms	(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

simplify1.6s

Counts

206 → 206

Iterations

Iter	Nodes
done	5001
2	2086
1	564
0	206

prune632.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 10.6b

localize28.0ms

Local error

Found 4 expressions with local error:

0.7b	(/ (cos (* 2.0 x)) (* (pow cos (/ 2.0 2)) (* (* (pow cos (/ 2.0 2)) x) (* x (pow sin 2.0)))))
5.6b	(* (pow cos (/ 2.0 2)) (* (* (pow cos (/ 2.0 2)) x) (* x (pow sin 2.0))))
7.0b	(* x (pow sin 2.0))
8.5b	(* (* (pow cos (/ 2.0 2)) x) (* x (pow sin 2.0)))

rewrite222.0ms

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` `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 → 211

Calls

4 calls:

91.0ms	(/ (cos (* 2.0 x)) (* (pow cos (/ 2.0 2)) (* (* (pow cos (/ 2.0 2)) x) (* x (pow sin 2.0)))))
79.0ms	(* (pow cos (/ 2.0 2)) (* (* (pow cos (/ 2.0 2)) x) (* x (pow sin 2.0))))
9.0ms	(* x (pow sin 2.0))
30.0ms	(* (* (pow cos (/ 2.0 2)) x) (* x (pow sin 2.0)))

series1.2s

Counts

4 → 12

Calls

4 calls:

354.0ms	(/ (cos (* 2.0 x)) (* (pow cos (/ 2.0 2)) (* (* (pow cos (/ 2.0 2)) x) (* x (pow sin 2.0)))))
316.0ms	(* (pow cos (/ 2.0 2)) (* (* (pow cos (/ 2.0 2)) x) (* x (pow sin 2.0))))
182.0ms	(* x (pow sin 2.0))
372.0ms	(* (* (pow cos (/ 2.0 2)) x) (* x (pow sin 2.0)))

simplify1.9s

Counts

223 → 223

Iterations

Iter	Nodes
done	5022
2	2132
1	588
0	219

prune862.0ms

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 8.8b

localize38.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))
0.7b	(/ (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))))))
5.6b	(* (pow cos (/ 2.0 2)) (* (* (pow cos (/ 2.0 2)) x) (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))))
8.5b	(* (* (pow cos (/ 2.0 2)) x) (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))))

rewrite651.0ms

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` `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 → 474

Calls

4 calls:

26.0ms	(* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))
235.0ms	(/ (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))))))
244.0ms	(* (pow cos (/ 2.0 2)) (* (* (pow cos (/ 2.0 2)) x) (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))))
87.0ms	(* (* (pow cos (/ 2.0 2)) x) (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))))

series1.5s

Counts

4 → 12

Calls

4 calls:

237.0ms	(* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))
443.0ms	(/ (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))))))
418.0ms	(* (pow cos (/ 2.0 2)) (* (* (pow cos (/ 2.0 2)) x) (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))))
406.0ms	(* (* (pow cos (/ 2.0 2)) x) (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))))

simplify2.5s

Counts

486 → 486

Iterations

Iter	Nodes
done	5012
2	2790
1	843
0	291

prune815.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 6.4b

regimes1.2s

Accuracy

15.5% (3.5b remaining)

Error of 9.2b against oracle of 5.7b and baseline of 9.9b

bsearch4.0ms

simplify15.0ms

Iterations

Iter	Nodes
done	43
1	43
0	29

end0.0ms

sample4.4s

Algorithm

intervals

Results

1.8s	9037×	body	80	valid
1.0s	790×	body	1280	valid
490.0ms	982×	body	640	valid
318.0ms	608×	body	320	valid
76.0ms	316×	body	160	valid