Details

sample113.0ms

Algorithm

intervals

Results

42.0ms	285×	body	80	valid
21.0ms	36×	body	1280	valid
10.0ms	24×	body	640	valid
6.0ms	18×	body	320	valid
2.0ms	9×	body	160	valid

simplify1.6s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
4	1263
3	241
2	67
1	26
0	12

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.1b

localize26.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
4.0b	(* (* x (pow sin 2.0)) x)
7.1b	(* x (pow sin 2.0))
18.4b	(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

rewrite188.0ms

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×	`cbrt-undiv` `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 → 115

Calls

4 calls:

74.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
26.0ms	(* (* x (pow sin 2.0)) x)
15.0ms	(* 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:

450.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
184.0ms	(* (* x (pow sin 2.0)) x)
185.0ms	(* x (pow sin 2.0))
383.0ms	(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

simplify1.8s

Counts

127 → 127

Iterations

Iter	Nodes
done	5002
2	2350
1	430
0	166

prune556.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 11.3b

localize32.0ms

Local error

Found 4 expressions with local error:

4.0b	(* (* x (pow sin 2.0)) x)
5.8b	(* (pow cos (/ 2.0 2)) (* (* x (pow sin 2.0)) x))
6.4b	(* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* (* x (pow sin 2.0)) x)))
7.1b	(* x (pow sin 2.0))

rewrite313.0ms

Algorithm

rewrite-expression-head

Rules

226×	`add-exp-log`
202×	`prod-exp`
50×	`pow-to-exp` `pow-exp`
34×	`add-cbrt-cube`
20×	`cbrt-unprod`
18×	`associate-l`
17×	`add-sqr-sqrt`
12×	`-un-lft-identity` `associate-r*` `add-cube-cbrt`
10×	`unpow-prod-down`
6×	`pow1`
4×	`*-commutative` `add-log-exp` `sqr-pow`
3×	`unswap-sqr`
1×	`pow-prod-down`

Counts

4 → 146

Calls

4 calls:

34.0ms	(* (* x (pow sin 2.0)) x)
84.0ms	(* (pow cos (/ 2.0 2)) (* (* x (pow sin 2.0)) x))
163.0ms	(* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* (* x (pow sin 2.0)) x)))
19.0ms	(* x (pow sin 2.0))

series1.1s

Counts

4 → 12

Calls

4 calls:

233.0ms	(* (* x (pow sin 2.0)) x)
348.0ms	(* (pow cos (/ 2.0 2)) (* (* x (pow sin 2.0)) x))
367.0ms	(* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* (* x (pow sin 2.0)) x)))
190.0ms	(* x (pow sin 2.0))

simplify1.7s

Counts

158 → 158

Iterations

Iter	Nodes
done	5001
2	2202
1	429
0	157

prune841.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 8.9b

localize37.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ (cos (* 2.0 x)) (* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))))
4.0b	(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
5.8b	(* (pow cos (/ 2.0 2)) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))
6.4b	(* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))

rewrite1.7s

Algorithm

rewrite-expression-head

Rules

1410×	`add-exp-log`
1300×	`prod-exp`
338×	`pow-to-exp` `pow-exp`
130×	`div-exp`
74×	`add-cbrt-cube`
46×	`cbrt-unprod`
15×	`associate-l`
11×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
6×	`pow1` `cbrt-undiv` `unpow-prod-down`
5×	`associate-r`
4×	`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 → 394

Calls

4 calls:

647.0ms	(/ (cos (* 2.0 x)) (* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))))
78.0ms	(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
292.0ms	(* (pow cos (/ 2.0 2)) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))
678.0ms	(* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))

series1.5s

Counts

4 → 12

Calls

4 calls:

417.0ms	(/ (cos (* 2.0 x)) (* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))))
211.0ms	(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
411.0ms	(* (pow cos (/ 2.0 2)) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))
411.0ms	(* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))

simplify2.9s

Counts

406 → 406

Iterations

Iter	Nodes
done	5001
2	3642
1	755
0	251

prune801.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 6.8b

localize55.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* x (pow sin (/ 2.0 2))) (* x (pow sin (/ 2.0 2))))
0.5b	(/ (cos (* 2.0 x)) (* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* (* x (pow sin (/ 2.0 2))) (* x (pow sin (/ 2.0 2)))))))
5.8b	(* (pow cos (/ 2.0 2)) (* (* x (pow sin (/ 2.0 2))) (* x (pow sin (/ 2.0 2)))))
6.4b	(* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* (* x (pow sin (/ 2.0 2))) (* x (pow sin (/ 2.0 2))))))

rewrite875.0ms

Algorithm

rewrite-expression-head

Rules

1691×	`add-exp-log`
1549×	`prod-exp`
399×	`pow-to-exp` `pow-exp`
157×	`div-exp`
92×	`add-cbrt-cube`
59×	`cbrt-unprod`
15×	`associate-l`
12×	`add-sqr-sqrt`
11×	`pow1`
10×	`*-un-lft-identity` `add-cube-cbrt`
7×	`cbrt-undiv` `unpow-prod-down`
4×	`add-log-exp`
3×	`times-frac` `associate-r` `-commutative` `associate-/l` `unswap-sqr` `sqr-pow`
1×	`pow2` `clear-num` `associate-/r*` `frac-2neg` `pow-plus` `swap-sqr` `pow-prod-down` `pow-sqr` `pow-prod-up` `div-inv`

Counts

4 → 470

Calls

4 calls:

35.0ms	(* (* x (pow sin (/ 2.0 2))) (* x (pow sin (/ 2.0 2))))
339.0ms	(/ (cos (* 2.0 x)) (* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* (* x (pow sin (/ 2.0 2))) (* x (pow sin (/ 2.0 2)))))))
135.0ms	(* (pow cos (/ 2.0 2)) (* (* x (pow sin (/ 2.0 2))) (* x (pow sin (/ 2.0 2)))))
297.0ms	(* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* (* x (pow sin (/ 2.0 2))) (* x (pow sin (/ 2.0 2))))))

series1.5s

Counts

4 → 12

Calls

4 calls:

215.0ms	(* (* x (pow sin (/ 2.0 2))) (* x (pow sin (/ 2.0 2))))
463.0ms	(/ (cos (* 2.0 x)) (* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* (* x (pow sin (/ 2.0 2))) (* x (pow sin (/ 2.0 2)))))))
416.0ms	(* (pow cos (/ 2.0 2)) (* (* x (pow sin (/ 2.0 2))) (* x (pow sin (/ 2.0 2)))))
364.0ms	(* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* (* x (pow sin (/ 2.0 2))) (* x (pow sin (/ 2.0 2))))))

simplify2.7s

Counts

482 → 482

Iterations

Iter	Nodes
done	5000
2	2859
1	773
0	264

prune845.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 3.9b

regimes866.0ms

Accuracy

0% (2.2b remaining)

Error of 6.1b against oracle of 3.9b and baseline of 6.1b

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
done	20
1	20
0	15

end0.0ms

sample4.4s

Algorithm

intervals

Results

2.1s	9169×	body	80	valid
664.0ms	1033×	body	640	valid
602.0ms	802×	body	1280	valid
239.0ms	578×	body	320	valid
84.0ms	329×	body	160	valid