Details

sample82.0ms

Algorithm

intervals

Results

26.0ms	272×	body	80	valid
19.0ms	31×	body	1280	valid
9.0ms	24×	body	640	valid
4.0ms	14×	body	320	valid
2.0ms	11×	body	160	valid

simplify1.5s

Counts

1 → 1

Iterations

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

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.5b

localize31.0ms

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)
9.6b	(* x (pow sin 2.0))
14.6b	(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

rewrite199.0ms

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:

76.0ms	(/ (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))
78.0ms	(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

series1.1s

Counts

4 → 12

Calls

4 calls:

380.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
191.0ms	(* (* x (pow sin 2.0)) x)
145.0ms	(* x (pow sin 2.0))
342.0ms	(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

simplify1.9s

Counts

135 → 135

Iterations

Iter	Nodes
done	5001
2	2402
1	448
0	174

prune721.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 11.2b

localize43.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* 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)
14.6b	(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

rewrite569.0ms

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:

33.0ms	(* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))
219.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
62.0ms	(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
238.0ms	(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

series1.1s

Counts

4 → 12

Calls

4 calls:

183.0ms	(* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))
415.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
175.0ms	(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
309.0ms	(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

simplify2.6s

Counts

206 → 206

Iterations

Iter	Nodes
done	5002
2	3801
1	588
0	206

prune726.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 3.1b

localize59.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2)))) (* x (pow sin (/ 2.0 2))))
0.6b	(/ (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))))))
4.0b	(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
4.1b	(* (pow cos (/ 2.0 2)) (* (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2)))) (* x (pow sin (/ 2.0 2)))))

rewrite646.0ms

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`
15×	`associate-l`
10×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
8×	`cbrt-undiv`
6×	`pow1` `unpow-prod-down`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`times-frac` `associate-r` `-commutative` `associate-/l`
2×	`sqr-pow`
1×	`clear-num` `associate-/r*` `frac-2neg` `pow-prod-down` `div-inv`

Counts

4 → 474

Calls

4 calls:

88.0ms	(* (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2)))) (* x (pow sin (/ 2.0 2))))
222.0ms	(/ (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))))))
44.0ms	(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
234.0ms	(* (pow cos (/ 2.0 2)) (* (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2)))) (* x (pow sin (/ 2.0 2)))))

series1.7s

Counts

4 → 12

Calls

4 calls:

405.0ms	(* (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2)))) (* x (pow sin (/ 2.0 2))))
468.0ms	(/ (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))))))
319.0ms	(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
474.0ms	(* (pow cos (/ 2.0 2)) (* (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2)))) (* x (pow sin (/ 2.0 2)))))

simplify2.6s

Counts

486 → 486

Iterations

Iter	Nodes
done	5000
2	3726
1	875
0	274

prune702.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 1.3b

localize31.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (cos (* 2.0 x)) (pow cos (/ 2.0 2)))
0.2b	(* (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2)))) (* x (pow sin (/ 2.0 2))))
4.0b	(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
4.3b	(/ (/ (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)))))

rewrite279.0ms

Algorithm

rewrite-expression-head

Rules

1287×	`add-exp-log`
896×	`prod-exp`
374×	`div-exp`
266×	`pow-to-exp` `pow-exp`
97×	`add-cbrt-cube`
88×	`times-frac`
50×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
48×	`cbrt-unprod`
33×	`unpow-prod-down`
28×	`associate-/l*`
22×	`cbrt-undiv`
11×	`sqr-pow`
8×	`associate-/r` `associate-l*`
6×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u` `div-inv` `add-log-exp`
2×	`clear-num` `frac-2neg` `associate-r` `*-commutative`
1×	`pow-prod-down` `associate-/l/`

Counts

4 → 440

Calls

4 calls:

12.0ms	(/ (cos (* 2.0 x)) (pow cos (/ 2.0 2)))
91.0ms	(* (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2)))) (* x (pow sin (/ 2.0 2))))
36.0ms	(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
89.0ms	(/ (/ (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)))))

series1.5s

Counts

4 → 12

Calls

4 calls:

278.0ms	(/ (cos (* 2.0 x)) (pow cos (/ 2.0 2)))
428.0ms	(* (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2)))) (* x (pow sin (/ 2.0 2))))
342.0ms	(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
427.0ms	(/ (/ (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)))))

simplify1.6s

Counts

452 → 452

Iterations

Iter	Nodes
done	5000
1	1208
0	359

prune1.4s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 1.2b

regimes786.0ms

Accuracy

0% (0.6b remaining)

Error of 2.8b against oracle of 2.3b and baseline of 2.8b

bsearch0.0ms

simplify7.0ms

Iterations

Iter	Nodes
done	22
1	22
0	18

end0.0ms

sample4.2s

Algorithm

intervals

Results

2.1s	9044×	body	80	valid
643.0ms	1001×	body	640	valid
637.0ms	852×	body	1280	valid
201.0ms	601×	body	320	valid
74.0ms	304×	body	160	valid