Details

sample53.0ms

Algorithm

intervals

Results

16.0ms	269×	body	80	valid
8.0ms	24×	body	1280	valid
8.0ms	33×	body	640	valid
4.0ms	21×	body	320	valid
1.0ms	11×	body	160	valid

simplify40.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	27	8
1	68	8
2	243	8
3	1266	8
4	5001	8
done	5001	8

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.3b

localize13.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
3.6b	(* (* x (pow sin 2.0)) x)
10.1b	(* x (pow sin 2.0))
18.6b	(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

rewrite166.0ms

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

Counts

4 → 123

Calls

4 calls:

61.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
23.0ms	(* (* x (pow sin 2.0)) x)
12.0ms	(* x (pow sin 2.0))
63.0ms	(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

series893.0ms

Counts

4 → 12

Calls

4 calls:

320.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
152.0ms	(* (* x (pow sin 2.0)) x)
140.0ms	(* x (pow sin 2.0))
281.0ms	(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

simplify57.0ms

Counts

135 → 135

Iterations

Useful iterations: 1 (11.0ms)

Iter	Nodes	Cost
0	448	971
1	2063	815
2	5002	815
done	5002	815

prune297.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 14.3b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))
0.3b	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
3.6b	(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
18.6b	(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

rewrite514.0ms

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` `add-cube-cbrt` `-un-lft-identity` `associate-r*`
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×	`frac-2neg` `pow-prod-down` `clear-num` `associate-/r*` `div-inv`

Counts

4 → 194

Calls

4 calls:

28.0ms	(* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))
193.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
76.0ms	(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
201.0ms	(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

series927.0ms

Counts

4 → 12

Calls

4 calls:

150.0ms	(* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))
330.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
160.0ms	(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
288.0ms	(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

simplify90.0ms

Counts

206 → 206

Iterations

Useful iterations: 2 (71.0ms)

Iter	Nodes	Cost
0	603	2216
1	2821	1509
2	5002	1497
done	5002	1497

prune315.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 3.2b

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))) (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))))
0.3b	(/ (cos (* 2.0 x)) (* (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))) (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2)))))))
4.8b	(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
4.8b	(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

rewrite86.0ms

Algorithm

rewrite-expression-head

Rules

63×	`add-exp-log`
44×	`prod-exp`
21×	`add-cbrt-cube`
17×	`associate-l`
16×	`add-sqr-sqrt`
14×	`pow-to-exp` `add-cube-cbrt` `*-un-lft-identity` `pow-exp`
11×	`pow1`
8×	`cbrt-unprod`
6×	`unpow-prod-down`
5×	`associate-r`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`times-frac` `swap-sqr` `-commutative` `associate-/l`
2×	`cbrt-undiv` `div-exp` `sqr-pow`
1×	`pow2` `frac-2neg` `pow-plus` `pow-prod-down` `clear-num` `associate-/r*` `pow-sqr` `pow-prod-up` `div-inv` `unswap-sqr`

Counts

4 → 114

Calls

4 calls:

7.0ms	(* (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))) (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))))
16.0ms	(/ (cos (* 2.0 x)) (* (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))) (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2)))))))
27.0ms	(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
30.0ms	(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

series620.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(* (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))) (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))))
122.0ms	(/ (cos (* 2.0 x)) (* (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))) (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2)))))))
230.0ms	(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
229.0ms	(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

simplify48.0ms

Counts

126 → 126

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	325	1562
1	1244	1292
2	5001	1217
done	5001	1217

prune397.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.1b

localize17.0ms

Local error

Found 3 expressions with local error:

0.3b	(pow (fabs (* (pow (* (pow cos 1.0) (pow sin 1.0)) 1.0) x)) 2)
0.3b	(/ (cos (* 2.0 x)) (pow (fabs (* (pow (* (pow cos 1.0) (pow sin 1.0)) 1.0) x)) 2))
4.5b	(* (pow (* (pow cos 1.0) (pow sin 1.0)) 1.0) x)

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

35×	`add-exp-log`
27×	`add-sqr-sqrt`
24×	`add-cube-cbrt` `*-un-lft-identity` `times-frac`
21×	`prod-exp`
18×	`pow-exp`
16×	`unpow-prod-down`
9×	`pow-to-exp`
8×	`associate-/r*`
7×	`add-cbrt-cube` `sqr-pow`
5×	`associate-l` `unpow2`
4×	`pow1`
3×	`expm1-log1p-u` `pow-unpow` `div-exp` `associate-r` `log1p-expm1-u` `associate-/l*` `add-log-exp`
2×	`unswap-sqr`
1×	`cbrt-undiv` `pow-pow` `frac-2neg` `clear-num` `*-commutative` `cbrt-unprod` `div-inv`

Counts

3 → 104

Calls

3 calls:

3.0ms	(pow (fabs (* (pow (* (pow cos 1.0) (pow sin 1.0)) 1.0) x)) 2)
19.0ms	(/ (cos (* 2.0 x)) (pow (fabs (* (pow (* (pow cos 1.0) (pow sin 1.0)) 1.0) x)) 2))
20.0ms	(* (pow (* (pow cos 1.0) (pow sin 1.0)) 1.0) x)

series501.0ms

Counts

3 → 9

Calls

3 calls:

34.0ms	(pow (fabs (* (pow (* (pow cos 1.0) (pow sin 1.0)) 1.0) x)) 2)
118.0ms	(/ (cos (* 2.0 x)) (pow (fabs (* (pow (* (pow cos 1.0) (pow sin 1.0)) 1.0) x)) 2))
349.0ms	(* (pow (* (pow cos 1.0) (pow sin 1.0)) 1.0) x)

simplify46.0ms

Counts

113 → 113

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	342	1364
1	1157	1248
2	5002	1239
done	5002	1239

prune340.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

regimes280.0ms

Accuracy

18.1% (2.0b remaining)

Error of 2.2b against oracle of 0.1b and baseline of 2.6b

bsearch157.0ms

Steps

Iters	Range		Point
10	2.035644573190885e-159	1.2099787919689018e-141	3.0992080613360915e-150
8	-8.676455186232331e-186	-3.033725472305409e-188	-3.8997952595148316e-188

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	48
1	46	48
done	46	48

end0.0ms

sample1.6s

Algorithm

intervals

Results

537.0ms	8962×	body	80	valid
288.0ms	829×	body	1280	valid
228.0ms	957×	body	640	valid
115.0ms	593×	body	320	valid
41.0ms	317×	body	160	valid