Details

sample96.0ms

Algorithm

intervals

Results

27.0ms	272×	body	80	valid
21.0ms	14×	body	320	valid
17.0ms	31×	body	1280	valid
9.0ms	24×	body	640	valid
2.0ms	11×	body	160	valid

simplify3.5s

Counts

1 → 1

Iterations

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

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.5b

localize22.0ms

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))

rewrite154.0ms

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:

49.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
18.0ms	(* (* x (pow sin 2.0)) x)
9.0ms	(* x (pow sin 2.0))
73.0ms	(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

series1.2s

Counts

4 → 12

Calls

4 calls:

453.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
196.0ms	(* (* x (pow sin 2.0)) x)
177.0ms	(* x (pow sin 2.0))
399.0ms	(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

simplify1.7s

Counts

135 → 135

Iterations

Iter	Nodes
done	5000
2	1436
1	432
0	174

prune741.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 11.5b

localize30.0ms

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))

rewrite615.0ms

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:

32.0ms	(* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))
264.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
73.0ms	(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
234.0ms	(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

series1.2s

Counts

4 → 12

Calls

4 calls:

200.0ms	(* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))
433.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
217.0ms	(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
374.0ms	(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

simplify2.0s

Counts

206 → 206

Iterations

Iter	Nodes
done	5001
2	2086
1	564
0	206

prune604.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 6.8b

localize33.0ms

Local error

Found 3 expressions with local error:

0.3b

(* (* x (pow sin (/ 2.0 2))) (* x (pow sin (/ 2.0 2))))

0.6b

(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin (/ 2.0 2))) (* x (pow sin (/ 2.0 2))))))

14.6b

(* (pow cos 2.0) (* (* x (pow sin (/ 2.0 2))) (* x (pow sin (/ 2.0 2)))))

rewrite308.0ms

Algorithm

rewrite-expression-head

Rules

466×	`add-exp-log`
382×	`prod-exp`
90×	`pow-to-exp` `pow-exp`
58×	`add-cbrt-cube`
52×	`div-exp`
34×	`cbrt-unprod`
10×	`pow1`
9×	`add-sqr-sqrt`
8×	`associate-l`
7×	`*-un-lft-identity` `add-cube-cbrt`
6×	`cbrt-undiv`
4×	`unpow-prod-down`
3×	`expm1-log1p-u` `times-frac` `log1p-expm1-u` `associate-/l*` `add-log-exp` `unswap-sqr`
2×	`associate-r` `*-commutative` `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

3 → 192

Calls

3 calls:

49.0ms

(* (* x (pow sin (/ 2.0 2))) (* x (pow sin (/ 2.0 2))))

115.0ms

(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin (/ 2.0 2))) (* x (pow sin (/ 2.0 2))))))

131.0ms

(* (pow cos 2.0) (* (* x (pow sin (/ 2.0 2))) (* x (pow sin (/ 2.0 2)))))

series1.0s

Counts

3 → 9

Calls

3 calls:

221.0ms

(* (* x (pow sin (/ 2.0 2))) (* x (pow sin (/ 2.0 2))))

418.0ms

(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin (/ 2.0 2))) (* x (pow sin (/ 2.0 2))))))

380.0ms

(* (pow cos 2.0) (* (* x (pow sin (/ 2.0 2))) (* x (pow sin (/ 2.0 2)))))

simplify2.1s

Counts

201 → 201

Iterations

Iter	Nodes
done	5001
2	1599
1	481
0	180

prune567.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 1.7b

localize32.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2)))) (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2)))))
0.6b	(/ (cos (* 2.0 x)) (* (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2)))) (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))))
4.0b	(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
4.0b	(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

rewrite322.0ms

Algorithm

rewrite-expression-head

Rules

1631×	`add-exp-log`
1472×	`prod-exp`
378×	`pow-to-exp` `pow-exp`
170×	`div-exp`
97×	`add-cbrt-cube`
60×	`cbrt-unprod`
15×	`associate-l`
11×	`pow1`
10×	`add-sqr-sqrt` `cbrt-undiv` `*-un-lft-identity` `add-cube-cbrt`
6×	`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×	`pow2` `clear-num` `associate-/r*` `frac-2neg` `pow-plus` `swap-sqr` `pow-prod-down` `pow-sqr` `pow-prod-up` `div-inv`

Counts

4 → 459

Calls

4 calls:

112.0ms	(* (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2)))) (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2)))))
106.0ms	(/ (cos (* 2.0 x)) (* (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2)))) (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))))
25.0ms	(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
26.0ms	(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

series1.6s

Counts

4 → 12

Calls

4 calls:

470.0ms	(* (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2)))) (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2)))))
489.0ms	(/ (cos (* 2.0 x)) (* (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2)))) (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))))
308.0ms	(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
358.0ms	(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

simplify2.5s

Counts

471 → 471

Iterations

Iter	Nodes
done	5080
2	2043
1	678
0	242

prune758.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 1.2b

regimes861.0ms

Accuracy

0% (0.3b remaining)

Error of 2.6b against oracle of 2.3b and baseline of 2.6b

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	17
1	17
0	14

end0.0ms

sample3.6s

Algorithm

intervals

Results

1.2s	9044×	body	80	valid
954.0ms	1001×	body	640	valid
627.0ms	852×	body	1280	valid
297.0ms	601×	body	320	valid
66.0ms	304×	body	160	valid