Details

sample80.0ms

Algorithm

intervals

Results

29.0ms	293×	body	80	valid
11.0ms	21×	body	1280	valid
9.0ms	22×	body	640	valid
5.0ms	17×	body	320	valid
2.0ms	12×	body	160	valid

simplify2.0s

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	16
1	26	16
2	67	16
3	241	16
4	1097	16
done	5000	16

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.9b

localize16.0ms

Local error

Found 4 expressions with local error:

0.8b	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
5.7b	(* (* x (pow sin 2.0)) x)
8.2b	(* x (pow sin 2.0))
15.1b	(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

rewrite231.0ms

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:

81.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
37.0ms	(* (* x (pow sin 2.0)) x)
20.0ms	(* x (pow sin 2.0))
85.0ms	(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

series1.1s

Counts

4 → 12

Calls

4 calls:

377.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
171.0ms	(* (* x (pow sin 2.0)) x)
153.0ms	(* x (pow sin 2.0))
428.0ms	(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

simplify979.0ms

Counts

135 → 135

Iterations

Useful iterations: 2 (278.0ms)

Iter	Nodes	Cost
0	179	2045
1	421	1897
2	1445	1617
done	5000	1617

prune441.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 13.4b

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))
0.8b	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
5.7b	(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
15.1b	(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

rewrite812.0ms

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:

57.0ms	(* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))
300.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
108.0ms	(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
318.0ms	(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

series1.3s

Counts

4 → 12

Calls

4 calls:

201.0ms	(* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))
491.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
199.0ms	(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
414.0ms	(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

simplify1.3s

Counts

206 → 206

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	211	5143
1	545	3013
2	2109	2569
done	5000	2565

prune407.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 9.5b

localize36.0ms

Local error

Found 3 expressions with local error:

0.3b

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

0.8b

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

15.1b

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

rewrite394.0ms

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

Counts

3 → 184

Calls

3 calls:

51.0ms

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

153.0ms

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

168.0ms

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

series1.1s

Counts

3 → 9

Calls

3 calls:

220.0ms

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

500.0ms

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

407.0ms

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

simplify1.3s

Counts

193 → 193

Iterations

Useful iterations: 2 (452.0ms)

Iter	Nodes	Cost
0	188	5240
1	480	3102
2	1864	2616
done	5000	2616

prune332.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 7.2b

localize38.0ms

Local error

Found 3 expressions with local error:

0.8b

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

3.5b

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

9.6b

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

rewrite325.0ms

Algorithm

rewrite-expression-head

Rules

455×	`add-exp-log`
371×	`prod-exp`
89×	`pow-to-exp` `pow-exp`
58×	`add-cbrt-cube`
53×	`div-exp`
33×	`cbrt-unprod`
8×	`associate-l`
7×	`cbrt-undiv` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
5×	`pow1`
3×	`expm1-log1p-u` `unpow-prod-down` `times-frac` `log1p-expm1-u` `associate-/l*` `add-log-exp`
2×	`associate-r` `*-commutative`
1×	`frac-2neg` `pow-prod-down` `clear-num` `associate-/r*` `div-inv` `sqr-pow`

Counts

3 → 182

Calls

3 calls:

133.0ms

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

115.0ms

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

45.0ms

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

series1.2s

Counts

3 → 9

Calls

3 calls:

451.0ms

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

437.0ms

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

320.0ms

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

simplify1.5s

Counts

191 → 191

Iterations

Useful iterations: 2 (542.0ms)

Iter	Nodes	Cost
0	191	5082
1	510	3288
2	1910	2764
done	5000	2764

prune307.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 3.0b

regimes385.0ms

Accuracy

0% (2.1b remaining)

Error of 6.8b against oracle of 4.8b and baseline of 6.8b

bsearch0.0ms

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	16	32
1	20	32
done	20	32

end0.0ms

sample4.2s

Algorithm

intervals

Results

1.6s	9128×	body	80	valid
1.0s	788×	body	1280	valid
687.0ms	950×	body	640	valid
249.0ms	611×	body	320	valid
65.0ms	293×	body	160	valid