Details

sample72.0ms

Algorithm

intervals

Results

24.0ms	304×	body	80	valid
10.0ms	32×	body	640	valid
10.0ms	23×	body	1280	valid
6.0ms	23×	body	320	valid
2.0ms	9×	body	160	valid

simplify1.5s

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: 28.6b

localize31.0ms

Local error

Found 4 expressions with local error:

0.7b	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
3.0b	(* (* x (pow sin 2.0)) x)
7.0b	(* x (pow sin 2.0))
20.7b	(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

rewrite158.0ms

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:

50.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
22.0ms	(* (* 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:

433.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
229.0ms	(* (* x (pow sin 2.0)) x)
194.0ms	(* x (pow sin 2.0))
308.0ms	(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

simplify2.2s

Counts

135 → 135

Iterations

Iter	Nodes
done	5001
2	2402
1	448
0	174

prune612.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 14.2b

localize50.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))
0.7b	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
3.0b	(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
20.7b	(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

rewrite558.0ms

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:

36.0ms	(* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))
190.0ms	(/ (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)
239.0ms	(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

series998.0ms

Counts

4 → 12

Calls

4 calls:

167.0ms	(* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))
306.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
171.0ms	(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
353.0ms	(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

simplify2.7s

Counts

206 → 206

Iterations

Iter	Nodes
done	5002
2	3801
1	588
0	206

prune704.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 5.7b

localize44.0ms

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))))
0.7b	(/ (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))))))
5.6b	(* (pow cos (/ 2.0 2)) (* (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2)))) (* x (pow sin (/ 2.0 2)))))
6.4b	(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

rewrite640.0ms

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:

96.0ms	(* (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2)))) (* x (pow sin (/ 2.0 2))))
198.0ms	(/ (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))))))
234.0ms	(* (pow cos (/ 2.0 2)) (* (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2)))) (* x (pow sin (/ 2.0 2)))))
21.0ms	(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

series1.5s

Counts

4 → 12

Calls

4 calls:

388.0ms	(* (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2)))) (* x (pow sin (/ 2.0 2))))
399.0ms	(/ (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))))))
393.0ms	(* (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))))

simplify2.8s

Counts

486 → 486

Iterations

Iter	Nodes
done	5001
2	3692
1	870
0	274

prune991.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 3.3b

localize53.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (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))))
5.9b	(/ (/ (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)))))
6.4b	(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

rewrite308.0ms

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:

24.0ms	(/ (cos (* 2.0 x)) (pow cos (/ 2.0 2)))
96.0ms	(* (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2)))) (* x (pow sin (/ 2.0 2))))
115.0ms	(/ (/ (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)))))
28.0ms	(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

series1.4s

Counts

4 → 12

Calls

4 calls:

282.0ms	(/ (cos (* 2.0 x)) (pow cos (/ 2.0 2)))
375.0ms	(* (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2)))) (* x (pow sin (/ 2.0 2))))
469.0ms	(/ (/ (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)))))
294.0ms	(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

simplify1.7s

Counts

452 → 452

Iterations

Iter	Nodes
done	5000
1	1204
0	359

prune1.4s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

regimes394.0ms

Accuracy

0% (2.5b remaining)

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

bsearch0.0ms

simplify6.0ms

Iterations

Iter	Nodes
done	22
1	22
0	16

end0.0ms

sample3.4s

Algorithm

intervals

Results

1.6s	9037×	body	80	valid
552.0ms	982×	body	640	valid
494.0ms	790×	body	1280	valid
304.0ms	608×	body	320	valid
65.0ms	316×	body	160	valid