Details

sample117.0ms

Algorithm

intervals

Results

37.0ms	288×	body	80	valid
20.0ms	28×	body	1280	valid
18.0ms	35×	body	640	valid
8.0ms	20×	body	320	valid
3.0ms	10×	body	160	valid

simplify980.0ms

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	1263	16
done	5000	16

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.6b

localize44.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
3.2b	(* (* x (pow sin 2.0)) x)
7.2b	(* x (pow sin 2.0))
18.7b	(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

rewrite171.0ms

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×	`cbrt-undiv` `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 → 115

Calls

4 calls:

76.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
17.0ms	(* (* x (pow sin 2.0)) x)
11.0ms	(* x (pow sin 2.0))
63.0ms	(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

series1.3s

Counts

4 → 12

Calls

4 calls:

477.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
207.0ms	(* (* x (pow sin 2.0)) x)
185.0ms	(* x (pow sin 2.0))
411.0ms	(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

simplify1.3s

Counts

127 → 127

Iterations

Useful iterations: 2 (433.0ms)

Iter	Nodes	Cost
0	166	1959
1	430	1809
2	2350	1563
done	5002	1563

prune699.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 15.3b

localize34.0ms

Local error

Found 4 expressions with local error:

0.2b	(cos (* 2.0 x))
0.5b	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
3.2b	(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
18.7b	(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

rewrite571.0ms

Algorithm

rewrite-expression-head

Rules

390×	`add-exp-log`
322×	`prod-exp`
77×	`pow-to-exp` `pow-exp`
47×	`add-cbrt-cube`
43×	`div-exp`
26×	`cbrt-unprod`
9×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
8×	`associate-l`
6×	`pow1`
5×	`cbrt-undiv`
4×	`associate-r` `add-log-exp`
3×	`unpow-prod-down` `times-frac` `associate-/l*`
2×	`*-commutative`
1×	`clear-num` `associate-/r*` `frac-2neg` `pow-prod-down` `div-inv` `sqr-pow`

Counts

4 → 163

Calls

4 calls:

11.0ms	(cos (* 2.0 x))
240.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
85.0ms	(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
222.0ms	(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

series1.1s

Counts

4 → 12

Calls

4 calls:

24.0ms	(cos (* 2.0 x))
431.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
192.0ms	(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
434.0ms	(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

simplify1.6s

Counts

175 → 175

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	182	4524
1	531	2693
2	2950	2359
done	5000	2341

prune656.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 10.0b

localize39.0ms

Local error

Found 4 expressions with local error:

3.2b	(* (* (pow cos (/ 2.0 2)) (* x (pow sin 2.0))) x)
4.6b	(* (pow cos (/ 2.0 2)) (* (* (pow cos (/ 2.0 2)) (* x (pow sin 2.0))) x))
6.9b	(* (pow cos (/ 2.0 2)) (* x (pow sin 2.0)))
7.2b	(* x (pow sin 2.0))

rewrite318.0ms

Algorithm

rewrite-expression-head

Rules

226×	`add-exp-log`
202×	`prod-exp`
50×	`pow-to-exp` `pow-exp`
34×	`add-cbrt-cube`
20×	`cbrt-unprod`
18×	`associate-l`
17×	`add-sqr-sqrt`
12×	`-un-lft-identity` `associate-r*` `add-cube-cbrt`
10×	`unpow-prod-down`
6×	`pow1`
4×	`*-commutative` `add-log-exp` `sqr-pow`
3×	`unswap-sqr`
1×	`pow-prod-down`

Counts

4 → 146

Calls

4 calls:

55.0ms	(* (* (pow cos (/ 2.0 2)) (* x (pow sin 2.0))) x)
205.0ms	(* (pow cos (/ 2.0 2)) (* (* (pow cos (/ 2.0 2)) (* x (pow sin 2.0))) x))
41.0ms	(* (pow cos (/ 2.0 2)) (* x (pow sin 2.0)))
9.0ms	(* x (pow sin 2.0))

series1.5s

Counts

4 → 12

Calls

4 calls:

461.0ms	(* (* (pow cos (/ 2.0 2)) (* x (pow sin 2.0))) x)
446.0ms	(* (pow cos (/ 2.0 2)) (* (* (pow cos (/ 2.0 2)) (* x (pow sin 2.0))) x))
353.0ms	(* (pow cos (/ 2.0 2)) (* x (pow sin 2.0)))
229.0ms	(* x (pow sin 2.0))

simplify1.6s

Counts

158 → 158

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	158	2886
1	441	2530
2	2210	1898
done	5000	1870

prune739.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 8.4b

localize59.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ (cos (* 2.0 x)) (* (pow cos (/ 2.0 2)) (* (* (pow cos (/ 2.0 2)) (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))) x)))
3.2b	(* (* (pow cos (/ 2.0 2)) (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))) x)
4.6b	(* (pow cos (/ 2.0 2)) (* (* (pow cos (/ 2.0 2)) (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))) x))
6.9b	(* (pow cos (/ 2.0 2)) (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))))

rewrite1.6s

Algorithm

rewrite-expression-head

Rules

1442×	`add-exp-log`
1342×	`prod-exp`
354×	`pow-to-exp` `pow-exp`
124×	`div-exp`
74×	`add-cbrt-cube`
46×	`cbrt-unprod`
15×	`associate-l`
11×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
6×	`pow1` `cbrt-undiv` `unpow-prod-down`
5×	`associate-r`
4×	`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 → 406

Calls

4 calls:

607.0ms	(/ (cos (* 2.0 x)) (* (pow cos (/ 2.0 2)) (* (* (pow cos (/ 2.0 2)) (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))) x)))
210.0ms	(* (* (pow cos (/ 2.0 2)) (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))) x)
707.0ms	(* (pow cos (/ 2.0 2)) (* (* (pow cos (/ 2.0 2)) (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))) x))
78.0ms	(* (pow cos (/ 2.0 2)) (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))))

series1.7s

Counts

4 → 12

Calls

4 calls:

567.0ms	(/ (cos (* 2.0 x)) (* (pow cos (/ 2.0 2)) (* (* (pow cos (/ 2.0 2)) (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))) x)))
371.0ms	(* (* (pow cos (/ 2.0 2)) (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))) x)
474.0ms	(* (pow cos (/ 2.0 2)) (* (* (pow cos (/ 2.0 2)) (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))) x))
329.0ms	(* (pow cos (/ 2.0 2)) (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))))

simplify1.7s

Counts

418 → 418

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	254	14097
1	795	8853
2	3697	6175
done	5001	6099

prune732.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 5.5b

regimes1.4s

Accuracy

0% (2.9b remaining)

Error of 8.6b against oracle of 5.7b and baseline of 8.6b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	32
1	22	32
done	22	32

end0.0ms

sample4.5s

Algorithm

intervals

Results

1.4s	9036×	body	80	valid
1.1s	576×	body	320	valid
674.0ms	830×	body	1280	valid
591.0ms	998×	body	640	valid
100.0ms	326×	body	160	valid