Details

sample134.0ms

Algorithm

intervals

Results

57.0ms	288×	body	80	valid
19.0ms	28×	body	1280	valid
17.0ms	35×	body	640	valid
7.0ms	20×	body	320	valid
3.0ms	10×	body	160	valid

simplify986.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	12	16
1	26	16
2	67	16
3	241	16
4	1263	16
done	5000	16

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.6b

localize29.0ms

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))

rewrite599.0ms

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:

89.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
33.0ms	(* (* x (pow sin 2.0)) x)
17.0ms	(* x (pow sin 2.0))
455.0ms	(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

series1.3s

Counts

4 → 12

Calls

4 calls:

499.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
230.0ms	(* (* x (pow sin 2.0)) x)
214.0ms	(* x (pow sin 2.0))
369.0ms	(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

simplify1.5s

Counts

135 → 135

Iterations

Useful iterations: 2 (426.0ms)

Iter	Nodes	Cost
0	174	2045
1	448	1895
2	2402	1649
done	5001	1649

prune686.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 15.3b

localize47.0ms

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))

rewrite638.0ms

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×	`expm1-log1p-u` `associate-r` `log1p-expm1-u` `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 → 171

Calls

4 calls:

11.0ms	(cos (* 2.0 x))
249.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
94.0ms	(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
264.0ms	(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

series1.2s

Counts

4 → 12

Calls

4 calls:

15.0ms	(cos (* 2.0 x))
517.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
242.0ms	(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
399.0ms	(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

simplify1.6s

Counts

183 → 183

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	190	4656
1	543	2776
2	3078	2442
done	5002	2424

prune585.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 13.7b

localize35.0ms

Local error

Found 4 expressions with local error:

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

rewrite268.0ms

Algorithm

rewrite-expression-head

Rules

467×	`add-exp-log`
382×	`prod-exp`
90×	`pow-to-exp` `pow-exp`
59×	`add-cbrt-cube`
52×	`div-exp`
34×	`cbrt-unprod`
8×	`add-sqr-sqrt` `-un-lft-identity` `associate-l*` `add-cube-cbrt`
6×	`pow1` `cbrt-undiv`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`unpow-prod-down` `times-frac` `associate-/l*`
2×	`associate-r` `*-commutative`
1×	`clear-num` `associate-/r*` `frac-2neg` `pow-prod-down` `div-inv` `sqr-pow`

Counts

4 → 193

Calls

4 calls:

31.0ms	(* (* x (pow sin (/ 2.0 2))) (* (pow sin (/ 2.0 2)) x))
5.0ms	(cos (* 2.0 x))
112.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin (/ 2.0 2))) (* (pow sin (/ 2.0 2)) x))))
106.0ms	(* (pow cos 2.0) (* (* x (pow sin (/ 2.0 2))) (* (pow sin (/ 2.0 2)) x)))

series1.1s

Counts

4 → 12

Calls

4 calls:

241.0ms	(* (* x (pow sin (/ 2.0 2))) (* (pow sin (/ 2.0 2)) x))
14.0ms	(cos (* 2.0 x))
485.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin (/ 2.0 2))) (* (pow sin (/ 2.0 2)) x))))
343.0ms	(* (pow cos 2.0) (* (* x (pow sin (/ 2.0 2))) (* (pow sin (/ 2.0 2)) x)))

simplify1.6s

Counts

205 → 205

Iterations

Useful iterations: 2 (526.0ms)

Iter	Nodes	Cost
0	193	5321
1	558	3170
2	2930	2688
done	5000	2688

prune594.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 12.2b

localize37.0ms

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)))
6.6b	(* (* (pow cos 2.0) (* x (pow sin (/ 2.0 2)))) (* (pow sin (/ 2.0 2)) x))
13.1b	(* (pow cos 2.0) (* x (pow sin (/ 2.0 2))))

rewrite224.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 191

Calls

4 calls:

5.0ms	(cos (* 2.0 x))
79.0ms	(/ (cos (* 2.0 x)) (* (* (pow cos 2.0) (* x (pow sin (/ 2.0 2)))) (* (pow sin (/ 2.0 2)) x)))
97.0ms	(* (* (pow cos 2.0) (* x (pow sin (/ 2.0 2)))) (* (pow sin (/ 2.0 2)) x))
23.0ms	(* (pow cos 2.0) (* x (pow sin (/ 2.0 2))))

series1.2s

Counts

4 → 12

Calls

4 calls:

16.0ms	(cos (* 2.0 x))
516.0ms	(/ (cos (* 2.0 x)) (* (* (pow cos 2.0) (* x (pow sin (/ 2.0 2)))) (* (pow sin (/ 2.0 2)) x)))
346.0ms	(* (* (pow cos 2.0) (* x (pow sin (/ 2.0 2)))) (* (pow sin (/ 2.0 2)) x))
325.0ms	(* (pow cos 2.0) (* x (pow sin (/ 2.0 2))))

simplify1.6s

Counts

203 → 203

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	195	5163
1	596	3356
2	3127	2934
done	5000	2826

prune495.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 6.7b

regimes963.0ms

Accuracy

0% (1.8b remaining)

Error of 7.3b against oracle of 5.6b and baseline of 7.3b

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	32
1	20	32
2	21	32
done	21	32

end0.0ms

sample3.9s

Algorithm

intervals

Results

1.3s	9036×	body	80	valid
1.1s	830×	body	1280	valid
634.0ms	998×	body	640	valid
226.0ms	576×	body	320	valid
118.0ms	326×	body	160	valid