Details

Time bar (total: 11.8s)

sample57.0ms

Algorithm
intervals
Results
19.0ms286×body80valid
10.0ms28×body1280valid
9.0ms33×body640valid
3.0ms16×body320valid
2.0ms14×body160valid

simplify1.4s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01216
12616
26616
322316
493116
done500016

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.7b

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
3.9b
(* (* x (pow sin 2.0)) x)
8.1b
(* x (pow sin 2.0))
20.4b
(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

rewrite74.0ms

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:
29.0ms
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
9.0ms
(* (* x (pow sin 2.0)) x)
5.0ms
(* x (pow sin 2.0))
26.0ms
(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

series848.0ms

Counts
4 → 12
Calls
4 calls:
293.0ms
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
149.0ms
(* (* x (pow sin 2.0)) x)
138.0ms
(* x (pow sin 2.0))
268.0ms
(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

simplify826.0ms

Counts
135 → 135
Iterations

Useful iterations: 2 (189.0ms)

IterNodesCost
01792045
14351897
215411627
done50001627

prune311.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 16.7b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))
0.2b
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
3.9b
(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
20.4b
(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

rewrite245.0ms

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:
11.0ms
(* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))
94.0ms
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
33.0ms
(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
94.0ms
(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

series868.0ms

Counts
4 → 12
Calls
4 calls:
144.0ms
(* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))
304.0ms
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
150.0ms
(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
270.0ms
(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

simplify912.0ms

Counts
206 → 206
Iterations

Useful iterations: 2 (295.0ms)

IterNodesCost
02115143
15883013
222802569
done50012569

prune324.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 14.6b

localize16.0ms

Local error

Found 3 expressions with local error:

0.2b
(* (* x (pow sin (/ 2.0 2))) (* (pow sin (/ 2.0 2)) x))
0.2b
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin (/ 2.0 2))) (* (pow sin (/ 2.0 2)) x))))
20.4b
(* (pow cos 2.0) (* (* x (pow sin (/ 2.0 2))) (* (pow sin (/ 2.0 2)) x)))

rewrite314.0ms

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:
213.0ms
(* (* x (pow sin (/ 2.0 2))) (* (pow sin (/ 2.0 2)) x))
41.0ms
(/ (cos (* 2.0 x)) (* (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))) (* (pow sin (/ 2.0 2)) x)))

series726.0ms

Counts
3 → 9
Calls
3 calls:
155.0ms
(* (* x (pow sin (/ 2.0 2))) (* (pow sin (/ 2.0 2)) x))
301.0ms
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin (/ 2.0 2))) (* (pow sin (/ 2.0 2)) x))))
269.0ms
(* (pow cos 2.0) (* (* x (pow sin (/ 2.0 2))) (* (pow sin (/ 2.0 2)) x)))

simplify715.0ms

Counts
193 → 193
Iterations

Useful iterations: 2 (186.0ms)

IterNodesCost
01885240
15023102
218502616
done50012616

prune241.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 12.6b

localize16.0ms

Local error

Found 3 expressions with local error:

0.2b
(/ (cos (* 2.0 x)) (* (* (pow cos 2.0) (* x (pow sin (/ 2.0 2)))) (* (pow sin (/ 2.0 2)) x)))
5.8b
(* (* (pow cos 2.0) (* x (pow sin (/ 2.0 2)))) (* (pow sin (/ 2.0 2)) x))
15.5b
(* (pow cos 2.0) (* x (pow sin (/ 2.0 2))))

rewrite95.0ms

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:
35.0ms
(/ (cos (* 2.0 x)) (* (* (pow cos 2.0) (* x (pow sin (/ 2.0 2)))) (* (pow sin (/ 2.0 2)) x)))
36.0ms
(* (* (pow cos 2.0) (* x (pow sin (/ 2.0 2)))) (* (pow sin (/ 2.0 2)) x))
11.0ms
(* (pow cos 2.0) (* x (pow sin (/ 2.0 2))))

series794.0ms

Counts
3 → 9
Calls
3 calls:
305.0ms
(/ (cos (* 2.0 x)) (* (* (pow cos 2.0) (* x (pow sin (/ 2.0 2)))) (* (pow sin (/ 2.0 2)) x)))
270.0ms
(* (* (pow cos 2.0) (* x (pow sin (/ 2.0 2)))) (* (pow sin (/ 2.0 2)) x))
219.0ms
(* (pow cos 2.0) (* x (pow sin (/ 2.0 2))))

simplify843.0ms

Counts
191 → 191
Iterations

Useful iterations: 2 (220.0ms)

IterNodesCost
01915082
15823288
219862754
done50012754

prune208.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 4.3b

regimes307.0ms

Accuracy

0% (1.7b remaining)

Error of 7.0b against oracle of 5.3b and baseline of 7.0b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01632
12032
done2032

end0.0ms

sample1.6s

Algorithm
intervals
Results
616.0ms9097×body80valid
307.0ms822×body1280valid
258.0ms984×body640valid
108.0ms565×body320valid
42.0ms322×body160valid