Details

Time bar (total: 12.6s)

sample58.0ms

Algorithm
intervals
Results
18.0ms300×body80valid
10.0ms30×body1280valid
7.0ms29×body640valid
4.0ms21×body320valid
1.0ms11×body160valid

simplify1.6s

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01216
12616
26716
324116
4109716
done500016

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.5b

localize14.0ms

Local error

Found 4 expressions with local error:

0.7b
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
3.7b
(* (* x (pow sin 2.0)) x)
8.9b
(* x (pow sin 2.0))
18.5b
(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

rewrite162.0ms

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 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 → 115
Calls
4 calls:
62.0ms
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
22.0ms
(* (* x (pow sin 2.0)) x)
11.0ms
(* x (pow sin 2.0))
60.0ms
(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

series890.0ms

Counts
4 → 12
Calls
4 calls:
328.0ms
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
150.0ms
(* (* x (pow sin 2.0)) x)
139.0ms
(* x (pow sin 2.0))
272.0ms
(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

simplify831.0ms

Counts
127 → 127
Iterations

Useful iterations: 2 (227.0ms)

IterNodesCost
01711959
14071811
214241531
done50011531

prune269.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 13.1b

localize16.0ms

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)))
3.7b
(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
18.5b
(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

rewrite511.0ms

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×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 → 186
Calls
4 calls:
29.0ms
(* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))
193.0ms
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
75.0ms
(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
201.0ms
(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

series920.0ms

Counts
4 → 12
Calls
4 calls:
148.0ms
(* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))
326.0ms
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
160.0ms
(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
286.0ms
(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

simplify1.0s

Counts
198 → 198
Iterations

Useful iterations: done (1.0s)

IterNodesCost
02034993
15272927
220882483
done50002479

prune263.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 11.3b

localize20.0ms

Local error

Found 3 expressions with local error:

0.3b
(* (* x (pow sin (/ 2.0 2))) (* (pow sin (/ 2.0 2)) x))
0.7b
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin (/ 2.0 2))) (* (pow sin (/ 2.0 2)) x))))
18.5b
(* (pow cos 2.0) (* (* x (pow sin (/ 2.0 2))) (* (pow sin (/ 2.0 2)) x)))

rewrite250.0ms

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×unpow-prod-down times-frac 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 → 178
Calls
3 calls:
39.0ms
(* (* x (pow sin (/ 2.0 2))) (* (pow sin (/ 2.0 2)) x))
94.0ms
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin (/ 2.0 2))) (* (pow sin (/ 2.0 2)) x))))
101.0ms
(* (pow cos 2.0) (* (* x (pow sin (/ 2.0 2))) (* (pow sin (/ 2.0 2)) x)))

series763.0ms

Counts
3 → 9
Calls
3 calls:
151.0ms
(* (* x (pow sin (/ 2.0 2))) (* (pow sin (/ 2.0 2)) x))
329.0ms
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin (/ 2.0 2))) (* (pow sin (/ 2.0 2)) x))))
283.0ms
(* (pow cos 2.0) (* (* x (pow sin (/ 2.0 2))) (* (pow sin (/ 2.0 2)) x)))

simplify817.0ms

Counts
187 → 187
Iterations

Useful iterations: 2 (267.0ms)

IterNodesCost
01825118
14613028
218472552
done50002552

prune206.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 10.1b

localize21.0ms

Local error

Found 3 expressions with local error:

0.7b
(/ (cos (* 2.0 x)) (* (* (pow cos 2.0) (* x (pow sin (/ 2.0 2)))) (* (pow sin (/ 2.0 2)) x)))
4.3b
(* (* (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))))

rewrite202.0ms

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×unpow-prod-down times-frac 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 → 176
Calls
3 calls:
81.0ms
(/ (cos (* 2.0 x)) (* (* (pow cos 2.0) (* x (pow sin (/ 2.0 2)))) (* (pow sin (/ 2.0 2)) x)))
80.0ms
(* (* (pow cos 2.0) (* x (pow sin (/ 2.0 2)))) (* (pow sin (/ 2.0 2)) x))
27.0ms
(* (pow cos 2.0) (* x (pow sin (/ 2.0 2))))

series830.0ms

Counts
3 → 9
Calls
3 calls:
318.0ms
(/ (cos (* 2.0 x)) (* (* (pow cos 2.0) (* x (pow sin (/ 2.0 2)))) (* (pow sin (/ 2.0 2)) x)))
284.0ms
(* (* (pow cos 2.0) (* x (pow sin (/ 2.0 2)))) (* (pow sin (/ 2.0 2)) x))
228.0ms
(* (pow cos 2.0) (* x (pow sin (/ 2.0 2))))

simplify866.0ms

Counts
185 → 185
Iterations

Useful iterations: 2 (301.0ms)

IterNodesCost
01854968
14983206
219132672
done50012672

prune183.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 3.1b

regimes328.0ms

Accuracy

0% (1.8b remaining)

Error of 7.0b against oracle of 5.2b 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
550.0ms9047×body80valid
294.0ms858×body1280valid
224.0ms945×body640valid
103.0ms582×body320valid
38.0ms322×body160valid