Details

Time bar (total: 7.5s)

sample56.0ms

Algorithm
intervals
Results
20.0ms310×body80valid
8.0ms23×body1280valid
7.0ms28×body640valid
3.0ms15×body320valid
1.0ms4×body160valid

simplify41.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0278
1688
22438
312668
450018
done50018

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.9b

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
4.8b
(* (* x (pow sin 2.0)) x)
7.0b
(* x (pow sin 2.0))
18.7b
(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

rewrite156.0ms

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:
60.0ms
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
22.0ms
(* (* x (pow sin 2.0)) x)
12.0ms
(* x (pow sin 2.0))
59.0ms
(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

series879.0ms

Counts
4 → 12
Calls
4 calls:
314.0ms
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
152.0ms
(* (* x (pow sin 2.0)) x)
139.0ms
(* x (pow sin 2.0))
274.0ms
(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

simplify58.0ms

Counts
127 → 127
Iterations

Useful iterations: 1 (11.0ms)

IterNodesCost
0435927
12042771
25002771
done5002771

prune269.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 15.0b

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)))
4.8b
(* (* (* 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))

rewrite494.0ms

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:
27.0ms
(* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))
184.0ms
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
74.0ms
(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
194.0ms
(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

series882.0ms

Counts
4 → 12
Calls
4 calls:
143.0ms
(* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))
308.0ms
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
158.0ms
(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
273.0ms
(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

simplify83.0ms

Counts
198 → 198
Iterations

Useful iterations: 2 (66.0ms)

IterNodesCost
05862140
127921433
250021421
done50021421

prune262.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 1.7b

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (cos (* 2.0 x)) (* (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))) (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2)))))))
0.3b
(* (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))) (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))))
4.6b
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
4.6b
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

rewrite81.0ms

Algorithm
rewrite-expression-head
Rules
63×add-exp-log
44×prod-exp
21×add-cbrt-cube
17×associate-*l*
16×add-sqr-sqrt
14×pow-to-exp add-cube-cbrt *-un-lft-identity pow-exp
11×pow1
8×cbrt-unprod
6×unpow-prod-down
5×associate-*r*
4×add-log-exp
3×times-frac swap-sqr *-commutative associate-/l*
2×cbrt-undiv div-exp sqr-pow
1×pow2 frac-2neg pow-plus pow-prod-down clear-num associate-/r* pow-sqr pow-prod-up div-inv unswap-sqr
Counts
4 → 106
Calls
4 calls:
16.0ms
(/ (cos (* 2.0 x)) (* (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))) (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2)))))))
8.0ms
(* (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))) (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))))
26.0ms
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
27.0ms
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

series580.0ms

Counts
4 → 12
Calls
4 calls:
108.0ms
(/ (cos (* 2.0 x)) (* (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))) (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2)))))))
38.0ms
(* (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))) (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))))
218.0ms
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
217.0ms
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

simplify44.0ms

Counts
118 → 118
Iterations

Useful iterations: 2 (32.0ms)

IterNodesCost
03161464
112291194
250011122
done50011122

prune337.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 0.1b

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1 (/ (* (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))) (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2)))))) (cos (* 2.0 x))))
0.3b
(* (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))) (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))))
4.6b
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
4.6b
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

rewrite85.0ms

Algorithm
rewrite-expression-head
Rules
79×add-exp-log
46×prod-exp
33×times-frac
30×add-sqr-sqrt
28×add-cube-cbrt *-un-lft-identity
25×add-cbrt-cube
17×associate-*l*
14×pow-to-exp pow-exp
12×pow1 div-exp
8×cbrt-unprod
7×associate-/r*
6×unpow-prod-down
5×cbrt-undiv associate-*r* div-inv
4×add-log-exp
3×rec-exp 1-exp swap-sqr *-commutative associate-/l*
2×sqr-pow
1×pow2 pow-flip frac-2neg pow-plus pow-prod-down clear-num associate-/r/ pow-sqr pow-prod-up inv-pow unswap-sqr
Counts
4 → 141
Calls
4 calls:
18.0ms
(/ 1 (/ (* (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))) (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2)))))) (cos (* 2.0 x))))
7.0ms
(* (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))) (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))))
29.0ms
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
26.0ms
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

series603.0ms

Counts
4 → 12
Calls
4 calls:
120.0ms
(/ 1 (/ (* (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))) (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2)))))) (cos (* 2.0 x))))
35.0ms
(* (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))) (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))))
223.0ms
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
225.0ms
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

simplify65.0ms

Counts
153 → 153
Iterations

Useful iterations: 2 (47.0ms)

IterNodesCost
04632358
120182026
250021874
done50021874

prune369.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.1b

regimes376.0ms

Accuracy

0% (2.5b remaining)

Error of 2.7b against oracle of 0.2b and baseline of 2.7b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02219
12219
done2219

end0.0ms

sample1.7s

Algorithm
intervals
Results
574.0ms8959×body80valid
297.0ms834×body1280valid
264.0ms1050×body640valid
107.0ms577×body320valid
38.0ms277×body160valid