Details

Time bar (total: 8.9s)

sample55.0ms

Algorithm
intervals
Results
18.0ms288×body80valid
9.0ms25×body1280valid
7.0ms28×body640valid
4.0ms21×body320valid
1.0ms8×body160valid

simplify40.0ms

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: 27.0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
3.1b
(* (* x (pow sin 2.0)) x)
7.3b
(* x (pow sin 2.0))
19.4b
(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

rewrite158.0ms

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)
11.0ms
(* x (pow sin 2.0))
60.0ms
(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

series881.0ms

Counts
4 → 12
Calls
4 calls:
312.0ms
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
154.0ms
(* (* x (pow sin 2.0)) x)
145.0ms
(* x (pow sin 2.0))
271.0ms
(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

simplify55.0ms

Counts
127 → 127
Iterations

Useful iterations: 1 (11.0ms)

IterNodesCost
0435927
12042771
25002771
done5002771

prune274.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 13.1b

localize15.0ms

Local error

Found 4 expressions with local error:

3.1b
(* (* x (pow sin 2.0)) x)
4.1b
(* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* (* x (pow sin 2.0)) x)))
7.3b
(* x (pow sin 2.0))
8.5b
(* (pow cos (/ 2.0 2)) (* (* x (pow sin 2.0)) x))

rewrite250.0ms

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×add-cube-cbrt *-un-lft-identity associate-*r*
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:
21.0ms
(* (* x (pow sin 2.0)) x)
146.0ms
(* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* (* x (pow sin 2.0)) x)))
12.0ms
(* x (pow sin 2.0))
61.0ms
(* (pow cos (/ 2.0 2)) (* (* x (pow sin 2.0)) x))

series864.0ms

Counts
4 → 12
Calls
4 calls:
153.0ms
(* (* x (pow sin 2.0)) x)
287.0ms
(* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* (* x (pow sin 2.0)) x)))
149.0ms
(* x (pow sin 2.0))
274.0ms
(* (pow cos (/ 2.0 2)) (* (* x (pow sin 2.0)) x))

simplify63.0ms

Counts
158 → 158
Iterations

Useful iterations: 1 (11.0ms)

IterNodesCost
04291240
11850941
25001941
done5001941

prune300.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 9.7b

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (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))))
3.1b
(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
4.1b
(* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
8.5b
(* (pow cos (/ 2.0 2)) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

rewrite1.3s

Algorithm
rewrite-expression-head
Rules
1410×add-exp-log
1300×prod-exp
338×pow-to-exp pow-exp
130×div-exp
74×add-cbrt-cube
46×cbrt-unprod
15×associate-*l*
11×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
6×pow1 cbrt-undiv unpow-prod-down
5×associate-*r*
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 → 394
Calls
4 calls:
499.0ms
(/ (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))))
74.0ms
(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
530.0ms
(* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
198.0ms
(* (pow cos (/ 2.0 2)) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

series1.1s

Counts
4 → 12
Calls
4 calls:
324.0ms
(/ (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))))
155.0ms
(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
287.0ms
(* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
291.0ms
(* (pow cos (/ 2.0 2)) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

simplify126.0ms

Counts
406 → 406
Iterations

Useful iterations: 2 (77.0ms)

IterNodesCost
07975960
131123941
250013351
done50013351

prune302.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 1.7b

localize16.0ms

Local error

Found 4 expressions with local error:

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))))))
0.3b
(/ (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)))))))
4.5b
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
4.5b
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

rewrite83.0ms

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:
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))))))
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)))))))
30.0ms
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
27.0ms
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

series610.0ms

Counts
4 → 12
Calls
4 calls:
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))))))
114.0ms
(/ (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)))))))
227.0ms
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
233.0ms
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

simplify47.0ms

Counts
118 → 118
Iterations

Useful iterations: 2 (35.0ms)

IterNodesCost
03161464
112291194
250021122
done50021122

prune313.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.0b

regimes345.0ms

Accuracy

0% (2.7b remaining)

Error of 2.9b against oracle of 0.2b and baseline of 2.9b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01910
11910
done1910

end0.0ms

sample1.6s

Algorithm
intervals
Results
544.0ms8915×body80valid
284.0ms814×body1280valid
237.0ms980×body640valid
101.0ms572×body320valid
38.0ms292×body160valid