Details

Time bar (total: 7.6s)

sample55.0ms

Algorithm
intervals
Results
18.0ms301×body80valid
9.0ms26×body1280valid
6.0ms28×body640valid
3.0ms20×body320valid
1.0ms10×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: 26.7b

localize14.0ms

Local error

Found 4 expressions with local error:

0.5b
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
4.9b
(* (* x (pow sin 2.0)) x)
8.6b
(* x (pow sin 2.0))
15.8b
(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

rewrite166.0ms

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:
62.0ms
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
24.0ms
(* (* x (pow sin 2.0)) x)
12.0ms
(* x (pow sin 2.0))
64.0ms
(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

series870.0ms

Counts
4 → 12
Calls
4 calls:
302.0ms
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
162.0ms
(* (* x (pow sin 2.0)) x)
138.0ms
(* x (pow sin 2.0))
269.0ms
(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

simplify56.0ms

Counts
135 → 135
Iterations

Useful iterations: 1 (11.0ms)

IterNodesCost
0448971
12063815
25002815
done5002815

prune291.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 14.1b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))
0.5b
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
4.9b
(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
15.8b
(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

rewrite506.0ms

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:
29.0ms
(* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))
190.0ms
(/ (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)
200.0ms
(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

series1.1s

Counts
4 → 12
Calls
4 calls:
150.0ms
(* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))
468.0ms
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
156.0ms
(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
277.0ms
(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

simplify87.0ms

Counts
206 → 206
Iterations

Useful iterations: 2 (69.0ms)

IterNodesCost
06032216
128211509
250021497
done50021497

prune317.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.6b

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))))))
0.5b
(/ (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)))))))
3.7b
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
3.7b
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

rewrite88.0ms

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×expm1-log1p-u log1p-expm1-u 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 → 114
Calls
4 calls:
9.0ms
(* (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))) (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))))
17.0ms
(/ (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)))))))
28.0ms
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
31.0ms
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

series594.0ms

Counts
4 → 12
Calls
4 calls:
34.0ms
(* (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))) (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))))
111.0ms
(/ (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)))))))
226.0ms
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
222.0ms
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

simplify51.0ms

Counts
126 → 126
Iterations

Useful iterations: 2 (34.0ms)

IterNodesCost
03251562
112441292
250011217
done50011217

prune384.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ 1 (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))))
0.4b
(/ (cos (* 2.0 x)) (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))))
3.7b
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
3.7b
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

rewrite81.0ms

Algorithm
rewrite-expression-head
Rules
62×add-exp-log
42×prod-exp
24×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
18×times-frac add-cbrt-cube
14×pow-to-exp associate-*l* pow-exp
6×unpow-prod-down associate-/r* cbrt-unprod associate-/l*
5×pow1
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×div-exp
2×cbrt-undiv frac-2neg associate-*r* clear-num *-commutative div-inv sqr-pow
1×rec-exp pow-flip 1-exp inv-pow
Counts
4 → 126
Calls
4 calls:
5.0ms
(/ 1 (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))))
13.0ms
(/ (cos (* 2.0 x)) (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))))
27.0ms
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
30.0ms
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

series559.0ms

Counts
4 → 12
Calls
4 calls:
35.0ms
(/ 1 (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))))
75.0ms
(/ (cos (* 2.0 x)) (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))))

simplify44.0ms

Counts
138 → 138
Iterations

Useful iterations: 2 (31.0ms)

IterNodesCost
03281475
111561327
250011313
done50011313

prune375.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

regimes316.0ms

Accuracy

0% (2.9b remaining)

Error of 3.0b against oracle of 0.2b and baseline of 3.0b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02740
12740
done2740

end0.0ms

sample1.6s

Algorithm
intervals
Results
542.0ms9004×body80valid
270.0ms793×body1280valid
244.0ms994×body640valid
99.0ms580×body320valid
37.0ms314×body160valid