Details

Time bar (total: 6.5s)

sample55.0ms

Algorithm
intervals
Results
20.0ms299×body80valid
9.0ms23×body1280valid
8.0ms29×body640valid
3.0ms16×body320valid
2.0ms12×body160valid

simplify39.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0278
1688
22438
312668
450018

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.1b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
4.1b
(* (* x (pow sin 2.0)) x)
7.0b
(* x (pow sin 2.0))
17.0b
(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

rewrite38.0ms

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:
14.0ms
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
6.0ms
(* (* x (pow sin 2.0)) x)
5.0ms
(* x (pow sin 2.0))
9.0ms
(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

series835.0ms

Counts
4 → 12
Calls
4 calls:
295.0ms
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
149.0ms
(* (* x (pow sin 2.0)) x)
136.0ms
(* x (pow sin 2.0))
255.0ms
(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

simplify60.0ms

Algorithm
egg-herbie
Counts
127 → 127
Iterations

Useful iterations: 1 (11.0ms)

IterNodesCost
0435927
12042771
25002771

prune269.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 13.6b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
0.1b
(* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))
4.1b
(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
17.0b
(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

rewrite60.0ms

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:
18.0ms
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
7.0ms
(* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))
9.0ms
(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
13.0ms
(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

series876.0ms

Counts
4 → 12
Calls
4 calls:
303.0ms
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
146.0ms
(* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))
151.0ms
(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
276.0ms
(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

simplify89.0ms

Algorithm
egg-herbie
Counts
198 → 198
Iterations

Useful iterations: 2 (71.0ms)

IterNodesCost
05862140
127921433
250021421

prune264.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 2.0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (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))))

rewrite26.0ms

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:
5.0ms
(/ (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)))))))
3.0ms
(* (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))) (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))))
7.0ms
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
7.0ms
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

series587.0ms

Counts
4 → 12
Calls
4 calls:
103.0ms
(/ (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)))))))
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))))))
227.0ms
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
223.0ms
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

simplify47.0ms

Algorithm
egg-herbie
Counts
118 → 118
Iterations

Useful iterations: 2 (34.0ms)

IterNodesCost
03161464
112291194
250011122

prune335.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

1.2b
(/ (cos (* 2.0 x)) (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))))
1.2b
(/ 1 (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))))

rewrite29.0ms

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×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 → 118
Calls
4 calls:
4.0ms
(/ (cos (* 2.0 x)) (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))))
3.0ms
(/ 1 (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))))
11.0ms
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
7.0ms
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

series533.0ms

Counts
4 → 12
Calls
4 calls:
65.0ms
(/ (cos (* 2.0 x)) (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))))
37.0ms
(/ 1 (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))))
215.0ms
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
216.0ms
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

simplify46.0ms

Algorithm
egg-herbie
Counts
130 → 130
Iterations

Useful iterations: 2 (33.0ms)

IterNodesCost
03191407
111421259
250011245

prune337.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

regimes204.0ms

Accuracy

0% (2.6b remaining)

Error of 2.7b against oracle of 0.1b and baseline of 2.7b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02529
12529

end0.0ms

sample1.7s

Algorithm
intervals
Results
642.0ms8890×body80valid
325.0ms801×body1280valid
291.0ms1013×body640valid
122.0ms603×body320valid
44.0ms313×body160valid