Details

Time bar (total: 21.0s)

sample115.0ms

Algorithm
intervals
Results
53.0ms293×body80valid
13.0ms21×body1280valid
10.0ms22×body640valid
6.0ms17×body320valid
3.0ms12×body160valid

simplify561.0ms

Counts
1 → 1

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.9b

localize23.0ms

Local error

Found 4 expressions with local error:

0.8b
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
5.7b
(* (* x (pow sin 2.0)) x)
8.2b
(* x (pow sin 2.0))
15.1b
(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

rewrite221.0ms

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:
76.0ms
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
31.0ms
(* (* x (pow sin 2.0)) x)
17.0ms
(* x (pow sin 2.0))
93.0ms
(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

series1.0s

Counts
4 → 12
Calls
4 calls:
350.0ms
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
160.0ms
(* (* x (pow sin 2.0)) x)
169.0ms
(* x (pow sin 2.0))
327.0ms
(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

simplify978.0ms

Counts
127 → 127

prune342.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 13.4b

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))
0.8b
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
5.7b
(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
15.1b
(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

rewrite762.0ms

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:
34.0ms
(* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))
287.0ms
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
124.0ms
(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
304.0ms
(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

series1.1s

Counts
4 → 12
Calls
4 calls:
182.0ms
(* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))
392.0ms
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
204.0ms
(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
353.0ms
(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

simplify1.3s

Counts
198 → 198

prune397.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 1.5b

localize37.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))) (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))))
0.8b
(/ (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)))))))
3.0b
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
3.0b
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

rewrite118.0ms

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))))))
18.0ms
(/ (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)))))))
55.0ms
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
34.0ms
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

series843.0ms

Counts
4 → 12
Calls
4 calls:
44.0ms
(* (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))) (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))))
138.0ms
(/ (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)))))))
328.0ms
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
333.0ms
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

simplify758.0ms

Counts
118 → 118

prune864.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.2b

localize47.0ms

Local error

Found 4 expressions with local error:

0.7b
(/ 1 (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))))
0.7b
(/ (cos (* 2.0 x)) (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))))
3.0b
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
3.0b
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

rewrite95.0ms

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:
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))))))
41.0ms
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
28.0ms
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

series752.0ms

Counts
4 → 12
Calls
4 calls:
54.0ms
(/ 1 (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))))
93.0ms
(/ (cos (* 2.0 x)) (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))))
324.0ms
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
280.0ms
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

simplify2.9s

Counts
130 → 130

prune573.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.2b

regimes573.0ms

Accuracy

-6.1% (2.9b remaining)

Error of 3.0b against oracle of 0.2b and baseline of 2.9b

bsearch0.0ms

simplify2.5s

end0.0ms

sample4.1s

Algorithm
intervals
Results
1.8s9128×body80valid
634.0ms950×body640valid
623.0ms788×body1280valid
275.0ms611×body320valid
76.0ms293×body160valid