Details

Time bar (total: 7.1s)

sample53.0ms

Algorithm
intervals
Results
16.0ms269×body80valid
8.0ms24×body1280valid
8.0ms33×body640valid
3.0ms21×body320valid
1.0ms11×body160valid

simplify39.0ms

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: 29.3b

localize12.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
3.6b
(* (* x (pow sin 2.0)) x)
10.1b
(* x (pow sin 2.0))
18.6b
(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

rewrite157.0ms

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))
59.0ms
(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

series851.0ms

Counts
4 → 12
Calls
4 calls:
302.0ms
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
149.0ms
(* (* x (pow sin 2.0)) x)
132.0ms
(* x (pow sin 2.0))
268.0ms
(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

simplify55.0ms

Counts
127 → 127
Iterations

Useful iterations: 1 (10.0ms)

IterNodesCost
0435927
12042771
25002771
done5002771

prune253.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 14.3b

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))
0.3b
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
3.6b
(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
18.6b
(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

rewrite487.0ms

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:
28.0ms
(* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))
183.0ms
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
73.0ms
(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
192.0ms
(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

series886.0ms

Counts
4 → 12
Calls
4 calls:
141.0ms
(* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))
320.0ms
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
151.0ms
(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
274.0ms
(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

simplify87.0ms

Counts
198 → 198
Iterations

Useful iterations: 2 (70.0ms)

IterNodesCost
05862140
127921433
250021421
done50021421

prune277.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 3.2b

localize15.0ms

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)))))))
4.8b
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
4.8b
(* (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:
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))))))
15.0ms
(/ (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)))))))
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))))

series595.0ms

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))))))
113.0ms
(/ (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)))))))
223.0ms
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
223.0ms
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

simplify46.0ms

Counts
118 → 118
Iterations

Useful iterations: 2 (34.0ms)

IterNodesCost
03161464
112291194
250021122
done50021122

prune344.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.1b

localize17.0ms

Local error

Found 3 expressions with local error:

0.3b
(pow (fabs (* (pow (* (pow cos 1.0) (pow sin 1.0)) 1.0) x)) 2)
0.3b
(/ (cos (* 2.0 x)) (pow (fabs (* (pow (* (pow cos 1.0) (pow sin 1.0)) 1.0) x)) 2))
4.5b
(* (pow (* (pow cos 1.0) (pow sin 1.0)) 1.0) x)

rewrite43.0ms

Algorithm
rewrite-expression-head
Rules
35×add-exp-log
27×add-sqr-sqrt
24×add-cube-cbrt *-un-lft-identity times-frac
21×prod-exp
18×pow-exp
16×unpow-prod-down
9×pow-to-exp
8×associate-/r*
7×add-cbrt-cube sqr-pow
5×associate-*l* unpow2
4×pow1
3×pow-unpow div-exp associate-*r* associate-/l* add-log-exp
2×unswap-sqr
1×cbrt-undiv pow-pow frac-2neg clear-num *-commutative cbrt-unprod div-inv
Counts
3 → 98
Calls
3 calls:
2.0ms
(pow (fabs (* (pow (* (pow cos 1.0) (pow sin 1.0)) 1.0) x)) 2)
15.0ms
(/ (cos (* 2.0 x)) (pow (fabs (* (pow (* (pow cos 1.0) (pow sin 1.0)) 1.0) x)) 2))
22.0ms
(* (pow (* (pow cos 1.0) (pow sin 1.0)) 1.0) x)

series476.0ms

Counts
3 → 9
Calls
3 calls:
35.0ms
(pow (fabs (* (pow (* (pow cos 1.0) (pow sin 1.0)) 1.0) x)) 2)
109.0ms
(/ (cos (* 2.0 x)) (pow (fabs (* (pow (* (pow cos 1.0) (pow sin 1.0)) 1.0) x)) 2))
331.0ms
(* (pow (* (pow cos 1.0) (pow sin 1.0)) 1.0) x)

simplify42.0ms

Counts
107 → 107
Iterations

Useful iterations: 2 (30.0ms)

IterNodesCost
03291314
111401198
250011189
done50011189

prune301.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

regimes265.0ms

Accuracy

18.1% (2.0b remaining)

Error of 2.2b against oracle of 0.1b and baseline of 2.6b

bsearch152.0ms

Steps
ItersRangePoint
10
2.035644573190885e-159
1.2099787919689018e-141
3.0992080613360915e-150
8
-8.676455186232331e-186
-3.033725472305409e-188
-3.8997952595148316e-188

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04648
14648
done4648

end0.0ms

sample1.6s

Algorithm
intervals
Results
523.0ms8962×body80valid
289.0ms829×body1280valid
225.0ms957×body640valid
103.0ms593×body320valid
36.0ms317×body160valid