Details

Time bar (total: 38.3s)

sample113.0ms

Algorithm
intervals
Results
41.0ms306×body80valid
20.0ms24×body1280valid
15.0ms27×body640valid
6.0ms14×body320valid
3.0ms10×body160valid

simplify6.1s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
012684
126684
257684
3160684
4728684
54217684
done5001684

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
3.9b
(* (* x (pow sin 2.0)) x)
8.2b
(* x (pow sin 2.0))
17.2b
(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

rewrite173.0ms

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×*-un-lft-identity add-cube-cbrt
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×clear-num associate-/r* frac-2neg pow-prod-down div-inv
Counts
4 → 115
Calls
4 calls:
74.0ms
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
19.0ms
(* (* x (pow sin 2.0)) x)
18.0ms
(* x (pow sin 2.0))
54.0ms
(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

series1.3s

Counts
4 → 12
Calls
4 calls:
456.0ms
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
235.0ms
(* (* x (pow sin 2.0)) x)
220.0ms
(* x (pow sin 2.0))
424.0ms
(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

simplify3.2s

Counts
127 → 127
Iterations

Useful iterations: done (3.2s)

IterNodesCost
016671820
141464327
2150264007
done500162367

prune743.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 11.2b

localize33.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))
0.4b
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
3.9b
(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
17.2b
(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

rewrite621.0ms

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 *-un-lft-identity associate-*r* add-cube-cbrt
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×clear-num associate-/r* frac-2neg pow-prod-down div-inv
Counts
4 → 186
Calls
4 calls:
45.0ms
(* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))
202.0ms
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
120.0ms
(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
232.0ms
(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

series1.3s

Counts
4 → 12
Calls
4 calls:
181.0ms
(* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))
414.0ms
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
291.0ms
(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
430.0ms
(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

simplify3.0s

Counts
198 → 198
Iterations

Useful iterations: done (3.0s)

IterNodesCost
0198138370
1556104337
21830101729
done500196376

prune687.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 8.1b

localize48.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (* x (pow sin (/ 2.0 2))) (* x (pow sin (/ 2.0 2))))
0.4b
(/ (cos (* 2.0 x)) (* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* (* x (pow sin (/ 2.0 2))) (* x (pow sin (/ 2.0 2)))))))
4.3b
(* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* (* x (pow sin (/ 2.0 2))) (* x (pow sin (/ 2.0 2))))))
6.9b
(* (pow cos (/ 2.0 2)) (* (* x (pow sin (/ 2.0 2))) (* x (pow sin (/ 2.0 2)))))

rewrite787.0ms

Algorithm
rewrite-expression-head
Rules
1691×add-exp-log
1549×prod-exp
399×pow-to-exp pow-exp
157×div-exp
92×add-cbrt-cube
59×cbrt-unprod
15×associate-*l*
12×add-sqr-sqrt
11×pow1
10×*-un-lft-identity add-cube-cbrt
7×cbrt-undiv unpow-prod-down
4×add-log-exp
3×times-frac associate-*r* *-commutative associate-/l* unswap-sqr sqr-pow
1×pow2 clear-num associate-/r* frac-2neg pow-plus swap-sqr pow-prod-down pow-sqr pow-prod-up div-inv
Counts
4 → 470
Calls
4 calls:
29.0ms
(* (* x (pow sin (/ 2.0 2))) (* x (pow sin (/ 2.0 2))))
257.0ms
(/ (cos (* 2.0 x)) (* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* (* x (pow sin (/ 2.0 2))) (* x (pow sin (/ 2.0 2)))))))
312.0ms
(* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* (* x (pow sin (/ 2.0 2))) (* x (pow sin (/ 2.0 2))))))
109.0ms
(* (pow cos (/ 2.0 2)) (* (* x (pow sin (/ 2.0 2))) (* x (pow sin (/ 2.0 2)))))

series1.4s

Counts
4 → 12
Calls
4 calls:
196.0ms
(* (* x (pow sin (/ 2.0 2))) (* x (pow sin (/ 2.0 2))))
412.0ms
(/ (cos (* 2.0 x)) (* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* (* x (pow sin (/ 2.0 2))) (* x (pow sin (/ 2.0 2)))))))
386.0ms
(* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* (* x (pow sin (/ 2.0 2))) (* x (pow sin (/ 2.0 2))))))
377.0ms
(* (pow cos (/ 2.0 2)) (* (* x (pow sin (/ 2.0 2))) (* x (pow sin (/ 2.0 2)))))

simplify5.2s

Counts
482 → 482
Iterations

Useful iterations: done (5.1s)

IterNodesCost
0264413447
1725282963
22227278348
done5013252136

prune704.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 3.3b

localize49.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2)))) (* x (pow sin (/ 2.0 2))))
0.4b
(/ (cos (* 2.0 x)) (* (pow cos (/ 2.0 2)) (* (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2)))) (* x (pow sin (/ 2.0 2))))))
4.3b
(* (pow cos (/ 2.0 2)) (* (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2)))) (* x (pow sin (/ 2.0 2)))))
5.1b
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

rewrite654.0ms

Algorithm
rewrite-expression-head
Rules
1711×add-exp-log
1564×prod-exp
400×pow-to-exp pow-exp
160×div-exp
97×add-cbrt-cube
62×cbrt-unprod
15×associate-*l*
10×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
8×cbrt-undiv
6×pow1 unpow-prod-down
4×add-log-exp
3×times-frac associate-*r* *-commutative associate-/l*
2×sqr-pow
1×clear-num associate-/r* frac-2neg pow-prod-down div-inv
Counts
4 → 466
Calls
4 calls:
99.0ms
(* (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2)))) (* x (pow sin (/ 2.0 2))))
254.0ms
(/ (cos (* 2.0 x)) (* (pow cos (/ 2.0 2)) (* (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2)))) (* x (pow sin (/ 2.0 2))))))
203.0ms
(* (pow cos (/ 2.0 2)) (* (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2)))) (* x (pow sin (/ 2.0 2)))))
22.0ms
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

series1.7s

Counts
4 → 12
Calls
4 calls:
403.0ms
(* (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2)))) (* x (pow sin (/ 2.0 2))))
462.0ms
(/ (cos (* 2.0 x)) (* (pow cos (/ 2.0 2)) (* (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2)))) (* x (pow sin (/ 2.0 2))))))
491.0ms
(* (pow cos (/ 2.0 2)) (* (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2)))) (* x (pow sin (/ 2.0 2)))))
360.0ms
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

simplify5.0s

Counts
478 → 478
Iterations

Useful iterations: done (4.9s)

IterNodesCost
0266423363
1779287862
22565269688
done5020269609

prune661.0ms

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 2.5b

regimes944.0ms

Accuracy

39.3% (1.5b remaining)

Error of 5.3b against oracle of 3.8b and baseline of 6.3b

bsearch3.0ms

simplify10.0ms

Iterations

Useful iterations: 0 (3.0ms)

IterNodesCost
0251357
1351357
done351357

end0.0ms

sample3.9s

Algorithm
intervals
Results
1.8s9164×body80valid
652.0ms980×body640valid
639.0ms809×body1280valid
246.0ms607×body320valid
110.0ms311×body160valid