Details

Time bar (total: 38.3s)

sample74.0ms

Algorithm
intervals
Results
26.0ms306×body80valid
14.0ms24×body1280valid
9.0ms27×body640valid
3.0ms14×body320valid
2.0ms10×body160valid

simplify6.0s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
012684
126684
257684
3160684
4728684
54217684
done5001684

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.0b

localize42.0ms

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))

rewrite167.0ms

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×expm1-log1p-u cbrt-undiv log1p-expm1-u 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 → 123
Calls
4 calls:
78.0ms
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
19.0ms
(* (* x (pow sin 2.0)) x)
10.0ms
(* x (pow sin 2.0))
52.0ms
(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

series1.4s

Counts
4 → 12
Calls
4 calls:
476.0ms
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
225.0ms
(* (* x (pow sin 2.0)) x)
229.0ms
(* x (pow sin 2.0))
437.0ms
(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

simplify2.9s

Counts
135 → 135
Iterations

Useful iterations: done (2.8s)

IterNodesCost
017476008
143267690
2143666320
done500066000

prune772.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 11.3b

localize34.0ms

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))

rewrite552.0ms

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×expm1-log1p-u log1p-expm1-u 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 → 194
Calls
4 calls:
33.0ms
(* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))
213.0ms
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
71.0ms
(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
223.0ms
(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

series1.3s

Counts
4 → 12
Calls
4 calls:
205.0ms
(* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))
432.0ms
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
242.0ms
(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
376.0ms
(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

simplify3.2s

Counts
206 → 206
Iterations

Useful iterations: done (3.2s)

IterNodesCost
0206143206
1564106350
22086101007
done500198389

prune766.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 9.1b

localize33.0ms

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

rewrite973.0ms

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
12×add-sqr-sqrt
11×pow1
10×*-un-lft-identity add-cube-cbrt
9×associate-*r* associate-*l*
7×cbrt-undiv unpow-prod-down
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×times-frac *-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 → 478
Calls
4 calls:
58.0ms
(* (* x (pow sin (/ 2.0 2))) (* x (pow sin (/ 2.0 2))))
357.0ms
(/ (cos (* 2.0 x)) (* (pow cos (/ 2.0 2)) (* (* (* x (pow sin (/ 2.0 2))) (* x (pow sin (/ 2.0 2)))) (pow cos (/ 2.0 2)))))
369.0ms
(* (pow cos (/ 2.0 2)) (* (* (* x (pow sin (/ 2.0 2))) (* x (pow sin (/ 2.0 2)))) (pow cos (/ 2.0 2))))
138.0ms
(* (* (* x (pow sin (/ 2.0 2))) (* x (pow sin (/ 2.0 2)))) (pow cos (/ 2.0 2)))

series1.5s

Counts
4 → 12
Calls
4 calls:
221.0ms
(* (* x (pow sin (/ 2.0 2))) (* x (pow sin (/ 2.0 2))))
473.0ms
(/ (cos (* 2.0 x)) (* (pow cos (/ 2.0 2)) (* (* (* x (pow sin (/ 2.0 2))) (* x (pow sin (/ 2.0 2)))) (pow cos (/ 2.0 2)))))
406.0ms
(* (pow cos (/ 2.0 2)) (* (* (* x (pow sin (/ 2.0 2))) (* x (pow sin (/ 2.0 2)))) (pow cos (/ 2.0 2))))
432.0ms
(* (* (* x (pow sin (/ 2.0 2))) (* x (pow sin (/ 2.0 2)))) (pow cos (/ 2.0 2)))

simplify5.3s

Counts
490 → 490
Iterations

Useful iterations: done (5.2s)

IterNodesCost
0279418867
1788289669
22314268368
done5013250771

prune624.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 3.3b

localize37.0ms

Local error

Found 4 expressions with local error:

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

rewrite790.0ms

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
10×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
9×associate-*r* associate-*l*
8×cbrt-undiv
6×pow1 unpow-prod-down
4×expm1-log1p-u log1p-expm1-u 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 → 474
Calls
4 calls:
119.0ms
(* (* x (pow sin (/ 2.0 2))) (* (* x (pow sin (/ 2.0 2))) (pow cos (/ 2.0 2))))
286.0ms
(/ (cos (* 2.0 x)) (* (pow cos (/ 2.0 2)) (* (* x (pow sin (/ 2.0 2))) (* (* x (pow sin (/ 2.0 2))) (pow cos (/ 2.0 2))))))
259.0ms
(* (pow cos (/ 2.0 2)) (* (* x (pow sin (/ 2.0 2))) (* (* x (pow sin (/ 2.0 2))) (pow cos (/ 2.0 2)))))
51.0ms
(* (* x (pow sin (/ 2.0 2))) (pow cos (/ 2.0 2)))

series2.0s

Counts
4 → 12
Calls
4 calls:
733.0ms
(* (* x (pow sin (/ 2.0 2))) (* (* x (pow sin (/ 2.0 2))) (pow cos (/ 2.0 2))))
438.0ms
(/ (cos (* 2.0 x)) (* (pow cos (/ 2.0 2)) (* (* x (pow sin (/ 2.0 2))) (* (* x (pow sin (/ 2.0 2))) (pow cos (/ 2.0 2))))))
468.0ms
(* (pow cos (/ 2.0 2)) (* (* x (pow sin (/ 2.0 2))) (* (* x (pow sin (/ 2.0 2))) (pow cos (/ 2.0 2)))))
316.0ms
(* (* x (pow sin (/ 2.0 2))) (pow cos (/ 2.0 2)))

simplify4.8s

Counts
486 → 486
Iterations

Useful iterations: done (4.7s)

IterNodesCost
0280429083
1840282031
22790255642
done5282250632

prune651.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 1.6b

regimes852.0ms

Accuracy

0% (0.7b remaining)

Error of 3.0b against oracle of 2.3b and baseline of 3.0b

bsearch0.0ms

simplify8.0ms

Iterations

Useful iterations: 1 (5.0ms)

IterNodesCost
015765
118725
done18725

end0.0ms

sample3.6s

Algorithm
intervals
Results
1.6s9164×body80valid
664.0ms809×body1280valid
547.0ms980×body640valid
243.0ms607×body320valid
126.0ms311×body160valid