Details

Time bar (total: 26.1s)

sample87.0ms

Algorithm
intervals
Results
29.0ms304×body80valid
13.0ms23×body1280valid
12.0ms32×body640valid
7.0ms23×body320valid
2.0ms9×body160valid

simplify3.4s

Counts
1 → 1
Iterations
IterNodes
done5001
54217
4728
3160
257
126
012

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.6b

localize33.0ms

Local error

Found 4 expressions with local error:

0.7b
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
3.0b
(* (* x (pow sin 2.0)) x)
7.0b
(* x (pow sin 2.0))
20.7b
(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

rewrite183.0ms

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:
71.0ms
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
26.0ms
(* (* x (pow sin 2.0)) x)
14.0ms
(* x (pow sin 2.0))
66.0ms
(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

series1.0s

Counts
4 → 12
Calls
4 calls:
320.0ms
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
178.0ms
(* (* x (pow sin 2.0)) x)
158.0ms
(* x (pow sin 2.0))
360.0ms
(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

simplify1.5s

Counts
135 → 135
Iterations
IterNodes
done5000
21436
1432
0174

prune677.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 14.2b

localize40.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))
0.7b
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
3.0b
(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
20.7b
(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

rewrite534.0ms

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:
29.0ms
(* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))
207.0ms
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
83.0ms
(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
203.0ms
(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

series1.2s

Counts
4 → 12
Calls
4 calls:
163.0ms
(* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))
412.0ms
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
198.0ms
(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
381.0ms
(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

simplify1.6s

Counts
206 → 206
Iterations
IterNodes
done5001
22086
1564
0206

prune671.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 10.6b

localize34.0ms

Local error

Found 4 expressions with local error:

0.7b
(/ (cos (* 2.0 x)) (* (pow cos (/ 2.0 2)) (* (* (pow cos (/ 2.0 2)) x) (* x (pow sin 2.0)))))
5.6b
(* (pow cos (/ 2.0 2)) (* (* (pow cos (/ 2.0 2)) x) (* x (pow sin 2.0))))
7.0b
(* x (pow sin 2.0))
8.5b
(* (* (pow cos (/ 2.0 2)) x) (* x (pow sin 2.0)))

rewrite241.0ms

Algorithm
rewrite-expression-head
Rules
472×add-exp-log
385×prod-exp
91×pow-to-exp pow-exp
61×add-cbrt-cube
52×div-exp
35×cbrt-unprod
16×add-sqr-sqrt
11×*-un-lft-identity associate-*l* add-cube-cbrt
9×associate-*r*
7×unpow-prod-down
6×pow1 cbrt-undiv
4×expm1-log1p-u 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 → 211
Calls
4 calls:
74.0ms
(/ (cos (* 2.0 x)) (* (pow cos (/ 2.0 2)) (* (* (pow cos (/ 2.0 2)) x) (* x (pow sin 2.0)))))
88.0ms
(* (pow cos (/ 2.0 2)) (* (* (pow cos (/ 2.0 2)) x) (* x (pow sin 2.0))))
15.0ms
(* x (pow sin 2.0))
51.0ms
(* (* (pow cos (/ 2.0 2)) x) (* x (pow sin 2.0)))

series1.3s

Counts
4 → 12
Calls
4 calls:
357.0ms
(/ (cos (* 2.0 x)) (* (pow cos (/ 2.0 2)) (* (* (pow cos (/ 2.0 2)) x) (* x (pow sin 2.0)))))
363.0ms
(* (pow cos (/ 2.0 2)) (* (* (pow cos (/ 2.0 2)) x) (* x (pow sin 2.0))))
229.0ms
(* x (pow sin 2.0))
370.0ms
(* (* (pow cos (/ 2.0 2)) x) (* x (pow sin 2.0)))

simplify2.1s

Counts
223 → 223
Iterations
IterNodes
done5022
22132
1588
0219

prune1.0s

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 8.8b

localize44.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))
0.7b
(/ (cos (* 2.0 x)) (* (pow cos (/ 2.0 2)) (* (* (pow cos (/ 2.0 2)) x) (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))))))
5.6b
(* (pow cos (/ 2.0 2)) (* (* (pow cos (/ 2.0 2)) x) (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))))
8.5b
(* (* (pow cos (/ 2.0 2)) x) (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))))

rewrite705.0ms

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:
36.0ms
(* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))
206.0ms
(/ (cos (* 2.0 x)) (* (pow cos (/ 2.0 2)) (* (* (pow cos (/ 2.0 2)) x) (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))))))
307.0ms
(* (pow cos (/ 2.0 2)) (* (* (pow cos (/ 2.0 2)) x) (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))))
94.0ms
(* (* (pow cos (/ 2.0 2)) x) (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))))

series1.5s

Counts
4 → 12
Calls
4 calls:
179.0ms
(* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))
416.0ms
(/ (cos (* 2.0 x)) (* (pow cos (/ 2.0 2)) (* (* (pow cos (/ 2.0 2)) x) (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))))))
473.0ms
(* (pow cos (/ 2.0 2)) (* (* (pow cos (/ 2.0 2)) x) (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))))
384.0ms
(* (* (pow cos (/ 2.0 2)) x) (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))))

simplify2.6s

Counts
486 → 486
Iterations
IterNodes
done5012
22790
1843
0291

prune752.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 6.4b

regimes1.1s

Accuracy

15.5% (3.5b remaining)

Error of 9.2b against oracle of 5.7b and baseline of 9.9b

bsearch3.0ms

simplify8.0ms

Iterations
IterNodes
done43
143
029

end0.0ms

sample3.9s

Algorithm
intervals
Results
1.9s9037×body80valid
608.0ms790×body1280valid
480.0ms982×body640valid
368.0ms608×body320valid
73.0ms316×body160valid