Details

Time bar (total: 28.1s)

sample69.0ms

Algorithm
intervals
Results
22.0ms292×body80valid
11.0ms26×body1280valid
10.0ms33×body640valid
6.0ms25×body320valid
1.0ms7×body160valid

simplify1.6s

Counts
1 → 1
Iterations
IterNodes
done5000
41263
3241
267
126
012

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.5b

localize21.0ms

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)
8.5b
(* x (pow sin 2.0))
19.2b
(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

rewrite180.0ms

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:
73.0ms
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
30.0ms
(* (* x (pow sin 2.0)) x)
15.0ms
(* x (pow sin 2.0))
54.0ms
(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

series1.1s

Counts
4 → 12
Calls
4 calls:
385.0ms
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
181.0ms
(* (* x (pow sin 2.0)) x)
203.0ms
(* x (pow sin 2.0))
375.0ms
(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

simplify2.1s

Counts
135 → 135
Iterations
IterNodes
done5001
22402
1448
0174

prune688.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 13.1b

localize40.0ms

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)
19.2b
(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

rewrite556.0ms

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:
23.0ms
(* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))
189.0ms
(/ (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)
247.0ms
(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

series1.3s

Counts
4 → 12
Calls
4 calls:
197.0ms
(* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))
456.0ms
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
216.0ms
(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
412.0ms
(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

simplify3.2s

Counts
206 → 206
Iterations
IterNodes
done5002
23801
1588
0206

prune641.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 5.4b

localize27.0ms

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))))))
4.1b
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
6.5b
(* (pow cos (/ 2.0 2)) (* (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2)))) (* x (pow sin (/ 2.0 2)))))

rewrite688.0ms

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×expm1-log1p-u log1p-expm1-u 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 → 474
Calls
4 calls:
86.0ms
(* (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2)))) (* x (pow sin (/ 2.0 2))))
205.0ms
(/ (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))))))
26.0ms
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
319.0ms
(* (pow cos (/ 2.0 2)) (* (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2)))) (* x (pow sin (/ 2.0 2)))))

series1.5s

Counts
4 → 12
Calls
4 calls:
325.0ms
(* (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2)))) (* x (pow sin (/ 2.0 2))))
471.0ms
(/ (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))))))
327.0ms
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
376.0ms
(* (pow cos (/ 2.0 2)) (* (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2)))) (* x (pow sin (/ 2.0 2)))))

simplify2.6s

Counts
486 → 486
Iterations
IterNodes
done5000
23726
1875
0274

prune828.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 1.9b

localize52.0ms

Local error

Found 4 expressions with local error:

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)))))
1.8b
(* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2)))))
4.1b
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
5.3b
(* (* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))) (* x (pow sin (/ 2.0 2))))

rewrite700.0ms

Algorithm
rewrite-expression-head
Rules
1643×add-exp-log
1499×prod-exp
393×pow-to-exp pow-exp
161×div-exp
92×add-cbrt-cube
57×cbrt-unprod
15×associate-*l*
10×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
9×cbrt-undiv
6×pow1 unpow-prod-down
4×expm1-log1p-u log1p-expm1-u 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 → 462
Calls
4 calls:
236.0ms
(/ (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)))))
72.0ms
(* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2)))))
44.0ms
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
262.0ms
(* (* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))) (* x (pow sin (/ 2.0 2))))

series1.5s

Counts
4 → 12
Calls
4 calls:
488.0ms
(/ (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)))))
320.0ms
(* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2)))))
341.0ms
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
393.0ms
(* (* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))) (* x (pow sin (/ 2.0 2))))

simplify3.3s

Counts
474 → 474
Iterations
IterNodes
done5000
24021
1901
0268

prune831.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 1.8b

regimes1.0s

Accuracy

0% (4.7b remaining)

Error of 6.9b against oracle of 2.2b and baseline of 6.9b

bsearch0.0ms

simplify8.0ms

Iterations
IterNodes
done22
122
017

end0.0ms

sample3.5s

Algorithm
intervals
Results
1.3s8991×body80valid
967.0ms834×body1280valid
587.0ms985×body640valid
177.0ms581×body320valid
64.0ms321×body160valid