Details

Time bar (total: 25.7s)

sample110.0ms

Algorithm
intervals
Results
35.0ms292×body80valid
16.0ms33×body640valid
14.0ms20×body1280valid
6.0ms17×body320valid
4.0ms15×body160valid

simplify1.8s

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

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.0b

localize27.0ms

Local error

Found 4 expressions with local error:

0.7b
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
4.8b
(* (* x (pow sin 2.0)) x)
7.8b
(* x (pow sin 2.0))
18.4b
(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

rewrite186.0ms

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:
68.0ms
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
18.0ms
(* (* x (pow sin 2.0)) x)
9.0ms
(* x (pow sin 2.0))
85.0ms
(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

series1.0s

Counts
4 → 12
Calls
4 calls:
372.0ms
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
164.0ms
(* (* x (pow sin 2.0)) x)
150.0ms
(* x (pow sin 2.0))
364.0ms
(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

simplify2.0s

Counts
135 → 135
Iterations
IterNodes
done5001
22402
1448
0174

prune725.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 15.5b

localize39.0ms

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)))
4.8b
(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
18.4b
(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

rewrite519.0ms

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:
30.0ms
(* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))
201.0ms
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
74.0ms
(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
197.0ms
(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

series1.1s

Counts
4 → 12
Calls
4 calls:
198.0ms
(* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))
370.0ms
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
192.0ms
(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
359.0ms
(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

simplify2.4s

Counts
206 → 206
Iterations
IterNodes
done5002
23801
1588
0206

prune749.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 3.4b

localize46.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2)))) (* x (pow sin (/ 2.0 2))))
0.7b
(/ (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))))))
3.3b
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
4.1b
(* (pow cos (/ 2.0 2)) (* (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2)))) (* x (pow sin (/ 2.0 2)))))

rewrite674.0ms

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:
105.0ms
(* (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2)))) (* x (pow sin (/ 2.0 2))))
217.0ms
(/ (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))))))
34.0ms
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
245.0ms
(* (pow cos (/ 2.0 2)) (* (* (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:
348.0ms
(* (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2)))) (* x (pow sin (/ 2.0 2))))
386.0ms
(/ (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))))))
287.0ms
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
405.0ms
(* (pow cos (/ 2.0 2)) (* (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2)))) (* x (pow sin (/ 2.0 2)))))

simplify2.5s

Counts
486 → 486
Iterations
IterNodes
done5000
23726
1875
0274

prune666.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 1.2b

localize29.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (cos (* 2.0 x)) (pow cos (/ 2.0 2)))
0.3b
(* (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2)))) (* x (pow sin (/ 2.0 2))))
3.3b
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
4.1b
(/ (/ (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)))))

rewrite265.0ms

Algorithm
rewrite-expression-head
Rules
1287×add-exp-log
896×prod-exp
374×div-exp
266×pow-to-exp pow-exp
97×add-cbrt-cube
88×times-frac
50×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
48×cbrt-unprod
33×unpow-prod-down
28×associate-/l*
22×cbrt-undiv
11×sqr-pow
8×associate-/r* associate-*l*
6×pow1
4×expm1-log1p-u log1p-expm1-u div-inv add-log-exp
2×clear-num frac-2neg associate-*r* *-commutative
1×pow-prod-down associate-/l/
Counts
4 → 440
Calls
4 calls:
22.0ms
(/ (cos (* 2.0 x)) (pow cos (/ 2.0 2)))
72.0ms
(* (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2)))) (* x (pow sin (/ 2.0 2))))
24.0ms
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
88.0ms
(/ (/ (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)))))

series1.4s

Counts
4 → 12
Calls
4 calls:
277.0ms
(/ (cos (* 2.0 x)) (pow cos (/ 2.0 2)))
412.0ms
(* (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2)))) (* x (pow sin (/ 2.0 2))))
326.0ms
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
426.0ms
(/ (/ (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)))))

simplify1.5s

Counts
452 → 452
Iterations
IterNodes
done5000
11208
0359

prune1.5s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 1.2b

regimes651.0ms

Accuracy

0% (0.8b remaining)

Error of 2.7b against oracle of 1.9b and baseline of 2.7b

bsearch0.0ms

simplify7.0ms

Iterations
IterNodes
done22
122
018

end0.0ms

sample4.1s

Algorithm
intervals
Results
1.5s780×body1280valid
1.2s9056×body80valid
571.0ms1005×body640valid
179.0ms537×body320valid
77.0ms330×body160valid