Details

Time bar (total: 23.3s)

sample79.0ms

Algorithm
intervals
Results
29.0ms297×body80valid
12.0ms21×body1280valid
9.0ms22×body640valid
4.0ms14×body320valid
2.0ms10×body160valid

simplify2.2s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01216
12616
26716
324116
4109716
done500016

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.6b

localize25.0ms

Local error

Found 4 expressions with local error:

0.6b
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
3.4b
(* (* x (pow sin 2.0)) x)
5.7b
(* x (pow sin 2.0))
19.6b
(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

rewrite241.0ms

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×add-cube-cbrt *-un-lft-identity
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×frac-2neg pow-prod-down clear-num associate-/r* div-inv
Counts
4 → 115
Calls
4 calls:
95.0ms
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
37.0ms
(* (* x (pow sin 2.0)) x)
18.0ms
(* x (pow sin 2.0))
84.0ms
(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

series1.3s

Counts
4 → 12
Calls
4 calls:
424.0ms
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
218.0ms
(* (* x (pow sin 2.0)) x)
211.0ms
(* x (pow sin 2.0))
398.0ms
(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

simplify1.1s

Counts
127 → 127
Iterations

Useful iterations: 2 (287.0ms)

IterNodesCost
01711959
14071811
214241531
done50011531

prune383.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 15.6b

localize27.0ms

Local error

Found 4 expressions with local error:

3.4b
(* (* x (pow sin 2.0)) x)
5.7b
(* x (pow sin 2.0))
6.5b
(* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* (* x (pow sin 2.0)) x)))
8.1b
(* (pow cos (/ 2.0 2)) (* (* x (pow sin 2.0)) x))

rewrite375.0ms

Algorithm
rewrite-expression-head
Rules
226×add-exp-log
202×prod-exp
50×pow-to-exp pow-exp
34×add-cbrt-cube
20×cbrt-unprod
18×associate-*l*
17×add-sqr-sqrt
12×add-cube-cbrt *-un-lft-identity associate-*r*
10×unpow-prod-down
6×pow1
4×*-commutative add-log-exp sqr-pow
3×unswap-sqr
1×pow-prod-down
Counts
4 → 146
Calls
4 calls:
33.0ms
(* (* x (pow sin 2.0)) x)
17.0ms
(* x (pow sin 2.0))
216.0ms
(* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* (* x (pow sin 2.0)) x)))
98.0ms
(* (pow cos (/ 2.0 2)) (* (* x (pow sin 2.0)) x))

series1.2s

Counts
4 → 12
Calls
4 calls:
208.0ms
(* (* x (pow sin 2.0)) x)
188.0ms
(* x (pow sin 2.0))
404.0ms
(* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* (* x (pow sin 2.0)) x)))
394.0ms
(* (pow cos (/ 2.0 2)) (* (* x (pow sin 2.0)) x))

simplify1.3s

Counts
158 → 158
Iterations

Useful iterations: 2 (285.0ms)

IterNodesCost
01632848
13952022
213741770
done50001770

prune353.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 11.2b

localize19.0ms

Local error

Found 4 expressions with local error:

3.3b
(* (* (pow cos (/ 2.0 2)) (* x (pow sin 2.0))) x)
5.7b
(* x (pow sin 2.0))
6.5b
(* (pow cos (/ 2.0 2)) (* (* (pow cos (/ 2.0 2)) (* x (pow sin 2.0))) x))
9.0b
(* (pow cos (/ 2.0 2)) (* x (pow sin 2.0)))

rewrite290.0ms

Algorithm
rewrite-expression-head
Rules
226×add-exp-log
202×prod-exp
50×pow-to-exp pow-exp
34×add-cbrt-cube
20×cbrt-unprod
18×associate-*l*
17×add-sqr-sqrt
12×add-cube-cbrt *-un-lft-identity associate-*r*
10×unpow-prod-down
6×pow1
4×*-commutative add-log-exp sqr-pow
3×unswap-sqr
1×pow-prod-down
Counts
4 → 146
Calls
4 calls:
64.0ms
(* (* (pow cos (/ 2.0 2)) (* x (pow sin 2.0))) x)
12.0ms
(* x (pow sin 2.0))
173.0ms
(* (pow cos (/ 2.0 2)) (* (* (pow cos (/ 2.0 2)) (* x (pow sin 2.0))) x))
33.0ms
(* (pow cos (/ 2.0 2)) (* x (pow sin 2.0)))

series1.2s

Counts
4 → 12
Calls
4 calls:
404.0ms
(* (* (pow cos (/ 2.0 2)) (* x (pow sin 2.0))) x)
189.0ms
(* x (pow sin 2.0))
375.0ms
(* (pow cos (/ 2.0 2)) (* (* (pow cos (/ 2.0 2)) (* x (pow sin 2.0))) x))
281.0ms
(* (pow cos (/ 2.0 2)) (* x (pow sin 2.0)))

simplify1.6s

Counts
158 → 158
Iterations

Useful iterations: done (1.6s)

IterNodesCost
01642886
14132084
214911836
done50001832

prune516.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 10.9b

localize22.0ms

Local error

Found 4 expressions with local error:

0.6b
(/ (cos (* 2.0 x)) (* (pow cos (/ 2.0 2)) (* (* (pow cos (/ 2.0 2)) (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))) x)))
3.3b
(* (* (pow cos (/ 2.0 2)) (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))) x)
6.5b
(* (pow cos (/ 2.0 2)) (* (* (pow cos (/ 2.0 2)) (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))) x))
9.0b
(* (pow cos (/ 2.0 2)) (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))))

rewrite2.1s

Algorithm
rewrite-expression-head
Rules
1442×add-exp-log
1342×prod-exp
354×pow-to-exp pow-exp
124×div-exp
74×add-cbrt-cube
46×cbrt-unprod
15×associate-*l*
11×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
6×pow1 cbrt-undiv unpow-prod-down
5×associate-*r*
4×add-log-exp
3×times-frac *-commutative associate-/l*
2×sqr-pow
1×frac-2neg pow-prod-down clear-num associate-/r* div-inv
Counts
4 → 406
Calls
4 calls:
717.0ms
(/ (cos (* 2.0 x)) (* (pow cos (/ 2.0 2)) (* (* (pow cos (/ 2.0 2)) (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))) x)))
285.0ms
(* (* (pow cos (/ 2.0 2)) (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))) x)
904.0ms
(* (pow cos (/ 2.0 2)) (* (* (pow cos (/ 2.0 2)) (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))) x))
144.0ms
(* (pow cos (/ 2.0 2)) (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))))

series1.7s

Counts
4 → 12
Calls
4 calls:
483.0ms
(/ (cos (* 2.0 x)) (* (pow cos (/ 2.0 2)) (* (* (pow cos (/ 2.0 2)) (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))) x)))
421.0ms
(* (* (pow cos (/ 2.0 2)) (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))) x)
457.0ms
(* (pow cos (/ 2.0 2)) (* (* (pow cos (/ 2.0 2)) (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))) x))
363.0ms
(* (pow cos (/ 2.0 2)) (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))))

simplify2.3s

Counts
418 → 418
Iterations

Useful iterations: done (2.3s)

IterNodesCost
026214097
17066633
224625985
done50005981

prune396.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 7.5b

regimes540.0ms

Accuracy

0% (2.2b remaining)

Error of 8.3b against oracle of 6.2b and baseline of 8.3b

bsearch0.0ms

simplify7.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01632
12232
done2232

end0.0ms

sample4.0s

Algorithm
intervals
Results
1.4s9077×body80valid
985.0ms985×body640valid
615.0ms808×body1280valid
274.0ms547×body320valid
71.0ms303×body160valid