Details

Time bar (total: 11.6s)

sample58.0ms

Algorithm
intervals
Results
17.0ms286×body80valid
10.0ms28×body1280valid
8.0ms33×body640valid
5.0ms14×body160valid
3.0ms16×body320valid

simplify1.5s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01216
12616
26616
322316
493116
done500016

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.7b

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
3.9b
(* (* x (pow sin 2.0)) x)
8.1b
(* x (pow sin 2.0))
20.4b
(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

rewrite71.0ms

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:
25.0ms
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
9.0ms
(* (* x (pow sin 2.0)) x)
7.0ms
(* x (pow sin 2.0))
25.0ms
(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

series1.1s

Counts
4 → 12
Calls
4 calls:
488.0ms
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
152.0ms
(* (* x (pow sin 2.0)) x)
139.0ms
(* x (pow sin 2.0))
272.0ms
(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

simplify849.0ms

Counts
127 → 127
Iterations

Useful iterations: 2 (182.0ms)

IterNodesCost
01711959
14251811
215321541
done50011541

prune282.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 16.7b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))
0.2b
(/ (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)
20.4b
(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

rewrite234.0ms

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 add-cube-cbrt *-un-lft-identity associate-*r*
9×associate-*l*
6×pow1 unpow-prod-down
5×cbrt-undiv
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 → 186
Calls
4 calls:
11.0ms
(* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))
89.0ms
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
31.0ms
(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
90.0ms
(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

series868.0ms

Counts
4 → 12
Calls
4 calls:
142.0ms
(* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))
305.0ms
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
153.0ms
(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
267.0ms
(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

simplify914.0ms

Counts
198 → 198
Iterations

Useful iterations: 2 (296.0ms)

IterNodesCost
02034993
15792927
222532493
done50002493

prune273.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 14.6b

localize16.0ms

Local error

Found 3 expressions with local error:

0.2b
(* (* x (pow sin (/ 2.0 2))) (* (pow sin (/ 2.0 2)) x))
0.2b
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin (/ 2.0 2))) (* (pow sin (/ 2.0 2)) x))))
20.4b
(* (pow cos 2.0) (* (* x (pow sin (/ 2.0 2))) (* (pow sin (/ 2.0 2)) x)))

rewrite108.0ms

Algorithm
rewrite-expression-head
Rules
466×add-exp-log
382×prod-exp
90×pow-to-exp pow-exp
58×add-cbrt-cube
52×div-exp
34×cbrt-unprod
8×associate-*l*
7×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
6×cbrt-undiv
5×pow1
3×unpow-prod-down times-frac associate-/l* add-log-exp
2×associate-*r* *-commutative
1×frac-2neg pow-prod-down clear-num associate-/r* div-inv sqr-pow
Counts
3 → 178
Calls
3 calls:
14.0ms
(* (* x (pow sin (/ 2.0 2))) (* (pow sin (/ 2.0 2)) x))
41.0ms
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin (/ 2.0 2))) (* (pow sin (/ 2.0 2)) x))))
39.0ms
(* (pow cos 2.0) (* (* x (pow sin (/ 2.0 2))) (* (pow sin (/ 2.0 2)) x)))

series750.0ms

Counts
3 → 9
Calls
3 calls:
158.0ms
(* (* x (pow sin (/ 2.0 2))) (* (pow sin (/ 2.0 2)) x))
311.0ms
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin (/ 2.0 2))) (* (pow sin (/ 2.0 2)) x))))
280.0ms
(* (pow cos 2.0) (* (* x (pow sin (/ 2.0 2))) (* (pow sin (/ 2.0 2)) x)))

simplify699.0ms

Counts
187 → 187
Iterations

Useful iterations: 2 (177.0ms)

IterNodesCost
01825118
14933028
218302542
done50012542

prune212.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 12.6b

localize16.0ms

Local error

Found 3 expressions with local error:

0.2b
(/ (cos (* 2.0 x)) (* (* (pow cos 2.0) (* x (pow sin (/ 2.0 2)))) (* (pow sin (/ 2.0 2)) x)))
5.8b
(* (* (pow cos 2.0) (* x (pow sin (/ 2.0 2)))) (* (pow sin (/ 2.0 2)) x))
15.5b
(* (pow cos 2.0) (* x (pow sin (/ 2.0 2))))

rewrite90.0ms

Algorithm
rewrite-expression-head
Rules
455×add-exp-log
371×prod-exp
89×pow-to-exp pow-exp
58×add-cbrt-cube
53×div-exp
33×cbrt-unprod
8×associate-*l*
7×cbrt-undiv add-sqr-sqrt add-cube-cbrt *-un-lft-identity
5×pow1
3×unpow-prod-down times-frac associate-/l* add-log-exp
2×associate-*r* *-commutative
1×frac-2neg pow-prod-down clear-num associate-/r* div-inv sqr-pow
Counts
3 → 176
Calls
3 calls:
36.0ms
(/ (cos (* 2.0 x)) (* (* (pow cos 2.0) (* x (pow sin (/ 2.0 2)))) (* (pow sin (/ 2.0 2)) x)))
31.0ms
(* (* (pow cos 2.0) (* x (pow sin (/ 2.0 2)))) (* (pow sin (/ 2.0 2)) x))
10.0ms
(* (pow cos 2.0) (* x (pow sin (/ 2.0 2))))

series792.0ms

Counts
3 → 9
Calls
3 calls:
304.0ms
(/ (cos (* 2.0 x)) (* (* (pow cos 2.0) (* x (pow sin (/ 2.0 2)))) (* (pow sin (/ 2.0 2)) x)))
269.0ms
(* (* (pow cos 2.0) (* x (pow sin (/ 2.0 2)))) (* (pow sin (/ 2.0 2)) x))
219.0ms
(* (pow cos 2.0) (* x (pow sin (/ 2.0 2))))

simplify840.0ms

Counts
185 → 185
Iterations

Useful iterations: 2 (218.0ms)

IterNodesCost
01854968
15723206
219752672
done50012672

prune186.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 4.3b

regimes297.0ms

Accuracy

0% (1.7b remaining)

Error of 7.0b against oracle of 5.3b and baseline of 7.0b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01632
12032
done2032

end0.0ms

sample1.5s

Algorithm
intervals
Results
532.0ms9097×body80valid
293.0ms822×body1280valid
245.0ms984×body640valid
104.0ms565×body320valid
38.0ms322×body160valid