Details

Time bar (total: 23.5s)

sample101.0ms

Algorithm
intervals
Results
32.0ms288×body80valid
18.0ms39×body640valid
14.0ms24×body1280valid
6.0ms17×body320valid
2.0ms9×body160valid

simplify1.5s

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01216
12616
26716
324216
4125516
done500116

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.3b

localize22.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
4.7b
(* (* x (pow sin 2.0)) x)
8.6b
(* x (pow sin 2.0))
15.7b
(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

rewrite240.0ms

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:
65.0ms
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
46.0ms
(* (* x (pow sin 2.0)) x)
25.0ms
(* x (pow sin 2.0))
99.0ms
(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

series1.4s

Counts
4 → 12
Calls
4 calls:
492.0ms
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
247.0ms
(* (* x (pow sin 2.0)) x)
221.0ms
(* x (pow sin 2.0))
401.0ms
(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

simplify1.8s

Counts
127 → 127
Iterations

Useful iterations: 2 (570.0ms)

IterNodesCost
01711959
14391821
223961563
done50001563

prune520.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 13.1b

localize19.0ms

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)))
4.7b
(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
15.7b
(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

rewrite733.0ms

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:
56.0ms
(* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))
287.0ms
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
135.0ms
(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
240.0ms
(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

series1.2s

Counts
4 → 12
Calls
4 calls:
227.0ms
(* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))
406.0ms
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
225.0ms
(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
365.0ms
(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

simplify2.5s

Counts
198 → 198
Iterations

Useful iterations: done (2.5s)

IterNodesCost
02034993
15842927
232652531
done50022525

prune481.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 10.6b

localize25.0ms

Local error

Found 3 expressions with local error:

0.2b
(* (* x (pow sin (/ 2.0 2))) (* (pow sin (/ 2.0 2)) x))
0.4b
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin (/ 2.0 2))) (* (pow sin (/ 2.0 2)) x))))
15.7b
(* (pow cos 2.0) (* (* x (pow sin (/ 2.0 2))) (* (pow sin (/ 2.0 2)) x)))

rewrite343.0ms

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:
62.0ms
(* (* x (pow sin (/ 2.0 2))) (* (pow sin (/ 2.0 2)) x))
139.0ms
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin (/ 2.0 2))) (* (pow sin (/ 2.0 2)) x))))
129.0ms
(* (pow cos 2.0) (* (* x (pow sin (/ 2.0 2))) (* (pow sin (/ 2.0 2)) x)))

series1.1s

Counts
3 → 9
Calls
3 calls:
250.0ms
(* (* x (pow sin (/ 2.0 2))) (* (pow sin (/ 2.0 2)) x))
467.0ms
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin (/ 2.0 2))) (* (pow sin (/ 2.0 2)) x))))
403.0ms
(* (pow cos 2.0) (* (* x (pow sin (/ 2.0 2))) (* (pow sin (/ 2.0 2)) x)))

simplify2.1s

Counts
187 → 187
Iterations

Useful iterations: 2 (476.0ms)

IterNodesCost
01825118
15303028
227382552
done50002552

prune367.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 9.1b

localize35.0ms

Local error

Found 3 expressions with local error:

0.4b
(/ (cos (* 2.0 x)) (* (* (pow cos 2.0) (* x (pow sin (/ 2.0 2)))) (* (pow sin (/ 2.0 2)) x)))
6.3b
(* (* (pow cos 2.0) (* x (pow sin (/ 2.0 2)))) (* (pow sin (/ 2.0 2)) x))
11.3b
(* (pow cos 2.0) (* x (pow sin (/ 2.0 2))))

rewrite310.0ms

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:
127.0ms
(/ (cos (* 2.0 x)) (* (* (pow cos 2.0) (* x (pow sin (/ 2.0 2)))) (* (pow sin (/ 2.0 2)) x)))
102.0ms
(* (* (pow cos 2.0) (* x (pow sin (/ 2.0 2)))) (* (pow sin (/ 2.0 2)) x))
54.0ms
(* (pow cos 2.0) (* x (pow sin (/ 2.0 2))))

series1.1s

Counts
3 → 9
Calls
3 calls:
416.0ms
(/ (cos (* 2.0 x)) (* (* (pow cos 2.0) (* x (pow sin (/ 2.0 2)))) (* (pow sin (/ 2.0 2)) x)))
367.0ms
(* (* (pow cos 2.0) (* x (pow sin (/ 2.0 2)))) (* (pow sin (/ 2.0 2)) x))
327.0ms
(* (pow cos 2.0) (* x (pow sin (/ 2.0 2))))

simplify2.6s

Counts
185 → 185
Iterations

Useful iterations: done (2.6s)

IterNodesCost
01854968
15833206
230512780
done50002672

prune288.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 4.4b

regimes603.0ms

Accuracy

0% (1.6b remaining)

Error of 6.5b against oracle of 4.9b and baseline of 6.5b

bsearch0.0ms

simplify7.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01632
12032
22132
done2132

end0.0ms

sample4.1s

Algorithm
intervals
Results
1.7s9053×body80valid
741.0ms987×body640valid
588.0ms776×body1280valid
282.0ms566×body320valid
125.0ms323×body160valid