Details

Time bar (total: 19.8s)

sample100.0ms

Algorithm
intervals
Results
41.0ms284×body80valid
15.0ms37×body640valid
14.0ms22×body1280valid
7.0ms22×body320valid
2.0ms9×body160valid

simplify2.3s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01216
12616
26716
324116
4109716
done500016

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.6b

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
4.7b
(* (* x (pow sin 2.0)) x)
6.5b
(* x (pow sin 2.0))
20.3b
(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

rewrite238.0ms

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:
102.0ms
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
26.0ms
(* (* x (pow sin 2.0)) x)
13.0ms
(* x (pow sin 2.0))
87.0ms
(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

series1.4s

Counts
4 → 12
Calls
4 calls:
469.0ms
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
242.0ms
(* (* x (pow sin 2.0)) x)
253.0ms
(* x (pow sin 2.0))
411.0ms
(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

simplify1.3s

Counts
127 → 127
Iterations

Useful iterations: 2 (395.0ms)

IterNodesCost
01711959
14071811
214241531
done50011531

prune440.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 16.1b

localize25.0ms

Local error

Found 4 expressions with local error:

4.7b
(* (* x (pow sin 2.0)) x)
5.9b
(* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* (* x (pow sin 2.0)) x)))
6.5b
(* x (pow sin 2.0))
7.8b
(* (pow cos (/ 2.0 2)) (* (* x (pow sin 2.0)) x))

rewrite429.0ms

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:
30.0ms
(* (* x (pow sin 2.0)) x)
262.0ms
(* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* (* x (pow sin 2.0)) x)))
24.0ms
(* x (pow sin 2.0))
105.0ms
(* (pow cos (/ 2.0 2)) (* (* x (pow sin 2.0)) x))

series1.3s

Counts
4 → 12
Calls
4 calls:
234.0ms
(* (* x (pow sin 2.0)) x)
376.0ms
(* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* (* x (pow sin 2.0)) x)))
225.0ms
(* x (pow sin 2.0))
430.0ms
(* (pow cos (/ 2.0 2)) (* (* x (pow sin 2.0)) x))

simplify1.7s

Counts
158 → 158
Iterations

Useful iterations: 2 (378.0ms)

IterNodesCost
01632848
13952022
213791770
done50001770

prune470.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 12.0b

localize41.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (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))))
4.7b
(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
5.9b
(* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
7.8b
(* (pow cos (/ 2.0 2)) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

rewrite1.9s

Algorithm
rewrite-expression-head
Rules
1410×add-exp-log
1300×prod-exp
338×pow-to-exp pow-exp
130×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 → 394
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))))
91.0ms
(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
756.0ms
(* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
275.0ms
(* (pow cos (/ 2.0 2)) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

series1.4s

Counts
4 → 12
Calls
4 calls:
503.0ms
(/ (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))))
186.0ms
(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
376.0ms
(* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
368.0ms
(* (pow cos (/ 2.0 2)) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

simplify1.7s

Counts
406 → 406
Iterations

Useful iterations: 2 (594.0ms)

IterNodesCost
025913801
16766413
224655761
done50005761

prune489.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 8.3b

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (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)))))
0.2b
(* (* x (pow sin (/ 2.0 2))) (* (pow sin (/ 2.0 2)) x))
5.9b
(* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* (* x (pow sin (/ 2.0 2))) (* (pow sin (/ 2.0 2)) x))))
7.8b
(* (pow cos (/ 2.0 2)) (* (* x (pow sin (/ 2.0 2))) (* (pow sin (/ 2.0 2)) x)))

rewrite938.0ms

Algorithm
rewrite-expression-head
Rules
1691×add-exp-log
1549×prod-exp
399×pow-to-exp pow-exp
157×div-exp
92×add-cbrt-cube
59×cbrt-unprod
15×associate-*l*
10×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
7×cbrt-undiv
6×pow1 unpow-prod-down
4×add-log-exp
3×times-frac associate-*r* *-commutative associate-/l*
2×sqr-pow
1×frac-2neg pow-prod-down clear-num associate-/r* div-inv
Counts
4 → 462
Calls
4 calls:
315.0ms
(/ (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)))))
40.0ms
(* (* x (pow sin (/ 2.0 2))) (* (pow sin (/ 2.0 2)) x))
349.0ms
(* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* (* x (pow sin (/ 2.0 2))) (* (pow sin (/ 2.0 2)) x))))
132.0ms
(* (pow cos (/ 2.0 2)) (* (* x (pow sin (/ 2.0 2))) (* (pow sin (/ 2.0 2)) x)))

series1.3s

Counts
4 → 12
Calls
4 calls:
408.0ms
(/ (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)))))
204.0ms
(* (* x (pow sin (/ 2.0 2))) (* (pow sin (/ 2.0 2)) x))
395.0ms
(* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* (* x (pow sin (/ 2.0 2))) (* (pow sin (/ 2.0 2)) x))))
339.0ms
(* (pow cos (/ 2.0 2)) (* (* x (pow sin (/ 2.0 2))) (* (pow sin (/ 2.0 2)) x)))

simplify1.8s

Counts
474 → 474
Iterations

Useful iterations: 2 (597.0ms)

IterNodesCost
027516226
16767516
224676720
done50006720

prune385.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 4.7b

regimes9.0ms