Details

Time bar (total: 10.0m)

sample106.0ms

Algorithm
intervals
Results
41.0ms285×body80valid
20.0ms36×body1280valid
9.0ms24×body640valid
5.0ms18×body320valid
2.0ms9×body160valid

simplify876.0ms

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

prune18.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 23.7b

localize30.0ms

Local error

Found 4 expressions with local error:

0.7b
(/ (cos (* 2.0 x)) (pow sin 2.0))
5.0b
(/ (/ (/ (cos (* 2.0 x)) (pow sin 2.0)) (* (pow cos 2.0) x)) x)
7.1b
(* (pow cos 2.0) x)
17.7b
(/ (/ (cos (* 2.0 x)) (pow sin 2.0)) (* (pow cos 2.0) x))

rewrite119.0ms

Algorithm
rewrite-expression-head
Rules
359×times-frac
146×add-sqr-sqrt
141×*-un-lft-identity add-cube-cbrt
128×add-exp-log
76×div-exp
70×unpow-prod-down
57×associate-/l*
38×add-cbrt-cube
27×prod-exp
24×sqr-pow
18×pow-to-exp cbrt-undiv pow-exp
13×div-inv
11×associate-/r*
7×associate-*l*
5×cbrt-unprod
4×pow1 add-log-exp
3×clear-num frac-2neg associate-*r* unswap-sqr
2×associate-/l/
1×*-commutative
Counts
4 → 304
Calls
4 calls:
16.0ms
(/ (cos (* 2.0 x)) (pow sin 2.0))
45.0ms
(/ (/ (/ (cos (* 2.0 x)) (pow sin 2.0)) (* (pow cos 2.0) x)) x)
13.0ms
(* (pow cos 2.0) x)
24.0ms
(/ (/ (cos (* 2.0 x)) (pow sin 2.0)) (* (pow cos 2.0) x))

series1.0s

Counts
4 → 12
Calls
4 calls:
213.0ms
(/ (cos (* 2.0 x)) (pow sin 2.0))
344.0ms
(/ (/ (/ (cos (* 2.0 x)) (pow sin 2.0)) (* (pow cos 2.0) x)) x)
199.0ms
(* (pow cos 2.0) x)
264.0ms
(/ (/ (cos (* 2.0 x)) (pow sin 2.0)) (* (pow cos 2.0) x))

simplify545.0ms

Counts
316 → 316
Iterations
IterNodes
done5000
11213
0460

prune1.8s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 10.9b

localize82.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt x)
0.6b
(cbrt x)
9.4b
(/ (/ (/ (cbrt (cos (* 2.0 x))) (/ (pow sin (/ 2.0 2)) (cbrt (cos (* 2.0 x))))) (* (cbrt x) (cbrt x))) (pow cos 2.0))
9.9b
(* (/ (/ (/ (cbrt (cos (* 2.0 x))) (/ (pow sin (/ 2.0 2)) (cbrt (cos (* 2.0 x))))) (* (cbrt x) (cbrt x))) (pow cos 2.0)) (/ (/ (/ (cbrt (cos (* 2.0 x))) (pow sin (/ 2.0 2))) (cbrt x)) x))

rewrite25.2s

Algorithm
rewrite-expression-head
Rules
23294×times-frac
10984×add-sqr-sqrt
6035×*-un-lft-identity add-cube-cbrt
6019×cbrt-prod
4301×unpow-prod-down
1999×associate-*l*
1863×sqr-pow
1540×add-exp-log
1143×div-exp
844×associate-*r*
784×unswap-sqr
309×prod-exp
285×associate-/l*
153×pow-to-exp pow-exp
149×add-cbrt-cube
144×div-inv
143×cbrt-undiv
47×cbrt-unprod
15×associate-/r/
7×associate-/r*
6×pow1
4×add-log-exp
2×pow1/3
1×frac-times clear-num frac-2neg pow-prod-down associate-*l/ associate-*r/ *-commutative associate-/l/
Counts
4 → 6235
Calls
4 calls:
1.0ms
(cbrt x)
1.0ms
(cbrt x)
218.0ms
(/ (/ (/ (cbrt (cos (* 2.0 x))) (/ (pow sin (/ 2.0 2)) (cbrt (cos (* 2.0 x))))) (* (cbrt x) (cbrt x))) (pow cos 2.0))
23.7s
(* (/ (/ (/ (cbrt (cos (* 2.0 x))) (/ (pow sin (/ 2.0 2)) (cbrt (cos (* 2.0 x))))) (* (cbrt x) (cbrt x))) (pow cos 2.0)) (/ (/ (/ (cbrt (cos (* 2.0 x))) (pow sin (/ 2.0 2))) (cbrt x)) x))

series1.7s

Counts
4 → 12
Calls
4 calls:
283.0ms
(cbrt x)
243.0ms
(cbrt x)
645.0ms
(/ (/ (/ (cbrt (cos (* 2.0 x))) (/ (pow sin (/ 2.0 2)) (cbrt (cos (* 2.0 x))))) (* (cbrt x) (cbrt x))) (pow cos 2.0))
493.0ms
(* (/ (/ (/ (cbrt (cos (* 2.0 x))) (/ (pow sin (/ 2.0 2)) (cbrt (cos (* 2.0 x))))) (* (cbrt x) (cbrt x))) (pow cos 2.0)) (/ (/ (/ (cbrt (cos (* 2.0 x))) (pow sin (/ 2.0 2))) (cbrt x)) x))

simplify3.3s

Counts
6247 → 6247
Iterations
IterNodes
done7418
07418

prune1.3m

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 2.0b

localize177.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt x)
0.6b
(cbrt x)
1.2b
(* (/ (/ (/ (cbrt (* (cbrt (cos (* 2.0 x))) (cbrt (cos (* 2.0 x))))) (* (cbrt (/ (pow sin (/ 2.0 2)) (cbrt (cos (* 2.0 x))))) (cbrt (/ (pow sin (/ 2.0 2)) (cbrt (cos (* 2.0 x))))))) (cbrt x)) (pow cos (/ 2.0 2))) (* (/ (/ (/ (cbrt (cbrt (cos (* 2.0 x)))) (cbrt (/ (pow sin (/ 2.0 2)) (cbrt (cos (* 2.0 x)))))) (cbrt x)) (pow cos (/ 2.0 2))) (/ (/ (/ (cbrt (cos (* 2.0 x))) (pow sin (/ 2.0 2))) (cbrt x)) x)))
4.2b
(* (/ (/ (/ (cbrt (cbrt (cos (* 2.0 x)))) (cbrt (/ (pow sin (/ 2.0 2)) (cbrt (cos (* 2.0 x)))))) (cbrt x)) (pow cos (/ 2.0 2))) (/ (/ (/ (cbrt (cos (* 2.0 x))) (pow sin (/ 2.0 2))) (cbrt x)) x))

rewrite3.0m

Algorithm
rewrite-expression-head
Rules
90628×times-frac
62671×cbrt-prod
47964×add-sqr-sqrt
29850×*-un-lft-identity add-cube-cbrt
19258×associate-*l*
17386×unpow-prod-down
7134×sqr-pow
6876×add-exp-log
4839×div-exp
2464×unswap-sqr
1816×prod-exp
845×associate-*r*
636×pow-to-exp pow-exp
500×div-inv
457×add-cbrt-cube
441×cbrt-undiv
210×cbrt-div
198×cbrt-unprod
168×associate-/r/
48×frac-times associate-*r/
46×associate-*l/
11×pow1
4×pow-prod-down add-log-exp
2×pow1/3 *-commutative
Counts
4 → 23572
Calls
4 calls:
1.0ms
(cbrt x)
1.0ms
(cbrt x)
3.6s
(* (/ (/ (/ (cbrt (* (cbrt (cos (* 2.0 x))) (cbrt (cos (* 2.0 x))))) (* (cbrt (/ (pow sin (/ 2.0 2)) (cbrt (cos (* 2.0 x))))) (cbrt (/ (pow sin (/ 2.0 2)) (cbrt (cos (* 2.0 x))))))) (cbrt x)) (pow cos (/ 2.0 2))) (* (/ (/ (/ (cbrt (cbrt (cos (* 2.0 x)))) (cbrt (/ (pow sin (/ 2.0 2)) (cbrt (cos (* 2.0 x)))))) (cbrt x)) (pow cos (/ 2.0 2))) (/ (/ (/ (cbrt (cos (* 2.0 x))) (pow sin (/ 2.0 2))) (cbrt x)) x)))
2.9m
(* (/ (/ (/ (cbrt (cbrt (cos (* 2.0 x)))) (cbrt (/ (pow sin (/ 2.0 2)) (cbrt (cos (* 2.0 x)))))) (cbrt x)) (pow cos (/ 2.0 2))) (/ (/ (/ (cbrt (cos (* 2.0 x))) (pow sin (/ 2.0 2))) (cbrt x)) x))

series1.5s

Counts
4 → 12
Calls
4 calls:
183.0ms
(cbrt x)
180.0ms
(cbrt x)
433.0ms
(* (/ (/ (/ (cbrt (* (cbrt (cos (* 2.0 x))) (cbrt (cos (* 2.0 x))))) (* (cbrt (/ (pow sin (/ 2.0 2)) (cbrt (cos (* 2.0 x))))) (cbrt (/ (pow sin (/ 2.0 2)) (cbrt (cos (* 2.0 x))))))) (cbrt x)) (pow cos (/ 2.0 2))) (* (/ (/ (/ (cbrt (cbrt (cos (* 2.0 x)))) (cbrt (/ (pow sin (/ 2.0 2)) (cbrt (cos (* 2.0 x)))))) (cbrt x)) (pow cos (/ 2.0 2))) (/ (/ (/ (cbrt (cos (* 2.0 x))) (pow sin (/ 2.0 2))) (cbrt x)) x)))
688.0ms
(* (/ (/ (/ (cbrt (cbrt (cos (* 2.0 x)))) (cbrt (/ (pow sin (/ 2.0 2)) (cbrt (cos (* 2.0 x)))))) (cbrt x)) (pow cos (/ 2.0 2))) (/ (/ (/ (cbrt (cos (* 2.0 x))) (pow sin (/ 2.0 2))) (cbrt x)) x))

simplify5.2s

Counts
23584 → 23584
Iterations
IterNodes
done13421
013421

prune4.9m

Pruning

23 alts after pruning (23 fresh and 0 done)

Merged error: 0.1b

localize167.0ms

Local error

Found 4 expressions with local error:

1.3b
(* (* (/ (/ (/ (cbrt (cbrt (cos (* 2.0 x)))) (cbrt (/ (pow sin (/ 2.0 2)) (cbrt (cos (* 2.0 x)))))) (cbrt x)) (pow cos (/ 2.0 2))) (/ (* (cbrt (/ (/ (cbrt (cos (* 2.0 x))) (pow sin (/ 2.0 2))) (cbrt x))) (cbrt (/ (/ (cbrt (cos (* 2.0 x))) (pow sin (/ 2.0 2))) (cbrt x)))) 1)) (/ (cbrt (/ (/ (cbrt (cos (* 2.0 x))) (pow sin (/ 2.0 2))) (cbrt x))) x))
2.3b
(cbrt (/ (/ (cbrt (cos (* 2.0 x))) (pow sin (/ 2.0 2))) (cbrt x)))
2.3b
(cbrt (/ (/ (cbrt (cos (* 2.0 x))) (pow sin (/ 2.0 2))) (cbrt x)))
2.3b
(cbrt (/ (/ (cbrt (cos (* 2.0 x))) (pow sin (/ 2.0 2))) (cbrt x)))

rewrite5.3s

Algorithm
rewrite-expression-head
Rules
4017×times-frac
3264×cbrt-prod
1821×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
853×associate-*r*
648×unpow-prod-down
589×add-exp-log
311×div-exp
242×prod-exp
216×sqr-pow
100×add-cbrt-cube
65×cbrt-undiv
58×cbrt-unprod
43×div-inv
40×1-exp
30×pow-to-exp pow-exp
9×pow1
5×frac-times associate-*l/
4×add-log-exp
3×cbrt-div pow1/3 pow-prod-down associate-*r/
1×associate-*l* *-commutative
Counts
4 → 1866
Calls
4 calls:
5.0s
(* (* (/ (/ (/ (cbrt (cbrt (cos (* 2.0 x)))) (cbrt (/ (pow sin (/ 2.0 2)) (cbrt (cos (* 2.0 x)))))) (cbrt x)) (pow cos (/ 2.0 2))) (/ (* (cbrt (/ (/ (cbrt (cos (* 2.0 x))) (pow sin (/ 2.0 2))) (cbrt x))) (cbrt (/ (/ (cbrt (cos (* 2.0 x))) (pow sin (/ 2.0 2))) (cbrt x)))) 1)) (/ (cbrt (/ (/ (cbrt (cos (* 2.0 x))) (pow sin (/ 2.0 2))) (cbrt x))) x))
18.0ms
(cbrt (/ (/ (cbrt (cos (* 2.0 x))) (pow sin (/ 2.0 2))) (cbrt x)))
18.0ms
(cbrt (/ (/ (cbrt (cos (* 2.0 x))) (pow sin (/ 2.0 2))) (cbrt x)))
19.0ms
(cbrt (/ (/ (cbrt (cos (* 2.0 x))) (pow sin (/ 2.0 2))) (cbrt x)))

series1.7s

Counts
4 → 12
Calls
4 calls:
691.0ms
(* (* (/ (/ (/ (cbrt (cbrt (cos (* 2.0 x)))) (cbrt (/ (pow sin (/ 2.0 2)) (cbrt (cos (* 2.0 x)))))) (cbrt x)) (pow cos (/ 2.0 2))) (/ (* (cbrt (/ (/ (cbrt (cos (* 2.0 x))) (pow sin (/ 2.0 2))) (cbrt x))) (cbrt (/ (/ (cbrt (cos (* 2.0 x))) (pow sin (/ 2.0 2))) (cbrt x)))) 1)) (/ (cbrt (/ (/ (cbrt (cos (* 2.0 x))) (pow sin (/ 2.0 2))) (cbrt x))) x))
331.0ms
(cbrt (/ (/ (cbrt (cos (* 2.0 x))) (pow sin (/ 2.0 2))) (cbrt x)))
333.0ms
(cbrt (/ (/ (cbrt (cos (* 2.0 x))) (pow sin (/ 2.0 2))) (cbrt x)))
336.0ms
(cbrt (/ (/ (cbrt (cos (* 2.0 x))) (pow sin (/ 2.0 2))) (cbrt x)))

simplify23.0ms