Details

Time bar (total: 10.0m)

sample1.1s

Algorithm
intervals
Results
320.0ms137×body1280valid
251.0ms67×body2560valid
236.0ms98×body640valid
191.0ms18×body5120valid
50.0ms66×body80valid
36.0ms26×body320valid
7.0ms10×body160valid

simplify1.1s

Counts
1 → 1
Iterations
IterNodes
done2005
42005
31013
2173
151
019

prune21.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 28.0b

localize35.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ 2 (* (* (/ t l) (/ t l)) t))
2.1b
(* (* (/ t l) (/ t l)) t)
2.1b
(/ (/ 2 (* (* (/ t l) (/ t l)) t)) (* (sin k) (tan k)))
26.2b
(/ (/ (/ 2 (* (* (/ t l) (/ t l)) t)) (* (sin k) (tan k))) (* (/ k t) (/ k t)))

rewrite189.0ms

Algorithm
rewrite-expression-head
Rules
685×add-cbrt-cube add-exp-log
353×cbrt-undiv div-exp
228×prod-exp cbrt-unprod
60×times-frac
28×associate-/l*
25×associate-*l/
21×associate-/r/
18×add-sqr-sqrt
17×*-un-lft-identity add-cube-cbrt
10×associate-*r/
9×pow1 div-inv
7×frac-times
4×insert-posit16 add-log-exp
3×clear-num associate-/r* frac-2neg associate-*r* pow-prod-down tan-quot
2×associate-/l/
1×associate-*l* *-commutative unswap-sqr
Counts
4 → 320
Calls
4 calls:
28.0ms
(/ 2 (* (* (/ t l) (/ t l)) t))
28.0ms
(* (* (/ t l) (/ t l)) t)
43.0ms
(/ (/ 2 (* (* (/ t l) (/ t l)) t)) (* (sin k) (tan k)))
76.0ms
(/ (/ (/ 2 (* (* (/ t l) (/ t l)) t)) (* (sin k) (tan k))) (* (/ k t) (/ k t)))

series667.0ms

Counts
4 → 12
Calls
4 calls:
68.0ms
(/ 2 (* (* (/ t l) (/ t l)) t))
41.0ms
(* (* (/ t l) (/ t l)) t)
242.0ms
(/ (/ 2 (* (* (/ t l) (/ t l)) t)) (* (sin k) (tan k)))
316.0ms
(/ (/ (/ 2 (* (* (/ t l) (/ t l)) t)) (* (sin k) (tan k))) (* (/ k t) (/ k t)))

simplify1.2s

Counts
332 → 332
Iterations
IterNodes
done2002
22002
11294
0452

prune4.5s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 8.4b

localize50.0ms

Local error

Found 4 expressions with local error:

1.3b
(/ (/ (sqrt 2) (* (/ t l) (/ t l))) (sin k))
6.7b
(* (/ (/ (/ (sqrt 2) (* (/ t l) (/ t l))) (sin k)) (/ k t)) (/ (/ (/ (sqrt 2) t) (tan k)) (/ k t)))
13.1b
(/ (/ (/ (sqrt 2) t) (tan k)) (/ k t))
14.8b
(/ (/ (/ (sqrt 2) (* (/ t l) (/ t l))) (sin k)) (/ k t))

rewrite812.0ms

Algorithm
rewrite-expression-head
Rules
10272×times-frac
4459×add-sqr-sqrt
3937×*-un-lft-identity add-cube-cbrt
1020×sqrt-prod
971×add-cbrt-cube add-exp-log
928×associate-*r*
663×cbrt-undiv div-exp
564×associate-*l*
455×div-inv
286×associate-/r/
173×prod-exp cbrt-unprod
127×associate-/l*
86×frac-times associate-*l/ associate-*r/
81×unswap-sqr
29×associate-/r*
27×tan-quot
6×pow1
4×insert-posit16 add-log-exp
3×clear-num frac-2neg associate-/l/
1×pow-prod-down *-commutative
Counts
4 → 3563
Calls
4 calls:
20.0ms
(/ (/ (sqrt 2) (* (/ t l) (/ t l))) (sin k))
467.0ms
(* (/ (/ (/ (sqrt 2) (* (/ t l) (/ t l))) (sin k)) (/ k t)) (/ (/ (/ (sqrt 2) t) (tan k)) (/ k t)))
18.0ms
(/ (/ (/ (sqrt 2) t) (tan k)) (/ k t))
46.0ms
(/ (/ (/ (sqrt 2) (* (/ t l) (/ t l))) (sin k)) (/ k t))

series1.2s

Counts
4 → 12
Calls
4 calls:
183.0ms
(/ (/ (sqrt 2) (* (/ t l) (/ t l))) (sin k))
626.0ms
(* (/ (/ (/ (sqrt 2) (* (/ t l) (/ t l))) (sin k)) (/ k t)) (/ (/ (/ (sqrt 2) t) (tan k)) (/ k t)))
177.0ms
(/ (/ (/ (sqrt 2) t) (tan k)) (/ k t))
225.0ms
(/ (/ (/ (sqrt 2) (* (/ t l) (/ t l))) (sin k)) (/ k t))

simplify4.0s

Counts
3575 → 3575
Iterations
IterNodes
done4315
04315

prune1.1m

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 6.8b

localize71.0ms

Local error

Found 4 expressions with local error:

2.5b
(/ (/ (sqrt (sqrt 2)) (/ t l)) (* (cbrt (sin k)) (cbrt (sin k))))
4.6b
(/ (/ (/ (sqrt (sqrt 2)) (/ t l)) (* (cbrt (sin k)) (cbrt (sin k)))) k)
11.8b
(/ (/ (/ (sqrt (sqrt 2)) (/ t l)) (cbrt (sin k))) (/ 1 t))
13.1b
(/ (/ (/ (sqrt 2) t) (tan k)) (/ k t))

rewrite1.6s

Algorithm
rewrite-expression-head
Rules
48508×times-frac
19366×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
10908×sqrt-prod
5124×cbrt-prod
1787×div-inv
1055×associate-/l*
135×add-exp-log
106×associate-/r/
94×div-exp
89×add-cbrt-cube
70×cbrt-undiv
30×associate-/r*
14×tan-quot
6×prod-exp cbrt-unprod
4×pow1 rec-exp clear-num frac-2neg 1-exp insert-posit16 add-log-exp associate-/l/
Counts
4 → 12188
Calls
4 calls:
47.0ms
(/ (/ (sqrt (sqrt 2)) (/ t l)) (* (cbrt (sin k)) (cbrt (sin k))))
44.0ms
(/ (/ (/ (sqrt (sqrt 2)) (/ t l)) (* (cbrt (sin k)) (cbrt (sin k)))) k)
41.0ms
(/ (/ (/ (sqrt (sqrt 2)) (/ t l)) (cbrt (sin k))) (/ 1 t))
26.0ms
(/ (/ (/ (sqrt 2) t) (tan k)) (/ k t))

series949.0ms

Counts
4 → 12
Calls
4 calls:
261.0ms
(/ (/ (sqrt (sqrt 2)) (/ t l)) (* (cbrt (sin k)) (cbrt (sin k))))
293.0ms
(/ (/ (/ (sqrt (sqrt 2)) (/ t l)) (* (cbrt (sin k)) (cbrt (sin k)))) k)
188.0ms
(/ (/ (/ (sqrt (sqrt 2)) (/ t l)) (cbrt (sin k))) (/ 1 t))
206.0ms
(/ (/ (/ (sqrt 2) t) (tan k)) (/ k t))

simplify18.9s

Counts
12200 → 12200
Iterations
IterNodes
done13640
013640

prune4.2m

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 4.9b

localize77.0ms

Local error

Found 4 expressions with local error:

2.5b
(/ (/ (sqrt (sqrt 2)) (/ t l)) (* (cbrt (sin k)) (cbrt (sin k))))
4.6b
(/ (/ (/ (sqrt (sqrt 2)) (/ t l)) (* (cbrt (sin k)) (cbrt (sin k)))) k)
6.7b
(* (/ (/ (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt t) (cbrt t))) 1) k) (/ (/ (/ (cbrt (sqrt 2)) (cbrt t)) (tan k)) (/ 1 t)))
11.8b
(/ (/ (/ (sqrt (sqrt 2)) (/ t l)) (cbrt (sin k))) (/ 1 t))

rewrite1.4s

Algorithm
rewrite-expression-head
Rules
54423×times-frac
22356×add-sqr-sqrt
21603×*-un-lft-identity
21505×add-cube-cbrt
11268×sqrt-prod
7707×cbrt-prod
2332×associate-*r*
1903×div-inv
1166×add-exp-log
984×associate-/l*
816×div-exp
320×add-cbrt-cube
266×prod-exp
265×cbrt-undiv
150×unswap-sqr
105×1-exp associate-/r/
83×cbrt-unprod
61×associate-*l*
40×rec-exp
17×associate-/r*
13×tan-quot
6×pow1
4×insert-posit16 add-log-exp
3×clear-num frac-2neg associate-/l/
1×frac-times pow-prod-down associate-*l/ associate-*r/ *-commutative
Counts
4 → 13917
Calls
4 calls:
17.0ms
(/ (/ (sqrt (sqrt 2)) (/ t l)) (* (cbrt (sin k)) (cbrt (sin k))))
36.0ms
(/ (/ (/ (sqrt (sqrt 2)) (/ t l)) (* (cbrt (sin k)) (cbrt (sin k)))) k)
168.0ms
(* (/ (/ (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt t) (cbrt t))) 1) k) (/ (/ (/ (cbrt (sqrt 2)) (cbrt t)) (tan k)) (/ 1 t)))
38.0ms
(/ (/ (/ (sqrt (sqrt 2)) (/ t l)) (cbrt (sin k))) (/ 1 t))

series734.0ms

Counts
4 → 12
Calls
4 calls:
167.0ms
(/ (/ (sqrt (sqrt 2)) (/ t l)) (* (cbrt (sin k)) (cbrt (sin k))))
233.0ms
(/ (/ (/ (sqrt (sqrt 2)) (/ t l)) (* (cbrt (sin k)) (cbrt (sin k)))) k)
178.0ms
(* (/ (/ (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt t) (cbrt t))) 1) k) (/ (/ (/ (cbrt (sqrt 2)) (cbrt t)) (tan k)) (/ 1 t)))
156.0ms
(/ (/ (/ (sqrt (sqrt 2)) (/ t l)) (cbrt (sin k))) (/ 1 t))

simplify17.2s

Counts
13929 → 13929
Iterations
IterNodes
done16637
016637

prune3.7m