Details

Time bar (total: 10.0m)

sample1.2s

Algorithm
intervals
Results
390.0ms139×body1280valid
290.0ms28×body5120valid
267.0ms61×body2560valid
119.0ms68×body640valid
31.0ms24×body320valid
31.0ms62×body80valid
10.0ms14×body160valid

simplify1.1s

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

prune13.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 32.7b

localize46.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin k) (tan k))
1.8b
(* (* (/ t l) (/ t l)) t)
5.5b
(/ (/ 2 (* (* (/ t l) (/ t l)) t)) (* (sin k) (tan k)))
30.1b
(/ (/ (/ 2 (* (* (/ t l) (/ t l)) t)) (* (sin k) (tan k))) (* (/ k t) (/ k t)))

rewrite260.0ms

Algorithm
rewrite-expression-head
Rules
662×add-cbrt-cube add-exp-log
343×cbrt-undiv div-exp
220×prod-exp cbrt-unprod
57×times-frac
25×associate-/l*
21×associate-*l/
20×add-sqr-sqrt
18×associate-/r/
17×*-un-lft-identity add-cube-cbrt
11×pow1
10×associate-*r/
8×div-inv
6×frac-times associate-*r*
4×associate-*l* pow-prod-down tan-quot insert-posit16 add-log-exp
2×clear-num associate-/r* frac-2neg *-commutative unswap-sqr associate-/l/
Counts
4 → 307
Calls
4 calls:
19.0ms
(* (sin k) (tan k))
52.0ms
(* (* (/ t l) (/ t l)) t)
80.0ms
(/ (/ 2 (* (* (/ t l) (/ t l)) t)) (* (sin k) (tan k)))
97.0ms
(/ (/ (/ 2 (* (* (/ t l) (/ t l)) t)) (* (sin k) (tan k))) (* (/ k t) (/ k t)))

series810.0ms

Counts
4 → 12
Calls
4 calls:
62.0ms
(* (sin k) (tan k))
57.0ms
(* (* (/ t l) (/ t l)) t)
299.0ms
(/ (/ 2 (* (* (/ t l) (/ t l)) t)) (* (sin k) (tan k)))
391.0ms
(/ (/ (/ 2 (* (* (/ t l) (/ t l)) t)) (* (sin k) (tan k))) (* (/ k t) (/ k t)))

simplify1.4s

Counts
319 → 319
Iterations
IterNodes
done2001
22001
11335
0468

prune1.4s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 11.4b

localize61.0ms

Local error

Found 4 expressions with local error:

1.4b
(/ (/ 1 (* (/ t l) (/ t l))) (sin k))
8.4b
(* (/ (/ (/ 1 (* (/ t l) (/ t l))) (sin k)) (/ k t)) (/ (/ (/ 2 t) (tan k)) (/ k t)))
15.3b
(/ (/ (/ 2 t) (tan k)) (/ k t))
18.6b
(/ (/ (/ 1 (* (/ t l) (/ t l))) (sin k)) (/ k t))

rewrite1.1s

Algorithm
rewrite-expression-head
Rules
6616×times-frac
2908×add-sqr-sqrt
2549×*-un-lft-identity
2535×add-cube-cbrt
2263×add-exp-log
1594×div-exp
971×add-cbrt-cube
663×cbrt-undiv
577×associate-*r*
449×prod-exp
447×associate-*l*
383×div-inv
286×associate-/r/
173×cbrt-unprod
88×associate-/l*
86×frac-times associate-*l/ associate-*r/
85×rec-exp 1-exp
63×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 → 2731
Calls
4 calls:
42.0ms
(/ (/ 1 (* (/ t l) (/ t l))) (sin k))
355.0ms
(* (/ (/ (/ 1 (* (/ t l) (/ t l))) (sin k)) (/ k t)) (/ (/ (/ 2 t) (tan k)) (/ k t)))
30.0ms
(/ (/ (/ 2 t) (tan k)) (/ k t))
49.0ms
(/ (/ (/ 1 (* (/ t l) (/ t l))) (sin k)) (/ k t))

series834.0ms

Counts
4 → 12
Calls
4 calls:
122.0ms
(/ (/ 1 (* (/ t l) (/ t l))) (sin k))
374.0ms
(* (/ (/ (/ 1 (* (/ t l) (/ t l))) (sin k)) (/ k t)) (/ (/ (/ 2 t) (tan k)) (/ k t)))
161.0ms
(/ (/ (/ 2 t) (tan k)) (/ k t))
176.0ms
(/ (/ (/ 1 (* (/ t l) (/ t l))) (sin k)) (/ k t))

simplify4.1s

Counts
2743 → 2743
Iterations
IterNodes
done3606
03606

prune27.6s

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 9.3b

localize87.0ms

Local error

Found 4 expressions with local error:

3.5b
(/ (/ 1 (/ t l)) (sin k))
7.2b
(/ (/ (/ 1 (/ t l)) 1) k)
11.3b
(/ (/ (/ 1 (/ t l)) (sin k)) (/ 1 t))
15.3b
(/ (/ (/ 2 t) (tan k)) (/ k t))

rewrite807.0ms

Algorithm
rewrite-expression-head
Rules
11646×times-frac
4790×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
492×div-inv
360×associate-/l*
211×add-exp-log
176×div-exp
80×add-cbrt-cube
74×associate-/r/
55×cbrt-undiv
32×associate-/r*
29×1-exp
22×rec-exp
14×tan-quot
4×pow1 clear-num frac-2neg insert-posit16 add-log-exp associate-/l/
Counts
4 → 3403
Calls
4 calls:
24.0ms
(/ (/ 1 (/ t l)) (sin k))
32.0ms
(/ (/ (/ 1 (/ t l)) 1) k)
50.0ms
(/ (/ (/ 1 (/ t l)) (sin k)) (/ 1 t))
29.0ms
(/ (/ (/ 2 t) (tan k)) (/ k t))

series406.0ms

Counts
4 → 12
Calls
4 calls:
105.0ms
(/ (/ 1 (/ t l)) (sin k))
36.0ms
(/ (/ (/ 1 (/ t l)) 1) k)
103.0ms
(/ (/ (/ 1 (/ t l)) (sin k)) (/ 1 t))
161.0ms
(/ (/ (/ 2 t) (tan k)) (/ k t))

simplify6.1s

Counts
3415 → 3415
Iterations
IterNodes
done5838
05838

prune36.0s

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 6.0b

localize113.0ms

Local error

Found 4 expressions with local error:

3.0b
(* (/ (/ (/ 1 (/ t l)) 1) k) (* (/ (/ (/ 1 (/ t l)) (sin k)) (/ 1 t)) (* (/ (/ (/ (sqrt 2) 1) 1) k) (/ (/ (/ (sqrt 2) t) (tan k)) (/ 1 t)))))
3.5b
(/ (/ 1 (/ t l)) (sin k))
7.2b
(/ (/ (/ 1 (/ t l)) 1) k)
11.3b
(/ (/ (/ 1 (/ t l)) (sin k)) (/ 1 t))

rewrite15.5s

Algorithm
rewrite-expression-head
Rules
676622×add-exp-log
567327×div-exp
165808×prod-exp
112027×1-exp
53438×rec-exp
15934×add-cbrt-cube
11143×times-frac
10730×cbrt-undiv
4572×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
3875×cbrt-unprod
430×div-inv
412×associate-*l*
316×associate-/l*
68×associate-/r/
19×associate-/r*
17×frac-times associate-*r/
13×pow1
7×associate-*l/
6×pow-prod-down
4×insert-posit16 add-log-exp
3×clear-num frac-2neg associate-/l/
1×associate-*r* *-commutative
Counts
4 → 59955
Calls
4 calls:
598.0ms
(* (/ (/ (/ 1 (/ t l)) 1) k) (* (/ (/ (/ 1 (/ t l)) (sin k)) (/ 1 t)) (* (/ (/ (/ (sqrt 2) 1) 1) k) (/ (/ (/ (sqrt 2) t) (tan k)) (/ 1 t)))))
17.0ms
(/ (/ 1 (/ t l)) (sin k))
23.0ms
(/ (/ (/ 1 (/ t l)) 1) k)
30.0ms
(/ (/ (/ 1 (/ t l)) (sin k)) (/ 1 t))

series726.0ms

Counts
4 → 12
Calls
4 calls:
527.0ms
(* (/ (/ (/ 1 (/ t l)) 1) k) (* (/ (/ (/ 1 (/ t l)) (sin k)) (/ 1 t)) (* (/ (/ (/ (sqrt 2) 1) 1) k) (/ (/ (/ (sqrt 2) t) (tan k)) (/ 1 t)))))
81.0ms
(/ (/ 1 (/ t l)) (sin k))
21.0ms
(/ (/ (/ 1 (/ t l)) 1) k)
96.0ms
(/ (/ (/ 1 (/ t l)) (sin k)) (/ 1 t))

simplify2.1m

Counts
59967 → 59967
Iterations
IterNodes
done65715
065715

prune6.2m