Details

Time bar (total: 10.0m)

sample363.0ms

Algorithm
intervals
Results
152.0ms68×body1280valid
96.0ms202×body80valid
72.0ms53×body640valid
19.0ms21×body320valid
6.0ms11×body160valid

simplify2.7s

Counts
1 → 1
Iterations
IterNodes
46286
31016
2179
152
019

prune29.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 18.3b

localize55.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (+ 2 (* (/ k t) (/ k t))) (tan k))
0.9b
(/ t (* (/ l t) (/ l t)))
3.3b
(/ (/ 2 (sin k)) (/ t (* (/ l t) (/ l t))))
14.7b
(/ (/ (/ 2 (sin k)) (/ t (* (/ l t) (/ l t)))) (* (+ 2 (* (/ k t) (/ k t))) (tan k)))

rewrite135.0ms

Algorithm
rewrite-expression-head
Rules
927×times-frac
309×add-sqr-sqrt
307×*-un-lft-identity add-cube-cbrt
233×add-cbrt-cube add-exp-log
151×associate-/l*
143×cbrt-undiv div-exp
131×associate-/r/
76×div-inv
45×frac-times associate-*l/
43×associate-*r/
42×prod-exp cbrt-unprod
12×associate-/r*
pow1 tan-quot
flip3-+ flip-+ insert-posit16 add-log-exp
clear-num frac-2neg associate-*r* associate-*l*
associate-/l/
pow-prod-down *-commutative unswap-sqr
Counts
4 → 585
Calls
4 calls:
25.0ms
(* (+ 2 (* (/ k t) (/ k t))) (tan k))
13.0ms
(/ t (* (/ l t) (/ l t)))
18.0ms
(/ (/ 2 (sin k)) (/ t (* (/ l t) (/ l t))))
53.0ms
(/ (/ (/ 2 (sin k)) (/ t (* (/ l t) (/ l t)))) (* (+ 2 (* (/ k t) (/ k t))) (tan k)))

series1.2s

Counts
4 → 12
Calls
4 calls:
102.0ms
(* (+ 2 (* (/ k t) (/ k t))) (tan k))
67.0ms
(/ t (* (/ l t) (/ l t)))
179.0ms
(/ (/ 2 (sin k)) (/ t (* (/ l t) (/ l t))))
855.0ms
(/ (/ (/ 2 (sin k)) (/ t (* (/ l t) (/ l t)))) (* (+ 2 (* (/ k t) (/ k t))) (tan k)))

simplify1.3s

Counts
597 → 597
Iterations
IterNodes
12669
0903

prune9.2s

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 9.8b

localize106.0ms

Local error

Found 4 expressions with local error:

2.2b
(/ (/ (sqrt 2) (cbrt (sin k))) (/ (cbrt t) (/ l t)))
3.6b
(/ (/ (sqrt 2) (* (cbrt (sin k)) (cbrt (sin k)))) (/ (* (cbrt t) (cbrt t)) (/ l t)))
8.1b
(/ (/ (/ (sqrt 2) (* (cbrt (sin k)) (cbrt (sin k)))) (/ (* (cbrt t) (cbrt t)) (/ l t))) (/ (* (+ 2 (* (/ k t) (/ k t))) (tan k)) (/ (/ (sqrt 2) (cbrt (sin k))) (/ (cbrt t) (/ l t)))))
8.1b
(/ (* (+ 2 (* (/ k t) (/ k t))) (tan k)) (/ (/ (sqrt 2) (cbrt (sin k))) (/ (cbrt t) (/ l t))))

rewrite2.0m

Algorithm
rewrite-expression-head
Rules
5120809×times-frac
1364117×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
577263×cbrt-prod
462315×sqrt-prod
198943×div-inv
44591×associate-/r/
6756×associate-/r*
2265×add-exp-log
1691×cbrt-undiv div-exp
1668×add-cbrt-cube
295×prod-exp cbrt-unprod
236×associate-/l*
associate-/l/
pow1 clear-num frac-2neg insert-posit16 add-log-exp
tan-quot
frac-times flip3-+ associate-*l/ flip-+
associate-*r/
Counts
4 → 630473
Calls
4 calls:
32.0ms
(/ (/ (sqrt 2) (cbrt (sin k))) (/ (cbrt t) (/ l t)))
66.0ms
(/ (/ (sqrt 2) (* (cbrt (sin k)) (cbrt (sin k)))) (/ (* (cbrt t) (cbrt t)) (/ l t)))
4.8s
(/ (/ (/ (sqrt 2) (* (cbrt (sin k)) (cbrt (sin k)))) (/ (* (cbrt t) (cbrt t)) (/ l t))) (/ (* (+ 2 (* (/ k t) (/ k t))) (tan k)) (/ (/ (sqrt 2) (cbrt (sin k))) (/ (cbrt t) (/ l t)))))
92.0ms
(/ (* (+ 2 (* (/ k t) (/ k t))) (tan k)) (/ (/ (sqrt 2) (cbrt (sin k))) (/ (cbrt t) (/ l t))))

series2.7s

Counts
4 → 12
Calls
4 calls:
342.0ms
(/ (/ (sqrt 2) (cbrt (sin k))) (/ (cbrt t) (/ l t)))
411.0ms
(/ (/ (sqrt 2) (* (cbrt (sin k)) (cbrt (sin k)))) (/ (* (cbrt t) (cbrt t)) (/ l t)))
1.3s
(/ (/ (/ (sqrt 2) (* (cbrt (sin k)) (cbrt (sin k)))) (/ (* (cbrt t) (cbrt t)) (/ l t))) (/ (* (+ 2 (* (/ k t) (/ k t))) (tan k)) (/ (/ (sqrt 2) (cbrt (sin k))) (/ (cbrt t) (/ l t)))))
645.0ms
(/ (* (+ 2 (* (/ k t) (/ k t))) (tan k)) (/ (/ (sqrt 2) (cbrt (sin k))) (/ (cbrt t) (/ l t))))

simplify7.7m