Details

Time bar (total: 2.6m)

sample405.0ms

Algorithm
intervals
Results
132.0ms56×body1280valid
114.0ms200×body80valid
81.0ms48×body640valid
49.0ms29×body320valid
10.0ms13×body160valid

simplify349.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
349.0ms
(/ 2 (* (* (* (/ (pow t 3) (* l l)) (sin k)) (tan k)) (+ (+ 1 (pow (/ k t) 2)) 1)))

prune32.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 23.5b

localize52.0ms

Local error

Found 4 expressions with local error:

14.8b
(/ (/ 2 (+ (* (/ k t) (/ k t)) 2)) (* (* (sin k) (tan k)) (/ t (* (/ l t) (/ l t)))))
10.6b
(* (* (sin k) (tan k)) (/ t (* (/ l t) (/ l t))))
1.8b
(/ t (* (/ l t) (/ l t)))
0.2b
(/ 2 (+ (* (/ k t) (/ k t)) 2))

rewrite249.0ms

Algorithm
rewrite-expression-head
Rules
233×add-cbrt-cube add-exp-log
103×cbrt-undiv div-exp
82×prod-exp cbrt-unprod
48×times-frac
30×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
21×associate-/l*
15×associate-/r/
10×associate-*r*
9×pow1
8×associate-*r/
6×div-inv
5×associate-/r*
4×frac-times associate-*l/ tan-quot insert-posit16 add-log-exp
3×clear-num frac-2neg flip3-+ pow-prod-down flip-+
1×associate-*l* *-commutative associate-/l/
Counts
4 → 208
Calls
4 calls:
Slowest
120.0ms
(/ (/ 2 (+ (* (/ k t) (/ k t)) 2)) (* (* (sin k) (tan k)) (/ t (* (/ l t) (/ l t)))))
89.0ms
(* (* (sin k) (tan k)) (/ t (* (/ l t) (/ l t))))
17.0ms
(/ t (* (/ l t) (/ l t)))
17.0ms
(/ 2 (+ (* (/ k t) (/ k t)) 2))

series1.2s

Counts
4 → 12
Calls
4 calls:
Slowest
862.0ms
(/ (/ 2 (+ (* (/ k t) (/ k t)) 2)) (* (* (sin k) (tan k)) (/ t (* (/ l t) (/ l t)))))
230.0ms
(* (* (sin k) (tan k)) (/ t (* (/ l t) (/ l t))))
65.0ms
(/ 2 (+ (* (/ k t) (/ k t)) 2))
48.0ms
(/ t (* (/ l t) (/ l t)))

simplify48.4s

Counts
197 → 220
Calls
197 calls:
Slowest
2.0s
(/ (* (* (/ 2 (+ (* (/ k t) (/ k t)) 2)) (/ 2 (+ (* (/ k t) (/ k t)) 2))) (/ 2 (+ (* (/ k t) (/ k t)) 2))) (* (* (* (* (sin k) (sin k)) (sin k)) (* (* (tan k) (tan k)) (tan k))) (/ (* (* t t) t) (* (* (* (/ l t) (/ l t)) (* (/ l t) (/ l t))) (* (/ l t) (/ l t))))))
1.8s
(/ (* (* (/ 2 (+ (* (/ k t) (/ k t)) 2)) (/ 2 (+ (* (/ k t) (/ k t)) 2))) (/ 2 (+ (* (/ k t) (/ k t)) 2))) (* (* (* (* (sin k) (sin k)) (sin k)) (* (* (tan k) (tan k)) (tan k))) (/ (* (* t t) t) (* (* (* (/ l t) (/ l t)) (/ l t)) (* (* (/ l t) (/ l t)) (/ l t))))))
1.7s
(/ (* (* (/ 2 (+ (* (/ k t) (/ k t)) 2)) (/ 2 (+ (* (/ k t) (/ k t)) 2))) (/ 2 (+ (* (/ k t) (/ k t)) 2))) (* (* (* (* (sin k) (tan k)) (* (sin k) (tan k))) (* (sin k) (tan k))) (/ (* (* t t) t) (* (* (* (/ l t) (/ l t)) (* (/ l t) (/ l t))) (* (/ l t) (/ l t))))))
1.6s
(/ (* (* (/ 2 (+ (* (/ k t) (/ k t)) 2)) (/ 2 (+ (* (/ k t) (/ k t)) 2))) (/ 2 (+ (* (/ k t) (/ k t)) 2))) (* (* (* (* (sin k) (tan k)) (/ t (* (/ l t) (/ l t)))) (* (* (sin k) (tan k)) (/ t (* (/ l t) (/ l t))))) (* (* (sin k) (tan k)) (/ t (* (/ l t) (/ l t))))))
1.3s
(/ (/ (* (* 2 2) 2) (* (* (+ (* (/ k t) (/ k t)) 2) (+ (* (/ k t) (/ k t)) 2)) (+ (* (/ k t) (/ k t)) 2))) (* (* (* (* (sin k) (tan k)) (/ t (* (/ l t) (/ l t)))) (* (* (sin k) (tan k)) (/ t (* (/ l t) (/ l t))))) (* (* (sin k) (tan k)) (/ t (* (/ l t) (/ l t))))))

prune3.4s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 12.7b

localize44.0ms

Local error

Found 4 expressions with local error:

14.8b
(/ (/ 2 (+ (* (/ k t) (/ k t)) 2)) (/ (* (* t (/ (sin k) (/ l t))) (/ (sin k) (/ l t))) (cos k)))
3.0b
(/ (sin k) (/ l t))
3.0b
(/ (sin k) (/ l t))
0.2b
(/ 2 (+ (* (/ k t) (/ k t)) 2))

rewrite153.0ms

Algorithm
rewrite-expression-head
Rules
384×times-frac
196×add-cbrt-cube add-exp-log
184×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
117×cbrt-undiv div-exp
42×prod-exp cbrt-unprod
36×associate-/r* div-inv
24×associate-/l*
21×associate-/r/
9×flip3-+ flip-+
4×pow1 clear-num frac-2neg insert-posit16 add-log-exp
1×associate-/l/
Counts
4 → 368
Calls
4 calls:
Slowest
86.0ms
(/ (/ 2 (+ (* (/ k t) (/ k t)) 2)) (/ (* (* t (/ (sin k) (/ l t))) (/ (sin k) (/ l t))) (cos k)))
21.0ms
(/ (sin k) (/ l t))
19.0ms
(/ (sin k) (/ l t))
18.0ms
(/ 2 (+ (* (/ k t) (/ k t)) 2))

series1.1s

Counts
4 → 12
Calls
4 calls:
Slowest
878.0ms
(/ (/ 2 (+ (* (/ k t) (/ k t)) 2)) (/ (* (* t (/ (sin k) (/ l t))) (/ (sin k) (/ l t))) (cos k)))
102.0ms
(/ (sin k) (/ l t))
74.0ms
(/ (sin k) (/ l t))
67.0ms
(/ 2 (+ (* (/ k t) (/ k t)) 2))

simplify1.6m

Counts
520 → 380
Calls
520 calls:
Slowest
1.8s
(/ (* (* (/ 2 (+ (* (/ k t) (/ k t)) 2)) (/ 2 (+ (* (/ k t) (/ k t)) 2))) (/ 2 (+ (* (/ k t) (/ k t)) 2))) (/ (* (* (* (* t t) t) (* (* (/ (sin k) (/ l t)) (/ (sin k) (/ l t))) (/ (sin k) (/ l t)))) (* (* (/ (sin k) (/ l t)) (/ (sin k) (/ l t))) (/ (sin k) (/ l t)))) (* (* (cos k) (cos k)) (cos k))))
1.8s
(/ (* (* (/ 2 (+ (* (/ k t) (/ k t)) 2)) (/ 2 (+ (* (/ k t) (/ k t)) 2))) (/ 2 (+ (* (/ k t) (/ k t)) 2))) (/ (* (* (* (* t (/ (sin k) (/ l t))) (* t (/ (sin k) (/ l t)))) (* t (/ (sin k) (/ l t)))) (* (* (/ (sin k) (/ l t)) (/ (sin k) (/ l t))) (/ (sin k) (/ l t)))) (* (* (cos k) (cos k)) (cos k))))
1.5s
(/ (* (* (/ 2 (+ (* (/ k t) (/ k t)) 2)) (/ 2 (+ (* (/ k t) (/ k t)) 2))) (/ 2 (+ (* (/ k t) (/ k t)) 2))) (/ (* (* (* (* t (/ (sin k) (/ l t))) (/ (sin k) (/ l t))) (* (* t (/ (sin k) (/ l t))) (/ (sin k) (/ l t)))) (* (* t (/ (sin k) (/ l t))) (/ (sin k) (/ l t)))) (* (* (cos k) (cos k)) (cos k))))
965.0ms
(/ (/ (* (* 2 2) 2) (* (* (+ (* (/ k t) (/ k t)) 2) (+ (* (/ k t) (/ k t)) 2)) (+ (* (/ k t) (/ k t)) 2))) (* (* (/ (* (* t (/ (sin k) (/ l t))) (/ (sin k) (/ l t))) (cos k)) (/ (* (* t (/ (sin k) (/ l t))) (/ (sin k) (/ l t))) (cos k))) (/ (* (* t (/ (sin k) (/ l t))) (/ (sin k) (/ l t))) (cos k))))
857.0ms
(/ (+ (* (* (/ k t) (/ k t)) (* (/ k t) (/ k t))) (- (* 2 2) (* (* (/ k t) (/ k t)) 2))) (/ (/ (sin k) (/ l t)) (cos k)))

prune5.9s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 11.3b

localize52.0ms

Local error

Found 4 expressions with local error:

10.3b
(* (/ (/ l (* (sin k) t)) t) (/ (/ 2 (+ (* (/ k t) (/ k t)) 2)) (/ (/ (sin k) (/ l t)) (cos k))))
5.1b
(/ (/ 2 (+ (* (/ k t) (/ k t)) 2)) (/ (/ (sin k) (/ l t)) (cos k)))
3.0b
(/ (sin k) (/ l t))
0.9b
(/ l (* (sin k) t))

rewrite579.0ms

Algorithm
rewrite-expression-head
Rules
16932×times-frac
6717×add-sqr-sqrt
6624×*-un-lft-identity add-cube-cbrt
2045×associate-*r*
688×div-inv
642×associate-/r/
273×flip3-+ flip-+
268×add-cbrt-cube add-exp-log
170×cbrt-undiv div-exp
150×associate-/r*
46×prod-exp cbrt-unprod
25×associate-*l*
21×associate-/l*
18×unswap-sqr
6×pow1
4×insert-posit16 add-log-exp
3×clear-num frac-2neg
1×frac-times pow-prod-down associate-*l/ associate-*r/ *-commutative associate-/l/
Counts
4 → 4486
Calls
4 calls:
Slowest
183.0ms
(* (/ (/ l (* (sin k) t)) t) (/ (/ 2 (+ (* (/ k t) (/ k t)) 2)) (/ (/ (sin k) (/ l t)) (cos k))))
53.0ms
(/ (/ 2 (+ (* (/ k t) (/ k t)) 2)) (/ (/ (sin k) (/ l t)) (cos k)))
31.0ms
(/ (sin k) (/ l t))
8.0ms
(/ l (* (sin k) t))

series975.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
478.0ms
(/ (/ 2 (+ (* (/ k t) (/ k t)) 2)) (/ (/ (sin k) (/ l t)) (cos k)))
320.0ms
(* (/ (/ l (* (sin k) t)) t) (/ (/ 2 (+ (* (/ k t) (/ k t)) 2)) (/ (/ (sin k) (/ l t)) (cos k))))
108.0ms
(/ (sin k) (/ l t))
68.0ms
(/ l (* (sin k) t))