Details

Time bar (total: 2.5m)

sample481.0ms

Algorithm
intervals
Results
194.0ms75×body1280valid
159.0ms55×body640valid
65.0ms175×body80valid
26.0ms20×body320valid
14.0ms16×body160valid

simplify631.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
631.0ms
(/ 2 (* (* (* (/ (pow t 3) (* l l)) (sin k)) (tan k)) (+ (+ 1 (pow (/ k t) 2)) 1)))

prune34.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 23.2b

localize44.0ms

Local error

Found 4 expressions with local error:

14.5b
(/ (/ 2 (+ (* (/ k t) (/ k t)) 2)) (* (* (sin k) (tan k)) (/ t (* (/ l t) (/ l t)))))
9.7b
(* (* (sin k) (tan k)) (/ t (* (/ l t) (/ l t))))
1.6b
(/ t (* (/ l t) (/ l t)))
0.3b
(/ 2 (+ (* (/ k t) (/ k t)) 2))

rewrite192.0ms

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
91.0ms
(/ (/ 2 (+ (* (/ k t) (/ k t)) 2)) (* (* (sin k) (tan k)) (/ t (* (/ l t) (/ l t)))))
62.0ms
(* (* (sin k) (tan k)) (/ t (* (/ l t) (/ l t))))
18.0ms
(/ t (* (/ l t) (/ l t)))
15.0ms
(/ 2 (+ (* (/ k t) (/ k t)) 2))

series1.1s

Counts
4 → 12
Calls
4 calls:
Slowest
774.0ms
(/ (/ 2 (+ (* (/ k t) (/ k t)) 2)) (* (* (sin k) (tan k)) (/ t (* (/ l t) (/ l t)))))
202.0ms
(* (* (sin k) (tan k)) (/ t (* (/ l t) (/ l t))))
86.0ms
(/ 2 (+ (* (/ k t) (/ k t)) 2))
57.0ms
(/ t (* (/ l t) (/ l t)))

simplify45.9s

Counts
197 → 220
Calls
197 calls:
Slowest
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))))))
1.6s
(/ (* (* (/ 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))))))
1.6s
(/ (* (* (/ 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))))))
1.4s
(/ (* (* (/ 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))))))
1.4s
(/ (/ (* (* 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))))))

prune3.1s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 11.6b

localize77.0ms

Local error

Found 4 expressions with local error:

14.5b
(/ (/ 2 (+ (* (/ k t) (/ k t)) 2)) (/ (* (* t (/ (sin k) (/ l t))) (/ (sin k) (/ l t))) (cos k)))
1.9b
(/ (sin k) (/ l t))
1.9b
(/ (sin k) (/ l t))
0.3b
(/ 2 (+ (* (/ k t) (/ k t)) 2))

rewrite149.0ms

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
79.0ms
(/ (/ 2 (+ (* (/ k t) (/ k t)) 2)) (/ (* (* t (/ (sin k) (/ l t))) (/ (sin k) (/ l t))) (cos k)))
32.0ms
(/ 2 (+ (* (/ k t) (/ k t)) 2))
13.0ms
(/ (sin k) (/ l t))
9.0ms
(/ (sin k) (/ l t))

series1.2s

Counts
4 → 12
Calls
4 calls:
Slowest
938.0ms
(/ (/ 2 (+ (* (/ k t) (/ k t)) 2)) (/ (* (* t (/ (sin k) (/ l t))) (/ (sin k) (/ l t))) (cos k)))
87.0ms
(/ (sin k) (/ l t))
78.0ms
(/ (sin k) (/ l t))
63.0ms
(/ 2 (+ (* (/ k t) (/ k t)) 2))

simplify1.5m

Counts
520 → 380
Calls
520 calls:
Slowest
1.6s
(/ (* (* (/ 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))))
1.6s
(/ (* (* (/ 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))))
1.4s
(/ (* (* (/ 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))))
1.1s
(/ (/ (* (cbrt 2) (cbrt 2)) (sqrt (+ (* (/ k t) (/ k t)) 2))) (/ (* t (/ (sin k) (/ l t))) (sqrt (cos k))))
989.0ms
(/ (/ (* (* 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))))

prune5.7s

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 10.6b

localize73.0ms

Local error

Found 4 expressions with local error:

10.7b
(* (/ (/ l t) (* (sin k) t)) (/ (/ 2 (+ (* (/ k t) (/ k t)) 2)) (/ (/ (sin k) (/ l t)) (cos k))))
6.7b
(/ (/ 2 (+ (* (/ k t) (/ k t)) 2)) (/ (/ (sin k) (/ l t)) (cos k)))
1.9b
(/ (sin k) (/ l t))
0.6b
(/ (/ l t) (* (sin k) t))

rewrite619.0ms

Algorithm
rewrite-expression-head
Rules
16919×times-frac
6672×add-sqr-sqrt
6630×*-un-lft-identity add-cube-cbrt
2045×associate-*r*
688×div-inv
642×associate-/r/
335×add-cbrt-cube add-exp-log
273×flip3-+ flip-+
207×cbrt-undiv div-exp
150×associate-/r*
65×prod-exp cbrt-unprod
31×associate-/l*
17×associate-*l*
9×unswap-sqr
6×pow1
4×insert-posit16 add-log-exp
3×clear-num frac-2neg
2×associate-/l/
1×frac-times pow-prod-down associate-*l/ associate-*r/ *-commutative
Counts
4 → 4512
Calls
4 calls:
Slowest
162.0ms
(* (/ (/ l t) (* (sin k) t)) (/ (/ 2 (+ (* (/ k t) (/ k t)) 2)) (/ (/ (sin k) (/ l t)) (cos k))))
47.0ms
(/ (/ 2 (+ (* (/ k t) (/ k t)) 2)) (/ (/ (sin k) (/ l t)) (cos k)))
24.0ms
(/ (sin k) (/ l t))
17.0ms
(/ (/ l t) (* (sin k) t))

series930.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
414.0ms
(/ (/ 2 (+ (* (/ k t) (/ k t)) 2)) (/ (/ (sin k) (/ l t)) (cos k)))
300.0ms
(* (/ (/ l t) (* (sin k) t)) (/ (/ 2 (+ (* (/ k t) (/ k t)) 2)) (/ (/ (sin k) (/ l t)) (cos k))))
124.0ms
(/ (/ l t) (* (sin k) t))
92.0ms
(/ (sin k) (/ l t))