Details

Time bar (total: 3.5m)

sample468.0ms

Algorithm
intervals
Results
175.0ms56×body1280valid
149.0ms61×body640valid
62.0ms175×body80valid
37.0ms32×body320valid
17.0ms22×body160valid

simplify314.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
314.0ms
(/ 2 (* (* (* (/ (pow t 3) (* l l)) (sin k)) (tan k)) (+ (+ 1 (pow (/ k t) 2)) 1)))

prune33.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 19.1b

localize36.0ms

Local error

Found 4 expressions with local error:

12.2b
(/ (/ 2 (+ (* (/ k t) (/ k t)) 2)) (* (* (sin k) (tan k)) (/ t (* (/ l t) (/ l t)))))
10.3b
(* (* (sin k) (tan k)) (/ t (* (/ l t) (/ l t))))
0.8b
(/ t (* (/ l t) (/ l t)))
0.2b
(* (/ l t) (/ l t))

rewrite193.0ms

Algorithm
rewrite-expression-head
Rules
243×add-cbrt-cube add-exp-log
106×cbrt-undiv div-exp
86×prod-exp cbrt-unprod
79×times-frac
62×add-sqr-sqrt
50×*-un-lft-identity add-cube-cbrt
23×associate-*r*
18×associate-/l*
16×pow1
14×associate-*l*
13×swap-sqr associate-/r/
9×associate-*r/ div-inv
5×frac-times associate-*l/
4×pow-prod-down tan-quot insert-posit16 add-log-exp unswap-sqr
2×clear-num associate-/r* frac-2neg flip3-+ *-commutative flip-+
1×pow2 pow-plus pow-sqr pow-prod-up associate-/l/
Counts
4 → 246
Calls
4 calls:
Slowest
94.0ms
(/ (/ 2 (+ (* (/ k t) (/ k t)) 2)) (* (* (sin k) (tan k)) (/ t (* (/ l t) (/ l t)))))
52.0ms
(* (* (sin k) (tan k)) (/ t (* (/ l t) (/ l t))))
25.0ms
(* (/ l t) (/ l t))
13.0ms
(/ t (* (/ l t) (/ l t)))

series1.2s

Counts
4 → 12
Calls
4 calls:
Slowest
852.0ms
(/ (/ 2 (+ (* (/ k t) (/ k t)) 2)) (* (* (sin k) (tan k)) (/ t (* (/ l t) (/ l t)))))
233.0ms
(* (* (sin k) (tan k)) (/ t (* (/ l t) (/ l t))))
50.0ms
(/ t (* (/ l t) (/ l t)))
36.0ms
(* (/ l t) (/ l t))

simplify1.1m

Counts
294 → 258
Calls
294 calls:
Slowest
1.7s
(/ (* (* (/ 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 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))))))
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))))))
1.5s
(/ (* (* (/ 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))))))

prune3.7s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 9.8b

localize78.0ms

Local error

Found 4 expressions with local error:

12.2b
(/ (/ 2 (+ (* (/ k t) (/ k t)) 2)) (/ (* (* t (/ t (/ l (sin k)))) (/ t (/ l (sin k)))) (cos k)))
1.4b
(/ t (/ l (sin k)))
1.4b
(/ t (/ l (sin k)))
0.2b
(* (* t (/ t (/ l (sin k)))) (/ t (/ l (sin k))))

rewrite157.0ms

Algorithm
rewrite-expression-head
Rules
441×times-frac
248×add-cbrt-cube add-exp-log
211×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
137×cbrt-undiv div-exp
63×prod-exp cbrt-unprod
44×associate-*r*
39×div-inv
33×associate-/r*
21×associate-/l*
20×associate-/r/
9×pow1
8×flip3-+ flip-+
4×insert-posit16 add-log-exp
3×clear-num frac-2neg pow-prod-down associate-*r/
1×frac-times associate-*l* associate-*l/ *-commutative associate-/l/
Counts
4 → 421
Calls
4 calls:
Slowest
79.0ms
(/ (/ 2 (+ (* (/ k t) (/ k t)) 2)) (/ (* (* t (/ t (/ l (sin k)))) (/ t (/ l (sin k)))) (cos k)))
52.0ms
(* (* t (/ t (/ l (sin k)))) (/ t (/ l (sin k))))
10.0ms
(/ t (/ l (sin k)))
7.0ms
(/ t (/ l (sin k)))

series1.5s

Counts
4 → 12
Calls
4 calls:
Slowest
1.2s
(/ (/ 2 (+ (* (/ k t) (/ k t)) 2)) (/ (* (* t (/ t (/ l (sin k)))) (/ t (/ l (sin k)))) (cos k)))
123.0ms
(* (* t (/ t (/ l (sin k)))) (/ t (/ l (sin k))))
100.0ms
(/ t (/ l (sin k)))
99.0ms
(/ t (/ l (sin k)))

simplify2.1m

Counts
619 → 433
Calls
619 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) (/ (* (* t t) t) (* (* (/ l (sin k)) (/ l (sin k))) (/ l (sin k))))) (/ (* (* t t) t) (* (* (/ l (sin k)) (/ l (sin k))) (/ l (sin k))))) (* (* (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 (/ t (/ l (sin k)))) (* t (/ t (/ l (sin k))))) (* t (/ t (/ l (sin k))))) (* (* (/ t (/ l (sin k))) (/ t (/ l (sin k)))) (/ t (/ l (sin k))))) (* (* (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 (/ t (/ l (sin k)))) (/ t (/ l (sin k)))) (* (* t (/ t (/ l (sin k)))) (/ t (/ l (sin k))))) (* (* t (/ t (/ l (sin k)))) (/ t (/ l (sin k))))) (* (* (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 t) t) (* (* (/ t (/ l (sin k))) (/ t (/ l (sin k)))) (/ t (/ l (sin k))))) (* (* (/ t (/ l (sin k))) (/ t (/ l (sin k)))) (/ t (/ l (sin k))))) (* (* (cos k) (cos k)) (cos k))))
943.0ms
(/ (/ (* (* 2 2) 2) (* (* (+ (* (/ k t) (/ k t)) 2) (+ (* (/ k t) (/ k t)) 2)) (+ (* (/ k t) (/ k t)) 2))) (* (* (/ (* (* t (/ t (/ l (sin k)))) (/ t (/ l (sin k)))) (cos k)) (/ (* (* t (/ t (/ l (sin k)))) (/ t (/ l (sin k)))) (cos k))) (/ (* (* t (/ t (/ l (sin k)))) (/ t (/ l (sin k)))) (cos k))))

prune6.7s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 9.3b

localize80.0ms

Local error

Found 4 expressions with local error:

12.2b
(/ (/ 1 (sqrt (+ (* (/ k t) (/ k t)) 2))) (/ (* t (/ t (/ l (sin k)))) 1))
9.1b
(sqrt (+ (* (/ k t) (/ k t)) 2))
9.1b
(sqrt (+ (* (/ k t) (/ k t)) 2))
6.0b
(/ (/ 2 (sqrt (+ (* (/ k t) (/ k t)) 2))) (/ (/ t (/ l (sin k))) (cos k)))

rewrite465.0ms

Algorithm
rewrite-expression-head
Rules
14367×times-frac
5693×add-sqr-sqrt
5691×*-un-lft-identity add-cube-cbrt
1311×sqrt-prod
497×div-inv
367×associate-/r/
294×sqrt-div
181×add-exp-log
147×flip3-+ flip-+
143×associate-/r*
134×div-exp
81×add-cbrt-cube
53×cbrt-undiv
48×associate-/l*
25×1-exp
24×prod-exp
9×rec-exp
6×pow1 cbrt-unprod
4×insert-posit16 add-log-exp
2×rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 associate-/l/
Counts
4 → 3743
Calls
4 calls:
Slowest
47.0ms
(/ (/ 2 (sqrt (+ (* (/ k t) (/ k t)) 2))) (/ (/ t (/ l (sin k))) (cos k)))
39.0ms
(/ (/ 1 (sqrt (+ (* (/ k t) (/ k t)) 2))) (/ (* t (/ t (/ l (sin k)))) 1))
27.0ms
(sqrt (+ (* (/ k t) (/ k t)) 2))
19.0ms
(sqrt (+ (* (/ k t) (/ k t)) 2))

series1.1s

Counts
4 → 12
Calls
4 calls:
Slowest
694.0ms
(/ (/ 1 (sqrt (+ (* (/ k t) (/ k t)) 2))) (/ (* t (/ t (/ l (sin k)))) 1))
338.0ms
(/ (/ 2 (sqrt (+ (* (/ k t) (/ k t)) 2))) (/ (/ t (/ l (sin k))) (cos k)))
68.0ms
(sqrt (+ (* (/ k t) (/ k t)) 2))
49.0ms
(sqrt (+ (* (/ k t) (/ k t)) 2))