Details

Time bar (total: 3.7m)

sample413.0ms

Algorithm
intervals
Results
126.0ms56×body1280valid
104.0ms61×body640valid
81.0ms175×body80valid
62.0ms32×body320valid
16.0ms22×body160valid

simplify359.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
358.0ms
(/ 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: 19.1b

localize66.0ms

Local error

Found 4 expressions with local error:

12.2b
(/ (/ 2 (fma (/ 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))

rewrite196.0ms

Algorithm
rewrite-expression-head
Rules
243×add-cbrt-cube add-exp-log
106×cbrt-undiv div-exp
86×prod-exp cbrt-unprod
77×times-frac
62×add-sqr-sqrt
50×*-un-lft-identity add-cube-cbrt
23×associate-*r*
16×pow1 associate-/l*
14×associate-*l*
13×swap-sqr
9×associate-*r/ associate-/r/ div-inv
5×frac-times associate-*l/
4×expm1-log1p-u pow-prod-down tan-quot insert-posit16 log1p-expm1-u add-log-exp unswap-sqr
2×clear-num associate-/r* frac-2neg *-commutative
1×pow2 pow-plus pow-sqr pow-prod-up associate-/l/
Counts
4 → 250
Calls
4 calls:
Slowest
92.0ms
(* (* (sin k) (tan k)) (/ t (* (/ l t) (/ l t))))
64.0ms
(/ (/ 2 (fma (/ k t) (/ k t) 2)) (* (* (sin k) (tan k)) (/ t (* (/ l t) (/ l t)))))
22.0ms
(/ t (* (/ l t) (/ l t)))
13.0ms
(* (/ l t) (/ l t))

series1.2s

Counts
4 → 12
Calls
4 calls:
Slowest
875.0ms
(/ (/ 2 (fma (/ k t) (/ k t) 2)) (* (* (sin k) (tan k)) (/ t (* (/ l t) (/ l t)))))
261.0ms
(* (* (sin k) (tan k)) (/ t (* (/ l t) (/ l t))))
57.0ms
(/ t (* (/ l t) (/ l t)))
45.0ms
(* (/ l t) (/ l t))

simplify1.3m

Counts
296 → 262
Calls
296 calls:
Slowest
1.9s
(/ (* (* (/ 2 (fma (/ k t) (/ k t) 2)) (/ 2 (fma (/ k t) (/ k t) 2))) (/ 2 (fma (/ k t) (/ k t) 2))) (* (* (* (* (sin k) (tan k)) (* (sin k) (tan k))) (* (sin k) (tan k))) (/ (* (* t t) t) (* (/ (* (* l l) l) (* (* t t) t)) (/ (* (* l l) l) (* (* t t) t))))))
1.8s
(/ (/ (* (* 2 2) 2) (* (* (fma (/ k t) (/ k t) 2) (fma (/ k t) (/ k t) 2)) (fma (/ k t) (/ k t) 2))) (* (* (* (* (sin k) (tan k)) (* (sin k) (tan k))) (* (sin k) (tan k))) (/ (* (* t t) t) (* (/ (* (* l l) l) (* (* t t) t)) (/ (* (* l l) l) (* (* t t) t))))))
1.8s
(/ (* (* (/ 2 (fma (/ k t) (/ k t) 2)) (/ 2 (fma (/ k t) (/ k t) 2))) (/ 2 (fma (/ 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 2) 2) (* (* (fma (/ k t) (/ k t) 2) (fma (/ k t) (/ k t) 2)) (fma (/ k t) (/ k t) 2))) (* (* (* (* (sin k) (sin k)) (sin k)) (* (* (tan k) (tan k)) (tan k))) (/ (* (* t t) t) (* (/ (* (* l l) l) (* (* t t) t)) (/ (* (* l l) l) (* (* t t) t))))))
1.8s
(/ (* (* (/ 2 (fma (/ k t) (/ k t) 2)) (/ 2 (fma (/ k t) (/ k t) 2))) (/ 2 (fma (/ 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))))))

prune3.8s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 10.1b

localize45.0ms

Local error

Found 4 expressions with local error:

12.2b
(/ (/ 2 (fma (/ 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))))

rewrite175.0ms

Algorithm
rewrite-expression-head
Rules
421×times-frac
248×add-cbrt-cube add-exp-log
207×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
137×cbrt-undiv div-exp
63×prod-exp cbrt-unprod
44×associate-*r*
37×div-inv
33×associate-/r*
19×associate-/l*
9×pow1
4×expm1-log1p-u associate-/r/ insert-posit16 log1p-expm1-u 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 → 413
Calls
4 calls:
Slowest
87.0ms
(/ (/ 2 (fma (/ k t) (/ k t) 2)) (/ (* (* t (/ t (/ l (sin k)))) (/ t (/ l (sin k)))) (cos k)))
53.0ms
(* (* t (/ t (/ l (sin k)))) (/ t (/ l (sin k))))
14.0ms
(/ t (/ l (sin k)))
9.0ms
(/ t (/ l (sin k)))

series1.2s

Counts
4 → 12
Calls
4 calls:
Slowest
878.0ms
(/ (/ 2 (fma (/ k t) (/ k t) 2)) (/ (* (* t (/ t (/ l (sin k)))) (/ t (/ l (sin k)))) (cos k)))
122.0ms
(* (* t (/ t (/ l (sin k)))) (/ t (/ l (sin k))))
100.0ms
(/ t (/ l (sin k)))
90.0ms
(/ t (/ l (sin k)))

simplify2.1m

Counts
597 → 425
Calls
597 calls:
Slowest
2.6s
(/ (* (* (/ 2 (fma (/ k t) (/ k t) 2)) (/ 2 (fma (/ k t) (/ k t) 2))) (/ 2 (fma (/ k t) (/ k t) 2))) (/ (* (* (* (* t t) t) (/ (* (* t t) t) (/ (* (* l l) l) (* (* (sin k) (sin k)) (sin k))))) (/ (* (* t t) t) (/ (* (* l l) l) (* (* (sin k) (sin k)) (sin k))))) (* (* (cos k) (cos k)) (cos k))))
1.9s
(/ (/ (* (* 2 2) 2) (* (* (fma (/ k t) (/ k t) 2) (fma (/ k t) (/ k t) 2)) (fma (/ 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))))
1.8s
(/ (* (* (/ 2 (fma (/ k t) (/ k t) 2)) (/ 2 (fma (/ k t) (/ k t) 2))) (/ 2 (fma (/ 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 (fma (/ k t) (/ k t) 2)) (/ 2 (fma (/ k t) (/ k t) 2))) (/ 2 (fma (/ 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))))
1.7s
(/ (/ (* (* 2 2) 2) (* (* (fma (/ k t) (/ k t) 2) (fma (/ k t) (/ k t) 2)) (fma (/ 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))))

prune6.4s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 9.3b

localize64.0ms

Local error

Found 4 expressions with local error:

10.1b
(* (* (/ (/ (cbrt (cos k)) t) (/ (sin k) l)) (/ (cbrt (cos k)) t)) (/ (/ 2 (fma (/ k t) (/ k t) 2)) (/ (/ t (/ l (sin k))) (cbrt (cos k)))))
4.8b
(/ (/ 2 (fma (/ k t) (/ k t) 2)) (/ (/ t (/ l (sin k))) (cbrt (cos k))))
1.5b
(/ (/ (cbrt (cos k)) t) (/ (sin k) l))
1.4b
(/ t (/ l (sin k)))

rewrite959.0ms

Algorithm
rewrite-expression-head
Rules
30441×times-frac
12222×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
3690×cbrt-prod
3489×associate-*r*
1257×div-inv
794×add-exp-log
639×add-cbrt-cube
488×cbrt-undiv div-exp
294×associate-/r*
189×prod-exp cbrt-unprod
166×associate-/r/
38×associate-/l*
9×pow1
5×frac-times associate-*l/
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×clear-num frac-2neg pow-prod-down associate-*r/
2×associate-/l/
1×associate-*l* *-commutative
Counts
4 → 7921
Calls
4 calls:
Slowest
176.0ms
(* (* (/ (/ (cbrt (cos k)) t) (/ (sin k) l)) (/ (cbrt (cos k)) t)) (/ (/ 2 (fma (/ k t) (/ k t) 2)) (/ (/ t (/ l (sin k))) (cbrt (cos k)))))
23.0ms
(/ (/ 2 (fma (/ k t) (/ k t) 2)) (/ (/ t (/ l (sin k))) (cbrt (cos k))))
21.0ms
(/ (/ (cbrt (cos k)) t) (/ (sin k) l))
14.0ms
(/ t (/ l (sin k)))

series1.8s

Counts
4 → 12
Calls
4 calls:
Slowest
896.0ms
(* (* (/ (/ (cbrt (cos k)) t) (/ (sin k) l)) (/ (cbrt (cos k)) t)) (/ (/ 2 (fma (/ k t) (/ k t) 2)) (/ (/ t (/ l (sin k))) (cbrt (cos k)))))
597.0ms
(/ (/ 2 (fma (/ k t) (/ k t) 2)) (/ (/ t (/ l (sin k))) (cbrt (cos k))))
200.0ms
(/ (/ (cbrt (cos k)) t) (/ (sin k) l))
118.0ms
(/ t (/ l (sin k)))