Details

Time bar (total: 3.2m)

sample443.0ms

Algorithm
intervals
Results
208.0ms66×body1280valid
101.0ms56×body640valid
65.0ms168×body80valid
30.0ms23×body320valid
11.0ms15×body160valid

simplify390.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
390.0ms
(/ 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: 22.9b

localize66.0ms

Local error

Found 4 expressions with local error:

13.7b
(/ (/ 2 (fma (/ k t) (/ k t) 2)) (* (* (sin k) (tan k)) (/ t (* (/ l t) (/ l t)))))
11.1b
(* (* (sin k) (tan k)) (/ t (* (/ l t) (/ l t))))
1.0b
(/ t (* (/ l t) (/ l t)))
0.5b
(/ 2 (fma (/ k t) (/ k t) 2))

rewrite153.0ms

Algorithm
rewrite-expression-head
Rules
233×add-cbrt-cube add-exp-log
103×cbrt-undiv div-exp
82×prod-exp cbrt-unprod
46×times-frac
30×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
19×associate-/l*
10×associate-*r*
9×pow1 associate-/r/
8×associate-*r/
6×div-inv
5×associate-/r*
4×expm1-log1p-u frac-times associate-*l/ tan-quot insert-posit16 log1p-expm1-u add-log-exp
3×clear-num frac-2neg pow-prod-down
1×associate-*l* *-commutative associate-/l/
Counts
4 → 210
Calls
4 calls:
Slowest
66.0ms
(/ (/ 2 (fma (/ k t) (/ k t) 2)) (* (* (sin k) (tan k)) (/ t (* (/ l t) (/ l t)))))
64.0ms
(* (* (sin k) (tan k)) (/ t (* (/ l t) (/ l t))))
14.0ms
(/ t (* (/ l t) (/ l t)))
4.0ms
(/ 2 (fma (/ k t) (/ k t) 2))

series1.3s

Counts
4 → 12
Calls
4 calls:
Slowest
914.0ms
(/ (/ 2 (fma (/ k t) (/ k t) 2)) (* (* (sin k) (tan k)) (/ t (* (/ l t) (/ l t)))))
200.0ms
(* (* (sin k) (tan k)) (/ t (* (/ l t) (/ l t))))
75.0ms
(/ 2 (fma (/ k t) (/ k t) 2))
61.0ms
(/ t (* (/ l t) (/ l t)))

simplify1.2m

Counts
250 → 222
Calls
250 calls:
Slowest
2.3s
(/ (* (* (/ 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))))))
1.9s
(/ (/ (* (* 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))))))
1.9s
(/ (/ (* (* 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 t) (/ l t)) (/ l t)) (* (* (/ l t) (/ l t)) (/ l 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 (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 l) l) (* (* t t) t)) (/ (* (* l l) l) (* (* t t) t))))))

prune3.2s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 12.5b

localize46.0ms

Local error

Found 4 expressions with local error:

13.7b
(/ (/ 2 (fma (/ k t) (/ k t) 2)) (/ (* (/ t (/ l (sin k))) (* (/ t (/ l (sin k))) t)) (cos k)))
3.0b
(/ t (/ l (sin k)))
3.0b
(/ t (/ l (sin k)))
0.5b
(/ 2 (fma (/ k t) (/ k t) 2))

rewrite105.0ms

Algorithm
rewrite-expression-head
Rules
364×times-frac
196×add-cbrt-cube add-exp-log
180×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
117×cbrt-undiv div-exp
42×prod-exp cbrt-unprod
36×associate-/r*
34×div-inv
22×associate-/l*
4×expm1-log1p-u pow1 clear-num frac-2neg insert-posit16 log1p-expm1-u add-log-exp
3×associate-/r/
1×associate-/l/
Counts
4 → 358
Calls
4 calls:
Slowest
77.0ms
(/ (/ 2 (fma (/ k t) (/ k t) 2)) (/ (* (/ t (/ l (sin k))) (* (/ t (/ l (sin k))) t)) (cos k)))
10.0ms
(/ t (/ l (sin k)))
7.0ms
(/ t (/ l (sin k)))
4.0ms
(/ 2 (fma (/ k t) (/ k t) 2))

series1.2s

Counts
4 → 12
Calls
4 calls:
Slowest
931.0ms
(/ (/ 2 (fma (/ k t) (/ k t) 2)) (/ (* (/ t (/ l (sin k))) (* (/ t (/ l (sin k))) t)) (cos k)))
113.0ms
(/ t (/ l (sin k)))
110.0ms
(/ t (/ l (sin k)))
81.0ms
(/ 2 (fma (/ k t) (/ k t) 2))

simplify1.7m

Counts
552 → 370
Calls
552 calls:
Slowest
2.5s
(/ (* (* (/ 2 (fma (/ k t) (/ k t) 2)) (/ 2 (fma (/ k t) (/ k t) 2))) (/ 2 (fma (/ k t) (/ k t) 2))) (/ (* (/ (* (* t t) t) (/ (* (* l l) l) (* (* (sin k) (sin k)) (sin k)))) (* (/ (* (* t t) t) (/ (* (* l l) l) (* (* (sin k) (sin k)) (sin k)))) (* (* t t) t))) (* (* (cos k) (cos k)) (cos k))))
2.2s
(/ (/ (* (* 2 2) 2) (* (* (fma (/ k t) (/ k t) 2) (fma (/ k t) (/ k t) 2)) (fma (/ k t) (/ k t) 2))) (/ (* (* (* (/ t (/ l (sin k))) (/ t (/ l (sin k)))) (/ t (/ l (sin k)))) (* (* (* (/ t (/ l (sin k))) (/ t (/ l (sin k)))) (/ t (/ l (sin k)))) (* (* t t) t))) (* (* (cos k) (cos k)) (cos k))))
1.8s
(/ (/ (* (* 2 2) 2) (* (* (fma (/ k t) (/ k t) 2) (fma (/ k t) (/ k t) 2)) (fma (/ k t) (/ k t) 2))) (/ (* (* (* (/ 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))) t))) (* (* (cos k) (cos k)) (cos k))))
1.7s
(/ (* (* (/ 2 (fma (/ k t) (/ k t) 2)) (/ 2 (fma (/ k t) (/ k t) 2))) (/ 2 (fma (/ k t) (/ k t) 2))) (/ (* (* (* (/ 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))) t))) (* (* (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 (/ l (sin k))) (/ t (/ l (sin k)))) (/ t (/ l (sin k)))) (* (* (* (/ t (/ l (sin k))) t) (* (/ t (/ l (sin k))) t)) (* (/ t (/ l (sin k))) t))) (* (* (cos k) (cos k)) (cos k))))

prune5.8s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 11.3b

localize55.0ms

Local error

Found 4 expressions with local error:

10.9b
(/ (/ (/ 2 (fma (/ k t) (/ k t) 2)) (/ (/ t (/ l (sin k))) (* (cbrt (cos k)) (cbrt (cos k))))) (/ (* (/ t (/ l (sin k))) t) (cbrt (cos k))))
4.8b
(/ (/ 2 (fma (/ k t) (/ k t) 2)) (/ (/ t (/ l (sin k))) (* (cbrt (cos k)) (cbrt (cos k)))))
3.0b
(/ t (/ l (sin k)))
3.0b
(/ t (/ l (sin k)))

rewrite891.0ms

Algorithm
rewrite-expression-head
Rules
40171×times-frac
11680×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
2015×div-inv
1890×cbrt-prod
648×associate-/l*
634×add-exp-log
502×add-cbrt-cube
456×cbrt-undiv div-exp
172×associate-/r/
84×associate-/r*
81×prod-exp cbrt-unprod
4×expm1-log1p-u pow1 clear-num frac-2neg insert-posit16 log1p-expm1-u add-log-exp
2×associate-/l/
Counts
4 → 7968
Calls
4 calls:
Slowest
87.0ms
(/ (/ (/ 2 (fma (/ k t) (/ k t) 2)) (/ (/ t (/ l (sin k))) (* (cbrt (cos k)) (cbrt (cos k))))) (/ (* (/ t (/ l (sin k))) t) (cbrt (cos k))))
48.0ms
(/ (/ 2 (fma (/ k t) (/ k t) 2)) (/ (/ t (/ l (sin k))) (* (cbrt (cos k)) (cbrt (cos k)))))
32.0ms
(/ t (/ l (sin k)))
15.0ms
(/ t (/ l (sin k)))

series2.1s

Counts
4 → 12
Calls
4 calls:
Slowest
1.3s
(/ (/ (/ 2 (fma (/ k t) (/ k t) 2)) (/ (/ t (/ l (sin k))) (* (cbrt (cos k)) (cbrt (cos k))))) (/ (* (/ t (/ l (sin k))) t) (cbrt (cos k))))
602.0ms
(/ (/ 2 (fma (/ k t) (/ k t) 2)) (/ (/ t (/ l (sin k))) (* (cbrt (cos k)) (cbrt (cos k)))))
102.0ms
(/ t (/ l (sin k)))
94.0ms
(/ t (/ l (sin k)))