Details

Time bar (total: 2.5m)

sample755.0ms

Algorithm
intervals
Results
440.0ms53×body640valid
183.0ms77×body1280valid
67.0ms186×body80valid
32.0ms26×body320valid
7.0ms9×body160valid

simplify352.0ms

Calls
1 calls:
Slowest
352.0ms
(/ 2 (* (* (* (/ (pow t 3) (* l l)) (sin k)) (tan k)) (+ (+ 1 (pow (/ k t) 2)) 1)))

prune31.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 22.5b

localize44.0ms

Local error

Found 4 expressions with local error:

14.6b
(/ (/ 2 (+ (* (/ k t) (/ k t)) 2)) (* (* (sin k) (tan k)) (/ t (* (/ l t) (/ l t)))))
10.9b
(* (* (sin k) (tan k)) (/ t (* (/ l t) (/ l t))))
1.3b
(/ t (* (/ l t) (/ l t)))
0.3b
(/ 2 (+ (* (/ k t) (/ k t)) 2))

rewrite217.0ms

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/
Calls
4 calls:
Slowest
111.0ms
(/ (/ 2 (+ (* (/ k t) (/ k t)) 2)) (* (* (sin k) (tan k)) (/ t (* (/ l t) (/ l t)))))
72.0ms
(* (* (sin k) (tan k)) (/ t (* (/ l t) (/ l t))))
16.0ms
(/ 2 (+ (* (/ k t) (/ k t)) 2))
12.0ms
(/ t (* (/ l t) (/ l t)))

series1.3s

Calls
4 calls:
Slowest
873.0ms
(/ (/ 2 (+ (* (/ k t) (/ k t)) 2)) (* (* (sin k) (tan k)) (/ t (* (/ l t) (/ l t)))))
253.0ms
(* (* (sin k) (tan k)) (/ t (* (/ l t) (/ l t))))
72.0ms
(/ 2 (+ (* (/ k t) (/ k t)) 2))
65.0ms
(/ t (* (/ l t) (/ l t)))

simplify47.9s

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))))))
1.5s
(/ (* (* (/ 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))))))
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

16 alts after pruning (16 fresh and 0 done)

Merged error: 12.7b

localize76.0ms

Local error

Found 4 expressions with local error:

14.6b
(/ (/ 2 (+ (* (/ k t) (/ k t)) 2)) (/ (* (* t (/ (sin k) (/ l t))) (/ (sin k) (/ l t))) (cos k)))
3.7b
(/ (sin k) (/ l t))
3.7b
(/ (sin k) (/ l t))
0.3b
(/ 2 (+ (* (/ k t) (/ k t)) 2))

rewrite157.0ms

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/
Calls
4 calls:
Slowest
87.0ms
(/ (/ 2 (+ (* (/ k t) (/ k t)) 2)) (/ (* (* t (/ (sin k) (/ l t))) (/ (sin k) (/ l t))) (cos k)))
28.0ms
(/ 2 (+ (* (/ k t) (/ k t)) 2))
19.0ms
(/ (sin k) (/ l t))
15.0ms
(/ (sin k) (/ l t))

series1.1s

Calls
4 calls:
Slowest
854.0ms
(/ (/ 2 (+ (* (/ k t) (/ k t)) 2)) (/ (* (* t (/ (sin k) (/ l t))) (/ (sin k) (/ l t))) (cos k)))
96.0ms
(/ (sin k) (/ l t))
92.0ms
(/ (sin k) (/ l t))
68.0ms
(/ 2 (+ (* (/ k t) (/ k t)) 2))

simplify1.5m

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 (/ (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))))
1.6s
(/ (* (* (/ 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))) (/ (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))))
862.0ms
(/ (/ (* (* 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))))
804.0ms
(/ (/ (* (cbrt 2) (cbrt 2)) (sqrt (+ (* (/ k t) (/ k t)) 2))) (* (cbrt (/ (* (* t (/ (sin k) (/ l t))) (/ (sin k) (/ l t))) (cos k))) (cbrt (/ (* (* t (/ (sin k) (/ l t))) (/ (sin k) (/ l t))) (cos k)))))

prune5.5s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 12.7b

localize68.0ms

Local error

Found 4 expressions with local error:

13.1b
(sqrt (+ (* (/ k t) (/ k t)) 2))
13.1b
(sqrt (+ (* (/ k t) (/ k t)) 2))
11.3b
(/ (/ 1 (sqrt (+ (* (/ k t) (/ k t)) 2))) (/ (* t (/ (sin k) (/ l t))) 1))
5.6b
(/ (/ 2 (sqrt (+ (* (/ k t) (/ k t)) 2))) (/ (/ (sin k) (/ l t)) (cos k)))

rewrite424.0ms

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/
Calls
4 calls:
Slowest
51.0ms
(/ (/ 2 (sqrt (+ (* (/ k t) (/ k t)) 2))) (/ (/ (sin k) (/ l t)) (cos k)))
44.0ms
(/ (/ 1 (sqrt (+ (* (/ k t) (/ k t)) 2))) (/ (* t (/ (sin k) (/ l t))) 1))
16.0ms
(sqrt (+ (* (/ k t) (/ k t)) 2))
13.0ms
(sqrt (+ (* (/ k t) (/ k t)) 2))

series697.0ms

Calls
4 calls:
Slowest
333.0ms
(/ (/ 2 (sqrt (+ (* (/ k t) (/ k t)) 2))) (/ (/ (sin k) (/ l t)) (cos k)))
240.0ms
(/ (/ 1 (sqrt (+ (* (/ k t) (/ k t)) 2))) (/ (* t (/ (sin k) (/ l t))) 1))
68.0ms
(sqrt (+ (* (/ k t) (/ k t)) 2))
56.0ms
(sqrt (+ (* (/ k t) (/ k t)) 2))