Details

Time bar (total: 2.5m)

sample463.0ms

Algorithm
intervals
Results
168.0ms66×body1280valid
120.0ms51×body640valid
103.0ms195×body80valid
35.0ms29×body320valid
12.0ms15×body160valid

simplify302.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
302.0ms
(/ 2 (* (* (* (/ (pow t 3) (* l l)) (sin k)) (tan k)) (+ (+ 1 (pow (/ k t) 2)) 1)))

prune21.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 18.9b

localize42.0ms

Local error

Found 4 expressions with local error:

12.9b
(/ (/ 2 (+ (* (/ k t) (/ k t)) 2)) (* (* (sin k) (tan k)) (/ t (* (/ l t) (/ l t)))))
8.8b
(* (* (sin k) (tan k)) (/ t (* (/ l t) (/ l t))))
1.9b
(/ t (* (/ l t) (/ l t)))
0.3b
(/ 2 (+ (* (/ k t) (/ k t)) 2))

rewrite208.0ms

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
77.0ms
(/ (/ 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))))
30.0ms
(/ 2 (+ (* (/ k t) (/ k t)) 2))
20.0ms
(/ t (* (/ l t) (/ l t)))

series1.3s

Counts
4 → 12
Calls
4 calls:
Slowest
877.0ms
(/ (/ 2 (+ (* (/ k t) (/ k t)) 2)) (* (* (sin k) (tan k)) (/ t (* (/ l t) (/ l t)))))
266.0ms
(* (* (sin k) (tan k)) (/ t (* (/ l t) (/ l t))))
75.0ms
(/ 2 (+ (* (/ k t) (/ k t)) 2))
60.0ms
(/ t (* (/ l t) (/ l t)))

simplify46.9s

Counts
197 → 220
Calls
197 calls:
Slowest
2.2s
(/ (* (* (/ 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))))))
1.8s
(/ (* (* (/ 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))))))
1.5s
(/ (* (* (/ 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 (+ (* (/ 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))))))
1.3s
(/ (/ (* (* 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))))))

prune3.2s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 10.9b

localize58.0ms

Local error

Found 4 expressions with local error:

12.9b
(/ (/ 2 (+ (* (/ k t) (/ k t)) 2)) (/ (* (* t (/ (sin k) (/ l t))) (/ (sin k) (/ l t))) (cos k)))
3.0b
(/ (sin k) (/ l t))
3.0b
(/ (sin k) (/ l t))
0.3b
(/ 2 (+ (* (/ k t) (/ k t)) 2))

rewrite156.0ms

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
98.0ms
(/ (/ 2 (+ (* (/ k t) (/ k t)) 2)) (/ (* (* t (/ (sin k) (/ l t))) (/ (sin k) (/ l t))) (cos k)))
18.0ms
(/ (sin k) (/ l t))
15.0ms
(/ (sin k) (/ l t))
15.0ms
(/ 2 (+ (* (/ k t) (/ k t)) 2))

series1.1s

Counts
4 → 12
Calls
4 calls:
Slowest
783.0ms
(/ (/ 2 (+ (* (/ k t) (/ k t)) 2)) (/ (* (* t (/ (sin k) (/ l t))) (/ (sin k) (/ l t))) (cos k)))
104.0ms
(/ (sin k) (/ l t))
93.0ms
(/ (sin k) (/ l t))
71.0ms
(/ 2 (+ (* (/ k t) (/ k t)) 2))

simplify1.5m

Counts
520 → 380
Calls
520 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) (* (* (/ (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))))
1.5s
(/ (* (* (/ 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))))
871.0ms
(/ (/ (* (* 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))))
797.0ms
(/ (* (cbrt (/ 2 (+ (* (/ k t) (/ k t)) 2))) (cbrt (/ 2 (+ (* (/ 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)))))

prune5.8s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 10.3b

localize90.0ms

Local error

Found 4 expressions with local error:

10.6b
(sqrt (+ (* (/ k t) (/ k t)) 2))
10.6b
(sqrt (+ (* (/ k t) (/ k t)) 2))
10.3b
(/ (/ (sqrt 2) (sqrt (+ (* (/ k t) (/ k t)) 2))) (/ (* t (/ (sin k) (/ l t))) 1))
5.2b
(/ (/ (sqrt 2) (sqrt (+ (* (/ k t) (/ k t)) 2))) (/ (/ (sin k) (/ l t)) (cos k)))

rewrite1.0s

Algorithm
rewrite-expression-head
Rules
25545×times-frac
10169×add-sqr-sqrt
10167×*-un-lft-identity add-cube-cbrt
5226×sqrt-prod
749×div-inv
421×associate-/r/
294×sqrt-div
147×flip3-+ flip-+
143×associate-/r*
113×add-exp-log
84×associate-/l*
81×add-cbrt-cube
79×div-exp
53×cbrt-undiv
12×prod-exp
8×1-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 → 6335
Calls
4 calls:
Slowest
40.0ms
(/ (/ (sqrt 2) (sqrt (+ (* (/ k t) (/ k t)) 2))) (/ (/ (sin k) (/ l t)) (cos k)))
35.0ms
(/ (/ (sqrt 2) (sqrt (+ (* (/ k t) (/ k t)) 2))) (/ (* t (/ (sin k) (/ l t))) 1))
25.0ms
(sqrt (+ (* (/ k t) (/ k t)) 2))
24.0ms
(sqrt (+ (* (/ k t) (/ k t)) 2))

series855.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
382.0ms
(/ (/ (sqrt 2) (sqrt (+ (* (/ k t) (/ k t)) 2))) (/ (/ (sin k) (/ l t)) (cos k)))
339.0ms
(/ (/ (sqrt 2) (sqrt (+ (* (/ k t) (/ k t)) 2))) (/ (* t (/ (sin k) (/ l t))) 1))
73.0ms
(sqrt (+ (* (/ k t) (/ k t)) 2))
60.0ms
(sqrt (+ (* (/ k t) (/ k t)) 2))