Details

Time bar (total: 2.5m)

sample367.0ms

Algorithm
intervals
Results
122.0ms51×body640valid
115.0ms56×body1280valid
65.0ms204×body80valid
31.0ms25×body320valid
13.0ms18×body160valid

simplify336.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
336.0ms
(/ 2 (* (* (* (/ (pow t 3) (* l l)) (sin k)) (tan k)) (+ (+ 1 (pow (/ k t) 2)) 1)))

prune25.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 22.6b

localize74.0ms

Local error

Found 4 expressions with local error:

15.4b
(/ (/ 2 (+ (* (/ k t) (/ k t)) 2)) (* (* (sin k) (tan k)) (/ t (* (/ l t) (/ l t)))))
10.2b
(* (* (sin k) (tan k)) (/ t (* (/ l t) (/ l t))))
1.0b
(/ t (* (/ l t) (/ l t)))
0.3b
(/ 2 (+ (* (/ k t) (/ k t)) 2))

rewrite226.0ms

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
84.0ms
(/ (/ 2 (+ (* (/ k t) (/ k t)) 2)) (* (* (sin k) (tan k)) (/ t (* (/ l t) (/ l t)))))
84.0ms
(* (* (sin k) (tan k)) (/ t (* (/ l t) (/ l t))))
29.0ms
(/ 2 (+ (* (/ k t) (/ k t)) 2))
19.0ms
(/ t (* (/ l t) (/ l t)))

series1.3s

Counts
4 → 12
Calls
4 calls:
Slowest
924.0ms
(/ (/ 2 (+ (* (/ k t) (/ k t)) 2)) (* (* (sin k) (tan k)) (/ t (* (/ l t) (/ l t)))))
268.0ms
(* (* (sin k) (tan k)) (/ t (* (/ l t) (/ l t))))
87.0ms
(/ 2 (+ (* (/ k t) (/ k t)) 2))
66.0ms
(/ t (* (/ l t) (/ l t)))

simplify45.6s

Counts
197 → 220
Calls
197 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 (+ (* (/ 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))))))
1.3s
(/ (/ (* (* 2 2) 2) (* (* (+ (* (/ k t) (/ k t)) 2) (+ (* (/ k t) (/ k t)) 2)) (+ (* (/ k t) (/ k t)) 2))) (* (* (* (* (sin k) (tan k)) (* (sin k) (tan k))) (* (sin k) (tan k))) (* (* (/ t (* (/ l t) (/ l t))) (/ t (* (/ l t) (/ l t)))) (/ t (* (/ l t) (/ l t))))))

prune3.3s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 12.8b

localize77.0ms

Local error

Found 4 expressions with local error:

15.4b
(/ (/ 2 (+ (* (/ k t) (/ k t)) 2)) (/ (* (* t (/ (sin k) (/ l t))) (/ (sin k) (/ l t))) (cos k)))
3.9b
(/ (sin k) (/ l t))
3.9b
(/ (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/
Counts
4 → 368
Calls
4 calls:
Slowest
103.0ms
(/ (/ 2 (+ (* (/ k t) (/ k t)) 2)) (/ (* (* t (/ (sin k) (/ l t))) (/ (sin k) (/ l t))) (cos k)))
20.0ms
(/ (sin k) (/ l t))
15.0ms
(/ 2 (+ (* (/ k t) (/ k t)) 2))
12.0ms
(/ (sin k) (/ l t))

series1.1s

Counts
4 → 12
Calls
4 calls:
Slowest
810.0ms
(/ (/ 2 (+ (* (/ k t) (/ k t)) 2)) (/ (* (* t (/ (sin k) (/ l t))) (/ (sin k) (/ l t))) (cos k)))
91.0ms
(/ 2 (+ (* (/ k t) (/ k t)) 2))
90.0ms
(/ (sin k) (/ l t))
89.0ms
(/ (sin k) (/ l t))

simplify1.5m

Counts
520 → 380
Calls
520 calls:
Slowest
1.7s
(/ (* (* (/ 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))))
1.4s
(/ (* (* (/ 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))))
859.0ms
(/ (/ 2 (+ (* (/ k t) (/ k t)) 2)) (cbrt (/ (* (* t (/ (sin k) (/ l t))) (/ (sin k) (/ l t))) (cos k))))
762.0ms
(/ (/ (* (* 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))))

prune5.5s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 11.3b

localize54.0ms

Local error

Found 4 expressions with local error:

12.2b
(/ (/ 2 (+ (* (/ k t) (/ k t)) 2)) (/ (* t (/ (sin k) (/ l t))) 1))
5.1b
(/ (/ (/ 2 (+ (* (/ k t) (/ k t)) 2)) (/ (* t (/ (sin k) (/ l t))) 1)) (/ (/ (sin k) (/ l t)) (cos k)))
3.9b
(/ (sin k) (/ l t))
3.9b
(/ (sin k) (/ l t))

rewrite2.1s

Algorithm
rewrite-expression-head
Rules
81146×times-frac
27786×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
4630×div-inv
2408×associate-/r/
967×flip3-+ flip-+
593×add-exp-log
471×div-exp
353×add-cbrt-cube
261×cbrt-undiv
169×associate-/r*
131×associate-/l*
60×prod-exp
40×1-exp
30×cbrt-unprod
4×pow1 clear-num frac-2neg insert-posit16 add-log-exp
2×associate-/l/
Counts
4 → 15649
Calls
4 calls:
Slowest
68.0ms
(/ (/ (/ 2 (+ (* (/ k t) (/ k t)) 2)) (/ (* t (/ (sin k) (/ l t))) 1)) (/ (/ (sin k) (/ l t)) (cos k)))
65.0ms
(/ (/ 2 (+ (* (/ k t) (/ k t)) 2)) (/ (* t (/ (sin k) (/ l t))) 1))
43.0ms
(/ (sin k) (/ l t))
18.0ms
(/ (sin k) (/ l t))

series1.2s

Counts
4 → 12
Calls
4 calls:
Slowest
818.0ms
(/ (/ (/ 2 (+ (* (/ k t) (/ k t)) 2)) (/ (* t (/ (sin k) (/ l t))) 1)) (/ (/ (sin k) (/ l t)) (cos k)))
254.0ms
(/ (/ 2 (+ (* (/ k t) (/ k t)) 2)) (/ (* t (/ (sin k) (/ l t))) 1))
86.0ms
(/ (sin k) (/ l t))
78.0ms
(/ (sin k) (/ l t))