Details

Time bar (total: 2.5m)

sample439.0ms

Algorithm
intervals
Results
171.0ms72×body640valid
134.0ms61×body1280valid
62.0ms181×body80valid
34.0ms26×body320valid
11.0ms13×body160valid

simplify294.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
294.0ms
(/ 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: 22.2b

localize35.0ms

Local error

Found 4 expressions with local error:

15.7b
(/ (/ 2 (+ (* (/ k t) (/ k t)) 2)) (* (* (sin k) (tan k)) (/ t (* (/ l t) (/ l t)))))
10.1b
(* (* (sin k) (tan k)) (/ t (* (/ l t) (/ l t))))
1.0b
(/ t (* (/ l t) (/ l t)))
0.3b
(/ 2 (+ (* (/ k t) (/ k t)) 2))

rewrite184.0ms

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
110.0ms
(/ (/ 2 (+ (* (/ k t) (/ k t)) 2)) (* (* (sin k) (tan k)) (/ t (* (/ l t) (/ l t)))))
44.0ms
(* (* (sin k) (tan k)) (/ t (* (/ l t) (/ l t))))
15.0ms
(/ 2 (+ (* (/ k t) (/ k t)) 2))
10.0ms
(/ t (* (/ l t) (/ l t)))

series1.3s

Counts
4 → 12
Calls
4 calls:
Slowest
941.0ms
(/ (/ 2 (+ (* (/ k t) (/ k t)) 2)) (* (* (sin k) (tan k)) (/ t (* (/ l t) (/ l t)))))
249.0ms
(* (* (sin k) (tan k)) (/ t (* (/ l t) (/ l t))))
78.0ms
(/ 2 (+ (* (/ k t) (/ k t)) 2))
39.0ms
(/ t (* (/ l t) (/ l t)))

simplify47.4s

Counts
197 → 220
Calls
197 calls:
Slowest
1.9s
(/ (* (* (/ 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))))))
1.7s
(/ (* (* (/ 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))))))
1.6s
(/ (* (* (/ 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))))))
1.4s
(/ (/ (* (* 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

17 alts after pruning (17 fresh and 0 done)

Merged error: 12.2b

localize58.0ms

Local error

Found 4 expressions with local error:

15.7b
(/ (/ 2 (+ (* (/ k t) (/ k t)) 2)) (/ (* (* t (/ (sin k) (/ l t))) (/ (sin k) (/ l t))) (cos k)))
3.3b
(/ (sin k) (/ l t))
3.3b
(/ (sin k) (/ l t))
0.3b
(/ 2 (+ (* (/ k t) (/ k t)) 2))

rewrite126.0ms

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
75.0ms
(/ (/ 2 (+ (* (/ k t) (/ k t)) 2)) (/ (* (* t (/ (sin k) (/ l t))) (/ (sin k) (/ l t))) (cos k)))
17.0ms
(/ 2 (+ (* (/ k t) (/ k t)) 2))
9.0ms
(/ (sin k) (/ l t))
9.0ms
(/ (sin k) (/ l t))

series1.0s

Counts
4 → 12
Calls
4 calls:
Slowest
780.0ms
(/ (/ 2 (+ (* (/ k t) (/ k t)) 2)) (/ (* (* t (/ (sin k) (/ l t))) (/ (sin k) (/ l t))) (cos k)))
92.0ms
(/ (sin k) (/ l t))
87.0ms
(/ (sin k) (/ l t))
75.0ms
(/ 2 (+ (* (/ k t) (/ k t)) 2))

simplify1.5m

Counts
520 → 380
Calls
520 calls:
Slowest
2.2s
(/ (* (* (/ 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))))
937.0ms
(/ (/ (* (* 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))))
803.0ms
(/ (/ (* (cbrt 2) (cbrt 2)) 1) (/ (* t (/ (sin k) (/ l t))) 1))

prune5.7s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 11.5b

localize84.0ms

Local error

Found 4 expressions with local error:

12.0b
(/ (/ (* (cbrt 2) (cbrt 2)) (sqrt (+ (* (/ k t) (/ k t)) 2))) (/ (* t (/ (sin k) (/ l t))) 1))
10.7b
(sqrt (+ (* (/ k t) (/ k t)) 2))
10.7b
(sqrt (+ (* (/ k t) (/ k t)) 2))
7.3b
(/ (/ (cbrt 2) (sqrt (+ (* (/ k t) (/ k t)) 2))) (/ (/ (sin k) (/ l t)) (cos k)))

rewrite1.1s

Algorithm
rewrite-expression-head
Rules
25005×times-frac
9933×add-sqr-sqrt
9931×*-un-lft-identity add-cube-cbrt
2496×sqrt-prod
2466×cbrt-prod
719×div-inv
421×associate-/r/
294×sqrt-div
165×add-exp-log
147×flip3-+ flip-+
143×associate-/r*
111×div-exp
97×add-cbrt-cube
70×cbrt-undiv
54×associate-/l*
27×prod-exp
14×cbrt-unprod
12×1-exp
6×pow1
4×insert-posit16 add-log-exp
2×rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 associate-/l/
Counts
4 → 6109
Calls
4 calls:
Slowest
58.0ms
(/ (/ (cbrt 2) (sqrt (+ (* (/ k t) (/ k t)) 2))) (/ (/ (sin k) (/ l t)) (cos k)))
43.0ms
(/ (/ (* (cbrt 2) (cbrt 2)) (sqrt (+ (* (/ k t) (/ k t)) 2))) (/ (* t (/ (sin k) (/ l t))) 1))
24.0ms
(sqrt (+ (* (/ k t) (/ k t)) 2))
15.0ms
(sqrt (+ (* (/ k t) (/ k t)) 2))

series1.0s

Counts
4 → 12
Calls
4 calls:
Slowest
515.0ms
(/ (/ (* (cbrt 2) (cbrt 2)) (sqrt (+ (* (/ k t) (/ k t)) 2))) (/ (* t (/ (sin k) (/ l t))) 1))
419.0ms
(/ (/ (cbrt 2) (sqrt (+ (* (/ k t) (/ k t)) 2))) (/ (/ (sin k) (/ l t)) (cos k)))
55.0ms
(sqrt (+ (* (/ k t) (/ k t)) 2))
55.0ms
(sqrt (+ (* (/ k t) (/ k t)) 2))