Details

Time bar (total: 5.5m)

sample419.0ms

Algorithm
intervals
Results
211.0ms84×body1280valid
93.0ms49×body640valid
56.0ms169×body80valid
26.0ms24×body320valid
11.0ms15×body160valid

simplify713.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
713.0ms
(/ 2 (* (* (* (/ (pow t 3) (* l l)) (sin k)) (tan k)) (+ (+ 1 (pow (/ k t) 2)) 1)))

prune22.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 24.8b

localize45.0ms

Local error

Found 4 expressions with local error:

17.4b
(/ (/ 2 (+ (* (/ k t) (/ k t)) 2)) (* (* (sin k) (tan k)) (/ t (* (/ l t) (/ l t)))))
10.0b
(* (* (sin k) (tan k)) (/ t (* (/ l t) (/ l t))))
2.1b
(/ t (* (/ l t) (/ l t)))
0.3b
(/ 2 (+ (* (/ k t) (/ k t)) 2))

rewrite162.0ms

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
65.0ms
(/ (/ 2 (+ (* (/ k t) (/ k t)) 2)) (* (* (sin k) (tan k)) (/ t (* (/ l t) (/ l t)))))
54.0ms
(* (* (sin k) (tan k)) (/ t (* (/ l t) (/ l t))))
23.0ms
(/ 2 (+ (* (/ k t) (/ k t)) 2))
10.0ms
(/ t (* (/ l t) (/ l t)))

series1.3s

Counts
4 → 12
Calls
4 calls:
Slowest
923.0ms
(/ (/ 2 (+ (* (/ k t) (/ k t)) 2)) (* (* (sin k) (tan k)) (/ t (* (/ l t) (/ l t)))))
298.0ms
(* (* (sin k) (tan k)) (/ t (* (/ l t) (/ l t))))
61.0ms
(/ t (* (/ l t) (/ l t)))
56.0ms
(/ 2 (+ (* (/ k t) (/ k t)) 2))

simplify46.4s

Counts
197 → 220
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))))))
1.7s
(/ (* (* (/ 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) (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))))))
1.6s
(/ (* (* (/ 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))))))
1.2s
(/ (/ (* (* 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

12 alts after pruning (12 fresh and 0 done)

Merged error: 12.5b

localize68.0ms

Local error

Found 4 expressions with local error:

17.4b
(/ (/ 2 (+ (* (/ k t) (/ k t)) 2)) (/ (* (* t (/ (sin k) (/ l t))) (/ (sin k) (/ l t))) (cos k)))
3.4b
(/ (sin k) (/ l t))
3.4b
(/ (sin k) (/ l t))
0.3b
(/ 2 (+ (* (/ k t) (/ k t)) 2))

rewrite142.0ms

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
84.0ms
(/ (/ 2 (+ (* (/ k t) (/ k t)) 2)) (/ (* (* t (/ (sin k) (/ l t))) (/ (sin k) (/ l t))) (cos k)))
25.0ms
(/ 2 (+ (* (/ k t) (/ k t)) 2))
9.0ms
(/ (sin k) (/ l t))
9.0ms
(/ (sin k) (/ l t))

series1.1s

Counts
4 → 12
Calls
4 calls:
Slowest
858.0ms
(/ (/ 2 (+ (* (/ k t) (/ k t)) 2)) (/ (* (* t (/ (sin k) (/ l t))) (/ (sin k) (/ l t))) (cos k)))
116.0ms
(/ (sin k) (/ l t))
85.0ms
(/ (sin k) (/ l t))
70.0ms
(/ 2 (+ (* (/ k t) (/ k t)) 2))

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))))
1.5s
(/ (* (* (/ 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))))
820.0ms
(/ (* (cbrt (sin k)) (cbrt (sin k))) (/ (* (cbrt l) (cbrt l)) (* (cbrt t) (cbrt t))))
806.0ms
(/ (/ (* (* 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))))

prune5.8s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 11.4b

localize76.0ms

Local error

Found 4 expressions with local error:

18.7b
(cbrt (+ (* (/ k t) (/ k t)) 2))
18.7b
(cbrt (+ (* (/ k t) (/ k t)) 2))
18.7b
(cbrt (+ (* (/ k t) (/ k t)) 2))
6.0b
(* (/ (/ (/ (sqrt 2) t) (* (/ (sin k) l) (* t (cbrt (+ (* (/ k t) (/ k t)) 2))))) (* (/ (sin k) l) (* t (cbrt (+ (* (/ k t) (/ k t)) 2))))) (* (/ (sqrt 2) (cbrt (+ (* (/ k t) (/ k t)) 2))) (cos k)))

rewrite561.0ms

Algorithm
rewrite-expression-head
Rules
1402×add-exp-log
1220×add-cbrt-cube
658×prod-exp cbrt-unprod
572×cbrt-undiv div-exp
71×times-frac
40×associate-*l*
22×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
14×cbrt-div
13×associate-*r/
10×associate-/r/
9×cbrt-prod pow1 sqrt-prod
7×flip3-+ flip-+
5×frac-times associate-*l/
4×insert-posit16 add-log-exp
3×pow1/3 pow-prod-down div-inv
1×associate-*r* *-commutative
Counts
4 → 433
Calls
4 calls:
Slowest
495.0ms
(* (/ (/ (/ (sqrt 2) t) (* (/ (sin k) l) (* t (cbrt (+ (* (/ k t) (/ k t)) 2))))) (* (/ (sin k) l) (* t (cbrt (+ (* (/ k t) (/ k t)) 2))))) (* (/ (sqrt 2) (cbrt (+ (* (/ k t) (/ k t)) 2))) (cos k)))
14.0ms
(cbrt (+ (* (/ k t) (/ k t)) 2))
12.0ms
(cbrt (+ (* (/ k t) (/ k t)) 2))
7.0ms
(cbrt (+ (* (/ k t) (/ k t)) 2))

series1.5s

Counts
4 → 12
Calls
4 calls:
Slowest
893.0ms
(* (/ (/ (/ (sqrt 2) t) (* (/ (sin k) l) (* t (cbrt (+ (* (/ k t) (/ k t)) 2))))) (* (/ (sin k) l) (* t (cbrt (+ (* (/ k t) (/ k t)) 2))))) (* (/ (sqrt 2) (cbrt (+ (* (/ k t) (/ k t)) 2))) (cos k)))
198.0ms
(cbrt (+ (* (/ k t) (/ k t)) 2))
184.0ms
(cbrt (+ (* (/ k t) (/ k t)) 2))
181.0ms
(cbrt (+ (* (/ k t) (/ k t)) 2))

simplify2.8m

Counts
409 → 445
Calls
409 calls:
Slowest
2.6s
(* (* (* (/ (/ (/ (sqrt 2) t) (* (/ (sin k) l) (* t (cbrt (+ (* (/ k t) (/ k t)) 2))))) (* (/ (sin k) l) (* t (cbrt (+ (* (/ k t) (/ k t)) 2))))) (/ (/ (/ (sqrt 2) t) (* (/ (sin k) l) (* t (cbrt (+ (* (/ k t) (/ k t)) 2))))) (* (/ (sin k) l) (* t (cbrt (+ (* (/ k t) (/ k t)) 2)))))) (/ (/ (/ (sqrt 2) t) (* (/ (sin k) l) (* t (cbrt (+ (* (/ k t) (/ k t)) 2))))) (* (/ (sin k) l) (* t (cbrt (+ (* (/ k t) (/ k t)) 2)))))) (* (* (* (/ (sqrt 2) (cbrt (+ (* (/ k t) (/ k t)) 2))) (/ (sqrt 2) (cbrt (+ (* (/ k t) (/ k t)) 2)))) (/ (sqrt 2) (cbrt (+ (* (/ k t) (/ k t)) 2)))) (* (* (cos k) (cos k)) (cos k))))
2.2s
(* (* (* (/ (/ (/ (sqrt 2) t) (* (/ (sin k) l) (* t (cbrt (+ (* (/ k t) (/ k t)) 2))))) (* (/ (sin k) l) (* t (cbrt (+ (* (/ k t) (/ k t)) 2))))) (/ (/ (/ (sqrt 2) t) (* (/ (sin k) l) (* t (cbrt (+ (* (/ k t) (/ k t)) 2))))) (* (/ (sin k) l) (* t (cbrt (+ (* (/ k t) (/ k t)) 2)))))) (/ (/ (/ (sqrt 2) t) (* (/ (sin k) l) (* t (cbrt (+ (* (/ k t) (/ k t)) 2))))) (* (/ (sin k) l) (* t (cbrt (+ (* (/ k t) (/ k t)) 2)))))) (* (* (* (/ (sqrt 2) (cbrt (+ (* (/ k t) (/ k t)) 2))) (cos k)) (* (/ (sqrt 2) (cbrt (+ (* (/ k t) (/ k t)) 2))) (cos k))) (* (/ (sqrt 2) (cbrt (+ (* (/ k t) (/ k t)) 2))) (cos k))))
2.0s
(* (* (* (/ (/ (/ (sqrt 2) t) (* (/ (sin k) l) (* t (cbrt (+ (* (/ k t) (/ k t)) 2))))) (* (/ (sin k) l) (* t (cbrt (+ (* (/ k t) (/ k t)) 2))))) (/ (/ (/ (sqrt 2) t) (* (/ (sin k) l) (* t (cbrt (+ (* (/ k t) (/ k t)) 2))))) (* (/ (sin k) l) (* t (cbrt (+ (* (/ k t) (/ k t)) 2)))))) (/ (/ (/ (sqrt 2) t) (* (/ (sin k) l) (* t (cbrt (+ (* (/ k t) (/ k t)) 2))))) (* (/ (sin k) l) (* t (cbrt (+ (* (/ k t) (/ k t)) 2)))))) (* (/ (* (* (sqrt 2) (sqrt 2)) (sqrt 2)) (+ (* (/ k t) (/ k t)) 2)) (* (* (cos k) (cos k)) (cos k))))
1.2s
(+ (- (- (- (log (sqrt 2)) (log t)) (+ (- (log (sin k)) (log l)) (log (* t (cbrt (+ (* (/ k t) (/ k t)) 2)))))) (+ (log (/ (sin k) l)) (+ (log t) (log (cbrt (+ (* (/ k t) (/ k t)) 2)))))) (+ (- (log (sqrt 2)) (log (cbrt (+ (* (/ k t) (/ k t)) 2)))) (log (cos k))))
1.0s
(+ (- (- (- (log (sqrt 2)) (log t)) (+ (- (log (sin k)) (log l)) (log (* t (cbrt (+ (* (/ k t) (/ k t)) 2)))))) (+ (log (/ (sin k) l)) (+ (log t) (log (cbrt (+ (* (/ k t) (/ k t)) 2)))))) (+ (log (/ (sqrt 2) (cbrt (+ (* (/ k t) (/ k t)) 2)))) (log (cos k))))

prune9.5s

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 11.4b

localize93.0ms

Local error

Found 4 expressions with local error:

15.3b
(/ (/ (* (cbrt 2) (cbrt 2)) (sqrt (+ (* (/ k t) (/ k t)) 2))) (/ (* t (/ (sin k) (/ l t))) 1))
9.6b
(sqrt (+ (* (/ k t) (/ k t)) 2))
9.6b
(sqrt (+ (* (/ k t) (/ k t)) 2))
8.2b
(/ (/ (cbrt 2) (sqrt (+ (* (/ k t) (/ k t)) 2))) (/ (/ (sin k) (/ l t)) (cos k)))

rewrite673.0ms

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
80.0ms
(/ (/ (* (cbrt 2) (cbrt 2)) (sqrt (+ (* (/ k t) (/ k t)) 2))) (/ (* t (/ (sin k) (/ l t))) 1))
64.0ms
(/ (/ (cbrt 2) (sqrt (+ (* (/ k t) (/ k t)) 2))) (/ (/ (sin k) (/ l t)) (cos k)))
16.0ms
(sqrt (+ (* (/ k t) (/ k t)) 2))
12.0ms
(sqrt (+ (* (/ k t) (/ k t)) 2))

series971.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
440.0ms
(/ (/ (* (cbrt 2) (cbrt 2)) (sqrt (+ (* (/ k t) (/ k t)) 2))) (/ (* t (/ (sin k) (/ l t))) 1))
405.0ms
(/ (/ (cbrt 2) (sqrt (+ (* (/ k t) (/ k t)) 2))) (/ (/ (sin k) (/ l t)) (cos k)))
68.0ms
(sqrt (+ (* (/ k t) (/ k t)) 2))
58.0ms
(sqrt (+ (* (/ k t) (/ k t)) 2))