Details

Time bar (total: 9.9m)

sample341.0ms

Algorithm
intervals
Results
117.0ms66×body1280valid
99.0ms168×body80valid
73.0ms56×body640valid
25.0ms23×body320valid
9.0ms15×body160valid

simplify281.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
281.0ms
(/ 2 (* (* (* (/ (pow t 3) (* l l)) (sin k)) (tan k)) (+ (+ 1 (pow (/ k t) 2)) 1)))

prune20.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 22.9b

localize49.0ms

Local error

Found 4 expressions with local error:

13.7b
(/ (/ 2 (+ (* (/ k t) (/ k t)) 2)) (* (* (sin k) (tan k)) (/ t (* (/ l t) (/ l t)))))
11.1b
(* (* (sin k) (tan k)) (/ t (* (/ l t) (/ l t))))
1.0b
(/ t (* (/ l t) (/ l t)))
0.5b
(/ 2 (+ (* (/ k t) (/ k t)) 2))

rewrite229.0ms

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
101.0ms
(/ (/ 2 (+ (* (/ k t) (/ k t)) 2)) (* (* (sin k) (tan k)) (/ t (* (/ l t) (/ l t)))))
88.0ms
(* (* (sin k) (tan k)) (/ t (* (/ l t) (/ l t))))
19.0ms
(/ t (* (/ l t) (/ l t)))
16.0ms
(/ 2 (+ (* (/ k t) (/ k t)) 2))

series1.2s

Counts
4 → 12
Calls
4 calls:
Slowest
881.0ms
(/ (/ 2 (+ (* (/ k t) (/ k t)) 2)) (* (* (sin k) (tan k)) (/ t (* (/ l t) (/ l t)))))
244.0ms
(* (* (sin k) (tan k)) (/ t (* (/ l t) (/ l t))))
68.0ms
(/ 2 (+ (* (/ k t) (/ k t)) 2))
42.0ms
(/ t (* (/ l t) (/ l t)))

simplify58.7s

Counts
250 → 220
Calls
250 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))))))
1.6s
(/ (* (* (/ 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 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))))))
1.5s
(/ (* (* (/ 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))))))

prune3.4s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 12.7b

localize42.0ms

Local error

Found 4 expressions with local error:

13.7b
(/ (/ 2 (+ (* (/ k t) (/ k t)) 2)) (/ (* (/ t (/ l (sin k))) (* (/ t (/ l (sin k))) t)) (cos k)))
3.0b
(/ t (/ l (sin k)))
3.0b
(/ t (/ l (sin k)))
0.5b
(/ 2 (+ (* (/ k t) (/ k t)) 2))

rewrite135.0ms

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
79.0ms
(/ (/ 2 (+ (* (/ k t) (/ k t)) 2)) (/ (* (/ t (/ l (sin k))) (* (/ t (/ l (sin k))) t)) (cos k)))
27.0ms
(/ 2 (+ (* (/ k t) (/ k t)) 2))
7.0ms
(/ t (/ l (sin k)))
7.0ms
(/ t (/ l (sin k)))

series1.1s

Counts
4 → 12
Calls
4 calls:
Slowest
831.0ms
(/ (/ 2 (+ (* (/ k t) (/ k t)) 2)) (/ (* (/ t (/ l (sin k))) (* (/ t (/ l (sin k))) t)) (cos k)))
103.0ms
(/ t (/ l (sin k)))
87.0ms
(/ t (/ l (sin k)))
74.0ms
(/ 2 (+ (* (/ k t) (/ k t)) 2))

simplify1.7m

Counts
576 → 380
Calls
576 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) (* (* (/ l (sin k)) (/ l (sin k))) (/ l (sin k)))) (* (/ (* (* t t) t) (* (* (/ l (sin k)) (/ l (sin k))) (/ l (sin k)))) (* (* t t) t))) (* (* (cos k) (cos k)) (cos k))))
1.7s
(/ (* (* (/ 2 (+ (* (/ k t) (/ k t)) 2)) (/ 2 (+ (* (/ k t) (/ k t)) 2))) (/ 2 (+ (* (/ k t) (/ k t)) 2))) (/ (* (* (* (/ t (/ l (sin k))) (* (/ t (/ l (sin k))) t)) (* (/ t (/ l (sin k))) (* (/ t (/ l (sin k))) t))) (* (/ t (/ l (sin k))) (* (/ t (/ l (sin k))) t))) (* (* (cos k) (cos k)) (cos k))))
1.7s
(/ (* (* (/ 2 (+ (* (/ k t) (/ k t)) 2)) (/ 2 (+ (* (/ k t) (/ k t)) 2))) (/ 2 (+ (* (/ k t) (/ k t)) 2))) (/ (* (* (* (/ t (/ l (sin k))) (/ t (/ l (sin k)))) (/ t (/ l (sin k)))) (* (* (* (/ t (/ l (sin k))) (/ t (/ l (sin k)))) (/ t (/ l (sin k)))) (* (* t t) t))) (* (* (cos k) (cos k)) (cos k))))
1.7s
(/ (* (* (/ 2 (+ (* (/ k t) (/ k t)) 2)) (/ 2 (+ (* (/ k t) (/ k t)) 2))) (/ 2 (+ (* (/ k t) (/ k t)) 2))) (/ (* (* (* (/ t (/ l (sin k))) (/ t (/ l (sin k)))) (/ t (/ l (sin k)))) (* (* (* (/ t (/ l (sin k))) t) (* (/ t (/ l (sin k))) t)) (* (/ t (/ l (sin k))) t))) (* (* (cos k) (cos k)) (cos k))))
966.0ms
(/ (/ (* (cbrt 2) (cbrt 2)) (* (cbrt (+ (* (/ k t) (/ k t)) 2)) (cbrt (+ (* (/ k t) (/ k t)) 2)))) (/ (/ t (/ l (sin k))) (sqrt (cos k))))

prune6.1s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 11.1b

localize73.0ms

Local error

Found 4 expressions with local error:

11.3b
(/ (/ (cbrt 2) (+ (* (/ k t) (/ k t)) 2)) (/ (* t (* (/ t l) (sin k))) (cbrt (cos k))))
6.2b
(* (/ (* (cbrt 2) (cbrt (cos k))) (/ (* (sin k) (/ t l)) (* (cbrt 2) (cbrt (cos k))))) (/ (/ (cbrt 2) (+ (* (/ k t) (/ k t)) 2)) (/ (* t (* (/ t l) (sin k))) (cbrt (cos k)))))
3.3b
(* (sin k) (/ t l))
3.3b
(* (/ t l) (sin k))

rewrite320.0ms

Algorithm
rewrite-expression-head
Rules
1475×add-exp-log
1183×times-frac
981×add-cbrt-cube
732×cbrt-undiv div-exp
560×prod-exp cbrt-unprod
466×add-sqr-sqrt
443×*-un-lft-identity add-cube-cbrt
337×cbrt-prod
261×associate-*r*
76×div-inv
45×associate-/r/
26×associate-*l*
24×associate-/l*
21×flip3-+ flip-+
10×pow1 associate-/r*
8×unswap-sqr
4×insert-posit16 add-log-exp
3×pow-prod-down *-commutative
2×associate-*l/ associate-*r/
1×frac-times clear-num frac-2neg associate-/l/
Counts
4 → 975
Calls
4 calls:
Slowest
174.0ms
(* (/ (* (cbrt 2) (cbrt (cos k))) (/ (* (sin k) (/ t l)) (* (cbrt 2) (cbrt (cos k))))) (/ (/ (cbrt 2) (+ (* (/ k t) (/ k t)) 2)) (/ (* t (* (/ t l) (sin k))) (cbrt (cos k)))))
61.0ms
(/ (/ (cbrt 2) (+ (* (/ k t) (/ k t)) 2)) (/ (* t (* (/ t l) (sin k))) (cbrt (cos k))))
19.0ms
(* (/ t l) (sin k))
12.0ms
(* (sin k) (/ t l))

series1.7s

Counts
4 → 12
Calls
4 calls:
Slowest
897.0ms
(* (/ (* (cbrt 2) (cbrt (cos k))) (/ (* (sin k) (/ t l)) (* (cbrt 2) (cbrt (cos k))))) (/ (/ (cbrt 2) (+ (* (/ k t) (/ k t)) 2)) (/ (* t (* (/ t l) (sin k))) (cbrt (cos k)))))
674.0ms
(/ (/ (cbrt 2) (+ (* (/ k t) (/ k t)) 2)) (/ (* t (* (/ t l) (sin k))) (cbrt (cos k))))
102.0ms
(* (/ t l) (sin k))
73.0ms
(* (sin k) (/ t l))

simplify6.6m

Counts
1234 → 987
Calls
1234 calls:
Slowest
2.1s
(* (* (* (/ (* (cbrt 2) (cbrt (cos k))) (/ (* (sin k) (/ t l)) (* (cbrt 2) (cbrt (cos k))))) (/ (/ (cbrt 2) (+ (* (/ k t) (/ k t)) 2)) (/ (* t (* (/ t l) (sin k))) (cbrt (cos k))))) (* (/ (* (cbrt 2) (cbrt (cos k))) (/ (* (sin k) (/ t l)) (* (cbrt 2) (cbrt (cos k))))) (/ (/ (cbrt 2) (+ (* (/ k t) (/ k t)) 2)) (/ (* t (* (/ t l) (sin k))) (cbrt (cos k)))))) (* (/ (* (cbrt 2) (cbrt (cos k))) (/ (* (sin k) (/ t l)) (* (cbrt 2) (cbrt (cos k))))) (/ (/ (cbrt 2) (+ (* (/ k t) (/ k t)) 2)) (/ (* t (* (/ t l) (sin k))) (cbrt (cos k))))))
2.1s
(* (* (* (/ (* (cbrt 2) (cbrt (cos k))) (/ (* (sin k) (/ t l)) (* (cbrt 2) (cbrt (cos k))))) (/ (* (cbrt 2) (cbrt (cos k))) (/ (* (sin k) (/ t l)) (* (cbrt 2) (cbrt (cos k)))))) (/ (* (cbrt 2) (cbrt (cos k))) (/ (* (sin k) (/ t l)) (* (cbrt 2) (cbrt (cos k)))))) (* (* (/ (/ (cbrt 2) (+ (* (/ k t) (/ k t)) 2)) (/ (* t (* (/ t l) (sin k))) (cbrt (cos k)))) (/ (/ (cbrt 2) (+ (* (/ k t) (/ k t)) 2)) (/ (* t (* (/ t l) (sin k))) (cbrt (cos k))))) (/ (/ (cbrt 2) (+ (* (/ k t) (/ k t)) 2)) (/ (* t (* (/ t l) (sin k))) (cbrt (cos k))))))
1.1s
(+ (- (log (* (cbrt 2) (cbrt (cos k)))) (- (+ (log (sin k)) (log (/ t l))) (log (* (cbrt 2) (cbrt (cos k)))))) (- (- (log (cbrt 2)) (log (+ (* (/ k t) (/ k t)) 2))) (- (+ (log t) (+ (- (log t) (log l)) (log (sin k)))) (log (cbrt (cos k))))))
1.0s
(+ (- (+ (log (cbrt 2)) (log (cbrt (cos k)))) (- (log (* (sin k) (/ t l))) (+ (log (cbrt 2)) (log (cbrt (cos k)))))) (- (- (log (cbrt 2)) (log (+ (* (/ k t) (/ k t)) 2))) (- (+ (log t) (log (* (/ t l) (sin k)))) (log (cbrt (cos k))))))
1.0s
(* (/ (* (cbrt 2) (cbrt (cos k))) (/ (* (sin k) (/ t l)) (* (cbrt 2) (cbrt (cos k))))) (/ (/ (* (cbrt (cbrt 2)) (cbrt (cbrt 2))) (* (cbrt (+ (* (/ k t) (/ k t)) 2)) (cbrt (+ (* (/ k t) (/ k t)) 2)))) (* t (* (/ t l) (sin k)))))

prune19.7s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 9.4b

localize75.0ms

Local error

Found 4 expressions with local error:

18.8b
(cbrt (+ (* (/ k t) (/ k t)) 2))
18.8b
(cbrt (+ (* (/ k t) (/ k t)) 2))
18.8b
(cbrt (+ (* (/ k t) (/ k t)) 2))
4.6b
(/ (/ (* (cbrt 2) (cbrt (cos k))) (/ (/ (sin k) (/ l t)) (* (cbrt 2) (cbrt (cos k))))) (cbrt (+ (* (/ k t) (/ k t)) 2)))

rewrite124.0ms

Algorithm
rewrite-expression-head
Rules
1424×times-frac
374×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
171×cbrt-prod
85×add-exp-log
53×cbrt-undiv div-exp associate-/l*
44×add-cbrt-cube
43×div-inv
16×associate-/r/
13×prod-exp cbrt-unprod
8×cbrt-div
6×associate-/r*
4×pow1 flip3-+ flip-+ insert-posit16 add-log-exp
3×pow1/3
1×clear-num frac-2neg associate-/l/
Counts
4 → 463
Calls
4 calls:
Slowest
68.0ms
(/ (/ (* (cbrt 2) (cbrt (cos k))) (/ (/ (sin k) (/ l t)) (* (cbrt 2) (cbrt (cos k))))) (cbrt (+ (* (/ k t) (/ k t)) 2)))
12.0ms
(cbrt (+ (* (/ k t) (/ k t)) 2))
7.0ms
(cbrt (+ (* (/ k t) (/ k t)) 2))
7.0ms
(cbrt (+ (* (/ k t) (/ k t)) 2))

series1.3s

Counts
4 → 12
Calls
4 calls:
Slowest
727.0ms
(/ (/ (* (cbrt 2) (cbrt (cos k))) (/ (/ (sin k) (/ l t)) (* (cbrt 2) (cbrt (cos k))))) (cbrt (+ (* (/ k t) (/ k t)) 2)))
194.0ms
(cbrt (+ (* (/ k t) (/ k t)) 2))
188.0ms
(cbrt (+ (* (/ k t) (/ k t)) 2))
168.0ms
(cbrt (+ (* (/ k t) (/ k t)) 2))