Details

Time bar (total: 2.5m)

sample406.0ms

Algorithm
intervals
Results
151.0ms63×body1280valid
115.0ms51×body640valid
77.0ms188×body80valid
32.0ms28×body320valid
11.0ms15×body160valid

simplify300.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
300.0ms
(/ 2 (* (* (* (/ (pow t 3) (* l l)) (sin k)) (tan k)) (+ (+ 1 (pow (/ k t) 2)) 1)))

prune26.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 21.9b

localize43.0ms

Local error

Found 4 expressions with local error:

15.0b
(/ (/ 2 (+ (* (/ k t) (/ k t)) 2)) (* (* (sin k) (tan k)) (/ t (* (/ l t) (/ l t)))))
10.3b
(* (* (sin k) (tan k)) (/ t (* (/ l t) (/ l t))))
0.9b
(/ t (* (/ l t) (/ l t)))
0.6b
(/ 2 (+ (* (/ k t) (/ k t)) 2))

rewrite207.0ms

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
88.0ms
(/ (/ 2 (+ (* (/ k t) (/ k t)) 2)) (* (* (sin k) (tan k)) (/ t (* (/ l t) (/ l t)))))
63.0ms
(* (* (sin k) (tan k)) (/ t (* (/ l t) (/ l t))))
28.0ms
(/ 2 (+ (* (/ k t) (/ k t)) 2))
19.0ms
(/ t (* (/ l t) (/ l t)))

series1.3s

Counts
4 → 12
Calls
4 calls:
Slowest
979.0ms
(/ (/ 2 (+ (* (/ k t) (/ k t)) 2)) (* (* (sin k) (tan k)) (/ t (* (/ l t) (/ l t)))))
214.0ms
(* (* (sin k) (tan k)) (/ t (* (/ l t) (/ l t))))
64.0ms
(/ 2 (+ (* (/ k t) (/ k t)) 2))
62.0ms
(/ t (* (/ l t) (/ l t)))

simplify46.7s

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)) (/ t (* (/ l t) (/ l t)))) (* (* (sin k) (tan k)) (/ t (* (/ l t) (/ l t))))) (* (* (sin k) (tan k)) (/ 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))))))
1.4s
(/ (/ (* (* 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))))))

prune3.0s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 13.5b

localize68.0ms

Local error

Found 4 expressions with local error:

15.0b
(/ (/ 2 (+ (* (/ k t) (/ k t)) 2)) (/ (* (* t (/ (sin k) (/ l t))) (/ (sin k) (/ l t))) (cos k)))
3.8b
(/ (sin k) (/ l t))
3.8b
(/ (sin k) (/ l t))
0.6b
(/ 2 (+ (* (/ k t) (/ k t)) 2))

rewrite141.0ms

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
81.0ms
(/ (/ 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
897.0ms
(/ (/ 2 (+ (* (/ k t) (/ k t)) 2)) (/ (* (* t (/ (sin k) (/ l t))) (/ (sin k) (/ l t))) (cos k)))
83.0ms
(/ (sin k) (/ l t))
75.0ms
(/ (sin k) (/ l t))
63.0ms
(/ 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 (/ (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))))
1.6s
(/ (* (* (/ 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))))
1.5s
(/ (* (* (/ 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))))
874.0ms
(/ (/ (sqrt 2) (sqrt (+ (* (/ 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)))))
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))))

prune5.5s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 13.0b

localize53.0ms

Local error

Found 4 expressions with local error:

12.8b
(/ (/ 2 (+ (* (/ k t) (/ k t)) 2)) (/ (* t (/ (sin k) (/ l t))) 1))
6.0b
(/ (/ (/ 2 (+ (* (/ k t) (/ k t)) 2)) (/ (* t (/ (sin k) (/ l t))) 1)) (/ (/ (sin k) (/ l t)) (cos k)))
3.8b
(/ (sin k) (/ l t))
3.8b
(/ (sin k) (/ l t))

rewrite2.2s

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
92.0ms
(/ (/ (/ 2 (+ (* (/ k t) (/ k t)) 2)) (/ (* t (/ (sin k) (/ l t))) 1)) (/ (/ (sin k) (/ l t)) (cos k)))
49.0ms
(/ (/ 2 (+ (* (/ k t) (/ k t)) 2)) (/ (* t (/ (sin k) (/ l t))) 1))
16.0ms
(/ (sin k) (/ l t))
9.0ms
(/ (sin k) (/ l t))

series1.4s

Counts
4 → 12
Calls
4 calls:
Slowest
884.0ms
(/ (/ (/ 2 (+ (* (/ k t) (/ k t)) 2)) (/ (* t (/ (sin k) (/ l t))) 1)) (/ (/ (sin k) (/ l t)) (cos k)))
310.0ms
(/ (/ 2 (+ (* (/ k t) (/ k t)) 2)) (/ (* t (/ (sin k) (/ l t))) 1))
95.0ms
(/ (sin k) (/ l t))
78.0ms
(/ (sin k) (/ l t))