Details

Time bar (total: 10.0m)

sample288.0ms

Algorithm
intervals
Results
122.0ms61×body1280valid
62.0ms59×body640valid
38.0ms192×body80valid
25.0ms37×body320valid
8.0ms20×body160valid

simplify838.0ms

Counts
1 → 1
Iterations
IterNodes
done5000
3873
2158
148
019

prune28.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 27.3b

localize56.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ 2.0 (* (/ (tan k) l) (/ (pow t 3.0) l)))
5.6b
(* (/ (tan k) l) (/ (pow t 3.0) l))
6.3b
(/ (pow t 3.0) l)
17.1b
(/ (/ 2.0 (* (/ (tan k) l) (/ (pow t 3.0) l))) (* (sin k) (+ (+ (pow (/ k t) 2.0) 1.0) 1.0)))

rewrite188.0ms

Algorithm
rewrite-expression-head
Rules
167×add-exp-log
92×add-cbrt-cube
90×div-exp
80×times-frac
71×add-sqr-sqrt
47×*-un-lft-identity add-cube-cbrt
44×cbrt-undiv
42×prod-exp
25×associate-*r*
23×unpow-prod-down
22×cbrt-unprod
20×associate-/l*
13×associate-*l*
11×associate-/r/
9×pow-to-exp pow-exp sqr-pow
8×unswap-sqr
7×div-inv
6×pow1 associate-*r/
5×associate-/r*
4×frac-times associate-*l/ add-log-exp
3×clear-num frac-2neg
1×flip3-+ pow-prod-down *-commutative flip-+ associate-/l/
Counts
4 → 215
Calls
4 calls:
16.0ms
(/ 2.0 (* (/ (tan k) l) (/ (pow t 3.0) l)))
48.0ms
(* (/ (tan k) l) (/ (pow t 3.0) l))
12.0ms
(/ (pow t 3.0) l)
102.0ms
(/ (/ 2.0 (* (/ (tan k) l) (/ (pow t 3.0) l))) (* (sin k) (+ (+ (pow (/ k t) 2.0) 1.0) 1.0)))

series1.5s

Counts
4 → 12
Calls
4 calls:
417.0ms
(/ 2.0 (* (/ (tan k) l) (/ (pow t 3.0) l)))
264.0ms
(* (/ (tan k) l) (/ (pow t 3.0) l))
220.0ms
(/ (pow t 3.0) l)
609.0ms
(/ (/ 2.0 (* (/ (tan k) l) (/ (pow t 3.0) l))) (* (sin k) (+ (+ (pow (/ k t) 2.0) 1.0) 1.0)))

simplify462.0ms

Counts
227 → 227
Iterations
IterNodes
done5000
11172
0374

prune2.0s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 12.3b

localize114.0ms

Local error

Found 4 expressions with local error:

0.7b
(pow (cbrt t) 3.0)
4.7b
(/ (pow (* (cbrt t) (cbrt t)) 3.0) (* (cbrt l) (cbrt l)))
7.7b
(* (/ (pow (* (cbrt t) (cbrt t)) 3.0) (* (cbrt l) (cbrt l))) (/ (tan k) l))
17.1b
(/ (/ 2.0 (* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) (* (cbrt l) (cbrt l))) (/ (tan k) l)) (/ (pow (cbrt t) 3.0) (cbrt l)))) (* (sin k) (+ (+ (pow (/ k t) 2.0) 1.0) 1.0)))

rewrite504.0ms

Algorithm
rewrite-expression-head
Rules
1274×add-exp-log
657×div-exp
506×prod-exp
206×add-cbrt-cube
115×pow-exp
113×cbrt-undiv
85×cbrt-unprod
77×pow-to-exp
49×times-frac
38×add-sqr-sqrt
22×*-un-lft-identity add-cube-cbrt
19×associate-/l*
16×associate-/r/
13×associate-*r*
11×frac-times unpow-prod-down associate-*l/
9×associate-*l* associate-*r/
8×unswap-sqr
7×pow1
6×div-inv sqr-pow
4×add-log-exp
3×cbrt-prod pow-unpow
2×clear-num associate-/r* pow-pow frac-2neg
1×flip3-+ pow1/3 pow-prod-down *-commutative flip-+ associate-/l/
Counts
4 → 348
Calls
4 calls:
5.0ms
(pow (cbrt t) 3.0)
21.0ms
(/ (pow (* (cbrt t) (cbrt t)) 3.0) (* (cbrt l) (cbrt l)))
71.0ms
(* (/ (pow (* (cbrt t) (cbrt t)) 3.0) (* (cbrt l) (cbrt l))) (/ (tan k) l))
339.0ms
(/ (/ 2.0 (* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) (* (cbrt l) (cbrt l))) (/ (tan k) l)) (/ (pow (cbrt t) 3.0) (cbrt l)))) (* (sin k) (+ (+ (pow (/ k t) 2.0) 1.0) 1.0)))

series2.3s

Counts
4 → 12
Calls
4 calls:
452.0ms
(pow (cbrt t) 3.0)
352.0ms
(/ (pow (* (cbrt t) (cbrt t)) 3.0) (* (cbrt l) (cbrt l)))
500.0ms
(* (/ (pow (* (cbrt t) (cbrt t)) 3.0) (* (cbrt l) (cbrt l))) (/ (tan k) l))
1.0s
(/ (/ 2.0 (* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) (* (cbrt l) (cbrt l))) (/ (tan k) l)) (/ (pow (cbrt t) 3.0) (cbrt l)))) (* (sin k) (+ (+ (pow (/ k t) 2.0) 1.0) 1.0)))

simplify1.1s

Counts
360 → 360
Iterations
IterNodes
done5001
12389
0622

prune2.3s

Pruning

24 alts after pruning (24 fresh and 0 done)

Merged error: 9.5b

localize169.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt t)
0.7b
(pow (cbrt t) 3.0)
2.2b
(* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (/ (tan k) l))
17.1b
(/ (/ 2.0 (* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l)) (/ (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (/ (tan k) l)) (cbrt l))) (/ (pow (cbrt t) 3.0) (cbrt l)))) (* (sin k) (+ (+ (pow (/ k t) 2.0) 1.0) 1.0)))

rewrite418.0ms

Algorithm
rewrite-expression-head
Rules
3637×add-exp-log
1972×div-exp
1504×prod-exp
427×pow-exp
265×pow-to-exp
239×add-cbrt-cube
145×cbrt-undiv
106×cbrt-unprod
32×times-frac
31×add-sqr-sqrt
20×*-un-lft-identity add-cube-cbrt
16×associate-/r/
14×associate-/l*
13×associate-*r*
10×frac-times associate-*l/
9×unpow-prod-down associate-*r/
6×cbrt-prod unswap-sqr
5×pow1 associate-*l*
4×div-inv add-log-exp sqr-pow
3×pow-unpow
2×pow-pow pow1/3
1×clear-num associate-/r* frac-2neg flip3-+ *-commutative flip-+ associate-/l/
Counts
4 → 569
Calls
4 calls:
1.0ms
(cbrt t)
3.0ms
(pow (cbrt t) 3.0)
31.0ms
(* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (/ (tan k) l))
269.0ms
(/ (/ 2.0 (* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l)) (/ (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (/ (tan k) l)) (cbrt l))) (/ (pow (cbrt t) 3.0) (cbrt l)))) (* (sin k) (+ (+ (pow (/ k t) 2.0) 1.0) 1.0)))

series2.5s

Counts
4 → 12
Calls
4 calls:
298.0ms
(cbrt t)
452.0ms
(pow (cbrt t) 3.0)
441.0ms
(* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (/ (tan k) l))
1.3s
(/ (/ 2.0 (* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l)) (/ (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (/ (tan k) l)) (cbrt l))) (/ (pow (cbrt t) 3.0) (cbrt l)))) (* (sin k) (+ (+ (pow (/ k t) 2.0) 1.0) 1.0)))

simplify1.4s

Counts
581 → 581
Iterations
IterNodes
done5000
13596
0849

prune2.4s

Pruning

30 alts after pruning (29 fresh and 1 done)

Merged error: 6.7b

localize183.0ms

Local error

Found 4 expressions with local error:

1.3b
(/ (sqrt 2.0) (* (+ (pow (/ k t) 2.0) (+ 1.0 1.0)) (/ (pow (cbrt t) 3.0) (cbrt l))))
2.9b
(* (+ (pow (/ k t) 2.0) (+ 1.0 1.0)) (/ (pow (cbrt t) 3.0) (cbrt l)))
3.4b
(/ (/ (/ (sqrt 2.0) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l))) (/ (/ (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (tan k)) l) (cbrt l))) (sin k))
12.3b
(* (/ (/ (/ (sqrt 2.0) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l))) (/ (/ (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (tan k)) l) (cbrt l))) (sin k)) (/ (sqrt 2.0) (* (+ (pow (/ k t) 2.0) (+ 1.0 1.0)) (/ (pow (cbrt t) 3.0) (cbrt l)))))

rewrite40.8s

Algorithm
rewrite-expression-head
Rules
336719×times-frac
114154×add-sqr-sqrt
113866×*-un-lft-identity
113861×add-cube-cbrt
59790×cbrt-prod
32874×sqrt-prod
28866×associate-*l*
12507×div-inv
11644×unpow-prod-down
11612×sqr-pow
9625×associate-/l*
2751×add-exp-log
1861×div-exp
707×prod-exp
421×add-cbrt-cube
339×associate-/r/
321×cbrt-undiv
228×pow-exp
137×pow-to-exp
103×cbrt-unprod
79×associate-*r*
56×unswap-sqr
8×pow1
7×frac-times associate-*l/
6×flip3-+ flip-+
4×associate-/r* associate-*r/ add-log-exp
3×distribute-lft-out
2×clear-num frac-2neg pow-prod-down *-commutative
1×associate-/l/
Counts
4 → 67935
Calls
4 calls:
62.0ms
(/ (sqrt 2.0) (* (+ (pow (/ k t) 2.0) (+ 1.0 1.0)) (/ (pow (cbrt t) 3.0) (cbrt l))))
296.0ms
(* (+ (pow (/ k t) 2.0) (+ 1.0 1.0)) (/ (pow (cbrt t) 3.0) (cbrt l)))
3.6s
(/ (/ (/ (sqrt 2.0) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l))) (/ (/ (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (tan k)) l) (cbrt l))) (sin k))
18.8s
(* (/ (/ (/ (sqrt 2.0) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l))) (/ (/ (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (tan k)) l) (cbrt l))) (sin k)) (/ (sqrt 2.0) (* (+ (pow (/ k t) 2.0) (+ 1.0 1.0)) (/ (pow (cbrt t) 3.0) (cbrt l)))))

series3.3s

Counts
4 → 12
Calls
4 calls:
672.0ms
(/ (sqrt 2.0) (* (+ (pow (/ k t) 2.0) (+ 1.0 1.0)) (/ (pow (cbrt t) 3.0) (cbrt l))))
596.0ms
(* (+ (pow (/ k t) 2.0) (+ 1.0 1.0)) (/ (pow (cbrt t) 3.0) (cbrt l)))
793.0ms
(/ (/ (/ (sqrt 2.0) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l))) (/ (/ (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (tan k)) l) (cbrt l))) (sin k))
1.2s
(* (/ (/ (/ (sqrt 2.0) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l))) (/ (/ (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (tan k)) l) (cbrt l))) (sin k)) (/ (sqrt 2.0) (* (+ (pow (/ k t) 2.0) (+ 1.0 1.0)) (/ (pow (cbrt t) 3.0) (cbrt l)))))

simplify32.6s

Counts
67947 → 67947
Iterations
IterNodes
done57186
057186

prune8.4m