Details

Time bar (total: 27.2s)

sample1.0s

Algorithm
intervals
Results
270.0ms36×body5120valid
264.0ms133×body1280valid
214.0ms67×body2560valid
119.0ms76×body640valid
25.0ms35×body320valid
17.0ms72×body80valid
10.0ms16×body160valid

simplify3.1s

Counts
1 → 1
Iterations

Useful iterations: 4 (1.4s)

IterNodesCost
01925
14425
214625
379823
4446721
done500021

prune12.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 38.3b

localize54.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (/ (pow t 3.0) (* l l)) (sin k))
0.6b
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
14.0b
(/ (pow t 3.0) (* l l))
26.9b
(/ (/ 2.0 (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))) (pow (/ k t) 2.0))

rewrite417.0ms

Algorithm
rewrite-expression-head
Rules
340×times-frac
272×add-exp-log
153×unpow-prod-down
144×add-sqr-sqrt
137×add-cube-cbrt *-un-lft-identity
128×div-exp
103×prod-exp
59×add-cbrt-cube
58×associate-*l/
54×associate-/r/
38×tan-quot
34×pow-exp
32×div-inv
24×pow-to-exp
21×cbrt-unprod
19×cbrt-undiv frac-times associate-*r/
18×associate-/r*
17×associate-/l*
15×sqr-pow
12×associate-*l*
11×pow1
6×associate-*r*
4×pow-prod-down add-log-exp unswap-sqr
2×frac-2neg clear-num *-commutative
1×associate-/l/
Counts
4 → 354
Calls
4 calls:
51.0ms
(* (/ (pow t 3.0) (* l l)) (sin k))
115.0ms
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
28.0ms
(/ (pow t 3.0) (* l l))
187.0ms
(/ (/ 2.0 (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))) (pow (/ k t) 2.0))

series1.9s

Counts
4 → 12
Calls
4 calls:
360.0ms
(* (/ (pow t 3.0) (* l l)) (sin k))
441.0ms
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
268.0ms
(/ (pow t 3.0) (* l l))
857.0ms
(/ (/ 2.0 (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))) (pow (/ k t) 2.0))

simplify1.1s

Counts
366 → 366
Iterations

Useful iterations: done (1.1s)

IterNodesCost
066210242
115049739
done50019233

prune2.2s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 13.9b

localize28.0ms

Local error

Found 4 expressions with local error:

0.4b
(pow (sin k) 2)
4.9b
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
6.5b
(* (pow k 2.0) (pow t 1.0))
15.3b
(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

rewrite314.0ms

Algorithm
rewrite-expression-head
Rules
1597×add-exp-log
1095×prod-exp
882×pow-exp
668×div-exp
492×pow-to-exp
130×rec-exp 1-exp
37×add-sqr-sqrt
32×unpow-prod-down
20×add-cube-cbrt *-un-lft-identity add-cbrt-cube
19×times-frac associate-*r*
18×associate-*l*
14×sqr-pow
12×unswap-sqr
8×associate-/r*
6×cbrt-unprod
5×pow1
4×cbrt-undiv unpow2 add-log-exp
3×pow-unpow div-inv
2×*-commutative
1×pow-pow frac-2neg associate-*r/ clear-num associate-/l*
Counts
4 → 567
Calls
4 calls:
8.0ms
(pow (sin k) 2)
35.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
38.0ms
(* (pow k 2.0) (pow t 1.0))
141.0ms
(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

series1.7s

Counts
4 → 12
Calls
4 calls:
35.0ms
(pow (sin k) 2)
133.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
454.0ms
(* (pow k 2.0) (pow t 1.0))
1.0s
(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

simplify1.5s

Counts
579 → 579
Iterations

Useful iterations: 2 (623.0ms)

IterNodesCost
043814412
194912754
2254512085
done500012085

prune895.0ms

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 11.6b

localize43.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
0.4b
(pow (sin k) 2)
4.9b
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
15.3b
(* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

rewrite1.1s

Algorithm
rewrite-expression-head
Rules
5603×add-exp-log
4515×prod-exp
3078×pow-exp
2032×div-exp
1869×pow-to-exp
434×rec-exp 1-exp
27×add-cbrt-cube
23×add-sqr-sqrt
22×times-frac
20×unpow-prod-down
18×add-cube-cbrt *-un-lft-identity
12×associate-*r*
11×associate-*l*
9×associate-/r*
8×cbrt-unprod
7×cbrt-undiv
6×pow1 sqr-pow
4×div-inv associate-/l* unpow2 add-log-exp
3×pow-unpow unswap-sqr
2×frac-2neg clear-num
1×pow-flip pow-pow associate-*r/ *-commutative inv-pow
Counts
4 → 1460
Calls
4 calls:
105.0ms
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
9.0ms
(pow (sin k) 2)
20.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
646.0ms
(* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

series1.7s

Counts
4 → 12
Calls
4 calls:
526.0ms
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
36.0ms
(pow (sin k) 2)
122.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
969.0ms
(* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

simplify1.9s

Counts
1472 → 1472
Iterations

Useful iterations: 2 (928.0ms)

IterNodesCost
059750343
1126233112
2294031574
done500131574

prune938.0ms

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 11.1b

localize40.0ms

Local error

Found 4 expressions with local error:

0.6b
(/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0)))
4.9b
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
4.9b
(* (pow (/ (sqrt 1) (pow k (/ 2.0 2))) 1.0) (* (/ (* (cos k) (pow l 2)) (pow (sin k) 2)) (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0)))
9.8b
(* (/ (* (cos k) (pow l 2)) (pow (sin k) 2)) (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0))

rewrite1.4s

Algorithm
rewrite-expression-head
Rules
13973×add-exp-log
10155×prod-exp
8251×pow-exp
5914×div-exp
4231×pow-to-exp
920×rec-exp 1-exp
81×unpow-prod-down
64×times-frac
62×associate-*l*
49×add-sqr-sqrt
44×add-cube-cbrt *-un-lft-identity
37×add-cbrt-cube
21×sqrt-prod
14×cbrt-unprod
12×associate-*r* sqr-pow
9×associate-/r*
8×cbrt-undiv
5×pow1 div-inv
4×associate-/l* add-log-exp
3×unpow2 unswap-sqr
2×frac-2neg associate-*l/ clear-num *-commutative
1×pow-flip associate-*r/ inv-pow
Counts
4 → 3203
Calls
4 calls:
21.0ms
(/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0)))
22.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
290.0ms
(* (pow (/ (sqrt 1) (pow k (/ 2.0 2))) 1.0) (* (/ (* (cos k) (pow l 2)) (pow (sin k) 2)) (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0)))
157.0ms
(* (/ (* (cos k) (pow l 2)) (pow (sin k) 2)) (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0))

series1.8s

Counts
4 → 12
Calls
4 calls:
486.0ms
(/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0)))
138.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
594.0ms
(* (pow (/ (sqrt 1) (pow k (/ 2.0 2))) 1.0) (* (/ (* (cos k) (pow l 2)) (pow (sin k) 2)) (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0)))
569.0ms
(* (/ (* (cos k) (pow l 2)) (pow (sin k) 2)) (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0))

simplify2.7s

Counts
3215 → 3215
Iterations

Useful iterations: 2 (1.4s)

IterNodesCost
01014126429
11933109188
24064105683
done5001105683

prune1.3s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 9.6b

regimes23.0ms