Details

Time bar (total: 50.1s)

sample314.0ms

Algorithm
intervals
Results
122.0ms56×body1280valid
75.0ms64×body640valid
50.0ms199×body80valid
18.0ms24×body320valid
11.0ms21×body160valid

simplify3.7s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01925
14825
215725
384225
4465725
done500125

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.9b

localize30.0ms

Local error

Found 4 expressions with local error:

3.2b
(* (/ (pow t 3.0) (* l l)) (sin k))
3.7b
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
17.0b
(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
17.1b
(/ (pow t 3.0) (* l l))

rewrite1.0s

Algorithm
rewrite-expression-head
Rules
108×add-exp-log
58×prod-exp
52×add-cbrt-cube
26×cbrt-unprod
24×div-exp
21×add-sqr-sqrt
20×pow1
19×*-un-lft-identity
17×times-frac
16×associate-*l/
14×add-cube-cbrt
13×associate-*l*
11×associate-*r*
10×frac-times unpow-prod-down pow-prod-down
8×tan-quot cbrt-undiv pow-to-exp pow-exp
7×associate-/l*
6×associate-*r/
4×flip3-+ flip-+ add-log-exp unswap-sqr sqr-pow
3×*-commutative distribute-lft-out
2×div-inv
1×distribute-rgt-in frac-2neg distribute-lft-in clear-num associate-/r*
Counts
4 → 144
Calls
4 calls:
52.0ms
(* (/ (pow t 3.0) (* l l)) (sin k))
81.0ms
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
868.0ms
(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
12.0ms
(/ (pow t 3.0) (* l l))

series2.2s

Counts
4 → 12
Calls
4 calls:
405.0ms
(* (/ (pow t 3.0) (* l l)) (sin k))
504.0ms
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
1.0s
(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
296.0ms
(/ (pow t 3.0) (* l l))

simplify2.5s

Counts
156 → 156
Iterations

Useful iterations: 2 (846.0ms)

IterNodesCost
02553209
17543070
234832565
done50002565

prune923.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 18.2b

localize76.0ms

Local error

Found 4 expressions with local error:

2.9b
(* (/ (pow (cbrt t) 3.0) l) (sin k))
3.7b
(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
7.8b
(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
17.0b
(* (* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

rewrite1.4s

Algorithm
rewrite-expression-head
Rules
304×add-exp-log
184×prod-exp
78×add-cbrt-cube
77×div-exp
50×add-sqr-sqrt
49×times-frac
44×associate-*l/ cbrt-unprod
42×*-un-lft-identity
37×add-cube-cbrt
36×associate-*l*
34×frac-times
33×pow-exp
29×pow1
24×unpow-prod-down
22×pow-to-exp
17×pow-prod-down
16×tan-quot
14×associate-*r/
12×cbrt-undiv
11×associate-*r*
10×cbrt-prod
8×flip3-+ flip-+ sqr-pow
5×associate-/l* unswap-sqr
4×add-log-exp
3×associate-/r* *-commutative distribute-lft-out
2×div-inv
1×distribute-rgt-in frac-2neg distribute-lft-in clear-num
Counts
4 → 229
Calls
4 calls:
46.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
212.0ms
(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
19.0ms
(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
1.1s
(* (* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

series2.6s

Counts
4 → 12
Calls
4 calls:
406.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
560.0ms
(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
302.0ms
(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
1.4s
(* (* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

simplify1.0s

Counts
241 → 241
Iterations

Useful iterations: done (1.0s)

IterNodesCost
04296958
112506583
done50015619

prune1.3s

Pruning

22 alts after pruning (21 fresh and 1 done)

Merged error: 12.3b

localize63.0ms

Local error

Found 4 expressions with local error:

0.7b
(pow (cbrt t) 3.0)
2.9b
(* (/ (pow (cbrt t) 3.0) l) (sin k))
3.7b
(* (* (* (/ (pow (cbrt t) 3.0) (* (cbrt l) (cbrt l))) (/ (pow (cbrt t) 3.0) (cbrt l))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
17.0b
(* (* (* (* (/ (pow (cbrt t) 3.0) (* (cbrt l) (cbrt l))) (/ (pow (cbrt t) 3.0) (cbrt l))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

rewrite5.2s

Algorithm
rewrite-expression-head
Rules
2085×add-exp-log
1365×prod-exp
627×div-exp
253×add-cbrt-cube
210×pow-to-exp pow-exp
187×cbrt-unprod
116×associate-*l/
98×frac-times
57×cbrt-undiv
50×pow1
43×add-sqr-sqrt
36×associate-*l*
35×*-un-lft-identity
34×times-frac
33×pow-prod-down
32×tan-quot
30×add-cube-cbrt associate-*r/
26×unpow-prod-down
16×flip3-+ flip-+
13×cbrt-prod
11×associate-*r*
5×unswap-sqr sqr-pow
4×add-log-exp
3×pow-unpow *-commutative distribute-lft-out
2×pow-pow
1×distribute-rgt-in distribute-lft-in pow1/3 div-inv
Counts
4 → 518
Calls
4 calls:
3.0ms
(pow (cbrt t) 3.0)
56.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
873.0ms
(* (* (* (/ (pow (cbrt t) 3.0) (* (cbrt l) (cbrt l))) (/ (pow (cbrt t) 3.0) (cbrt l))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
4.1s
(* (* (* (* (/ (pow (cbrt t) 3.0) (* (cbrt l) (cbrt l))) (/ (pow (cbrt t) 3.0) (cbrt l))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

series2.7s

Counts
4 → 12
Calls
4 calls:
553.0ms
(pow (cbrt t) 3.0)
377.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
589.0ms
(* (* (* (/ (pow (cbrt t) 3.0) (* (cbrt l) (cbrt l))) (/ (pow (cbrt t) 3.0) (cbrt l))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
1.2s
(* (* (* (* (/ (pow (cbrt t) 3.0) (* (cbrt l) (cbrt l))) (/ (pow (cbrt t) 3.0) (cbrt l))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

simplify1.4s

Counts
530 → 530
Iterations

Useful iterations: done (1.3s)

IterNodesCost
069223346
1210819711
done500017138

prune2.2s

Pruning

27 alts after pruning (26 fresh and 1 done)

Merged error: 11.5b

localize51.0ms

Local error

Found 4 expressions with local error:

0.7b
(pow (cbrt t) 3.0)
1.0b
(* (tan k) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
2.9b
(* (/ (pow (cbrt t) 3.0) l) (sin k))
20.3b
(* (* (* (/ (pow (cbrt t) 3.0) (* (cbrt l) (cbrt l))) (/ (pow (cbrt t) 3.0) (cbrt l))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (* (tan k) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0)))

rewrite1.9s

Algorithm
rewrite-expression-head
Rules
2085×add-exp-log
1365×prod-exp
627×div-exp
253×add-cbrt-cube
210×pow-to-exp pow-exp
187×cbrt-unprod
83×frac-times
71×associate-*l/
57×cbrt-undiv
50×pow1
45×add-sqr-sqrt
41×associate-*r/
38×associate-*l*
35×*-un-lft-identity
34×times-frac
33×pow-prod-down
30×add-cube-cbrt
27×tan-quot
26×unpow-prod-down
18×flip3-+ flip-+
13×cbrt-prod
9×associate-*r*
6×unswap-sqr
5×distribute-rgt-in distribute-lft-in sqr-pow
4×add-log-exp
3×pow-unpow *-commutative distribute-lft-out
2×pow-pow
1×pow1/3 div-inv
Counts
4 → 513
Calls
4 calls:
3.0ms
(pow (cbrt t) 3.0)
419.0ms
(* (tan k) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
50.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
1.3s
(* (* (* (/ (pow (cbrt t) 3.0) (* (cbrt l) (cbrt l))) (/ (pow (cbrt t) 3.0) (cbrt l))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (* (tan k) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0)))

series2.2s

Counts
4 → 12
Calls
4 calls:
427.0ms
(pow (cbrt t) 3.0)
156.0ms
(* (tan k) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
315.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
1.3s
(* (* (* (/ (pow (cbrt t) 3.0) (* (cbrt l) (cbrt l))) (/ (pow (cbrt t) 3.0) (cbrt l))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (* (tan k) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0)))

simplify995.0ms

Counts
525 → 525
Iterations

Useful iterations: done (969.0ms)

IterNodesCost
068924909
1196221378
done500018461

prune1.7s

Pruning

26 alts after pruning (25 fresh and 1 done)

Merged error: 11.5b

regimes1.6s

Accuracy

12.2% (6.5b remaining)

Error of 16.8b against oracle of 10.3b and baseline of 17.7b

bsearch1.3s

Steps
ItersRangePoint
9
2.567683059766632e+106
6.314650550415426e+112
4.159535746736078e+112
9
4.8307314062134995e-18
4.0226559123014505e-11
4.9086239140483104e-18
7
-1.6298779679627079e-108
-9.823299607801205e-111
-6.271868012243787e-110
10
-1.3880569002884752e+141
-8.1181122972964275e+127
-3.748902034743021e+138

simplify15.0ms

Iterations

Useful iterations: 1 (10.0ms)

IterNodesCost
067230
189187
done89187

end0.0ms

sample11.7s

Algorithm
intervals
Results
5.2s2063×body1280valid
2.1s5870×body80valid
2.1s1706×body640valid
1.3s872×body320valid
320.0ms481×body160valid