Details

Time bar (total: 50.3s)

sample295.0ms

Algorithm
intervals
Results
90.0ms59×body1280valid
61.0ms57×body640valid
53.0ms36×body320valid
41.0ms177×body80valid
12.0ms18×body160valid

simplify477.0ms

Counts
1 → 1

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.3b

localize36.0ms

Local error

Found 4 expressions with local error:

2.2b
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
4.1b
(* (/ (pow t 3.0) (* l l)) (sin k))
12.9b
(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
15.9b
(/ (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:
138.0ms
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
61.0ms
(* (/ (pow t 3.0) (* l l)) (sin k))
742.0ms
(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
57.0ms
(/ (pow t 3.0) (* l l))

series2.0s

Counts
4 → 12
Calls
4 calls:
460.0ms
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
350.0ms
(* (/ (pow t 3.0) (* l l)) (sin k))
927.0ms
(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
271.0ms
(/ (pow t 3.0) (* l l))

simplify1.9s

Counts
156 → 156

prune706.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 15.6b

localize71.0ms

Local error

Found 4 expressions with local error:

2.2b
(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
2.8b
(* (/ (pow (cbrt t) 3.0) l) (sin k))
7.7b
(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
12.9b
(* (* (* (/ (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:
224.0ms
(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
48.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
9.0ms
(/ (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))

series2.2s

Counts
4 → 12
Calls
4 calls:
574.0ms
(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
367.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
292.0ms
(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
976.0ms
(* (* (* (/ (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))

simplify796.0ms

Counts
241 → 241

prune1.6s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 10.1b

localize69.0ms

Local error

Found 4 expressions with local error:

0.8b
(* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (cbrt l) (cbrt l))) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l))) (* (/ (pow (cbrt t) 3.0) l) (sin k)))
2.2b
(* (* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (cbrt l) (cbrt l))) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
2.8b
(* (/ (pow (cbrt t) 3.0) l) (sin k))
12.9b
(* (* (* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (cbrt l) (cbrt l))) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

rewrite4.7s

Algorithm
rewrite-expression-head
Rules
5034×add-exp-log
3200×prod-exp
1557×div-exp
709×pow-exp
424×pow-to-exp
340×add-cbrt-cube
246×cbrt-unprod
125×associate-*l/
103×frac-times
85×cbrt-undiv
61×pow1
41×pow-prod-down
40×add-sqr-sqrt
37×associate-*l*
34×times-frac
33×associate-*r/
32×tan-quot *-un-lft-identity
27×add-cube-cbrt
20×unpow-prod-down
16×flip3-+ flip-+
12×associate-*r*
10×cbrt-prod
5×unswap-sqr
4×*-commutative add-log-exp sqr-pow
3×distribute-lft-out
1×distribute-rgt-in distribute-lft-in div-inv
Counts
4 → 939
Calls
4 calls:
189.0ms
(* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (cbrt l) (cbrt l))) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l))) (* (/ (pow (cbrt t) 3.0) l) (sin k)))
844.0ms
(* (* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (cbrt l) (cbrt l))) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
46.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
3.4s
(* (* (* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (cbrt l) (cbrt l))) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

series2.4s

Counts
4 → 12
Calls
4 calls:
429.0ms
(* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (cbrt l) (cbrt l))) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l))) (* (/ (pow (cbrt t) 3.0) l) (sin k)))
549.0ms
(* (* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (cbrt l) (cbrt l))) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
326.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
1.1s
(* (* (* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (cbrt l) (cbrt l))) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

simplify2.1s

Counts
951 → 951

prune2.6s

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 8.8b

localize70.0ms

Local error

Found 4 expressions with local error:

0.7b
(pow (cbrt t) 3.0)
2.2b
(* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (cbrt l) (cbrt l))) (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l)) (* (/ (pow (cbrt t) 3.0) l) (sin k)))) (tan k))
2.8b
(* (/ (pow (cbrt t) 3.0) l) (sin k))
12.9b
(* (* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (cbrt l) (cbrt l))) (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l)) (* (/ (pow (cbrt t) 3.0) l) (sin k)))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

rewrite4.2s

Algorithm
rewrite-expression-head
Rules
3634×add-exp-log
2390×prod-exp
1049×div-exp
480×pow-exp
286×pow-to-exp
249×add-cbrt-cube
185×cbrt-unprod
100×associate-*l/
98×frac-times
59×cbrt-undiv
46×associate-*r/
43×add-sqr-sqrt
41×pow1
36×associate-*l*
35×*-un-lft-identity
34×times-frac
32×tan-quot
30×add-cube-cbrt
26×unpow-prod-down pow-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 → 694
Calls
4 calls:
6.0ms
(pow (cbrt t) 3.0)
806.0ms
(* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (cbrt l) (cbrt l))) (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l)) (* (/ (pow (cbrt t) 3.0) l) (sin k)))) (tan k))
41.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
3.2s
(* (* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (cbrt l) (cbrt l))) (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l)) (* (/ (pow (cbrt t) 3.0) l) (sin k)))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

series2.8s

Counts
4 → 12
Calls
4 calls:
447.0ms
(pow (cbrt t) 3.0)
512.0ms
(* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (cbrt l) (cbrt l))) (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l)) (* (/ (pow (cbrt t) 3.0) l) (sin k)))) (tan k))
327.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
1.5s
(* (* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (cbrt l) (cbrt l))) (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l)) (* (/ (pow (cbrt t) 3.0) l) (sin k)))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

simplify1.7s

Counts
706 → 706

prune2.3s

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 7.8b

regimes818.0ms

Accuracy

-4.4% (8.2b remaining)

Error of 16.3b against oracle of 8.1b and baseline of 15.9b

bsearch705.0ms

Steps
ItersRangePoint
8
2.682426594397128e-114
6.591065062367509e-110
1.9207117194670935e-110
8
-2.9553699421558828e-254
-4.9050177650334747e-259
-2.9025962241290474e-254

simplify2.3s

end0.0ms

sample11.1s

Algorithm
intervals
Results
4.6s2065×body1280valid
2.3s1668×body640valid
2.0s5900×body80valid
1.3s888×body320valid
266.0ms426×body160valid