Details

Time bar (total: 45.1s)

sample260.0ms

Algorithm
intervals
Results
103.0ms72×body1280valid
60.0ms204×body80valid
40.0ms42×body640valid
19.0ms26×body320valid
6.0ms16×body160valid

simplify1.5s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01925
14825
215725
388125
done500125

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.3b

localize28.0ms

Local error

Found 4 expressions with local error:

2.3b
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
3.1b
(* (/ (pow t 3.0) (* l l)) (sin k))
13.5b
(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
18.3b
(/ (pow t 3.0) (* l l))

rewrite880.0ms

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:
110.0ms
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
55.0ms
(* (/ (pow t 3.0) (* l l)) (sin k))
679.0ms
(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
23.0ms
(/ (pow t 3.0) (* l l))

series2.2s

Counts
4 → 12
Calls
4 calls:
526.0ms
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
350.0ms
(* (/ (pow t 3.0) (* l l)) (sin k))
1.1s
(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
224.0ms
(/ (pow t 3.0) (* l l))

simplify585.0ms

Counts
156 → 156
Iterations

Useful iterations: done (575.0ms)

IterNodesCost
02553209
18253073
done50002625

prune889.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 17.1b

localize57.0ms

Local error

Found 4 expressions with local error:

2.3b
(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
3.5b
(* (/ (pow (cbrt t) 3.0) l) (sin k))
9.4b
(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
13.5b
(* (* (* (/ (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))

rewrite1.5s

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:
254.0ms
(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
68.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
18.0ms
(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
1.2s
(* (* (* (/ (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))

series2.4s

Counts
4 → 12
Calls
4 calls:
627.0ms
(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
350.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
314.0ms
(/ (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))

simplify717.0ms

Counts
241 → 241
Iterations

Useful iterations: done (703.0ms)

IterNodesCost
04296958
113626586
done50005737

prune1.8s

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 12.4b

localize76.0ms

Local error

Found 4 expressions with local error:

1.1b
(* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k)))
2.3b
(* (* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
3.5b
(* (/ (pow (cbrt t) 3.0) l) (sin k))
13.5b
(* (* (* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

rewrite2.7s

Algorithm
rewrite-expression-head
Rules
1050×add-exp-log
674×times-frac
554×prod-exp
435×div-exp
404×unpow-prod-down
381×associate-*l*
343×add-sqr-sqrt
335×*-un-lft-identity
330×add-cube-cbrt
202×cbrt-prod
151×add-cbrt-cube
145×pow-to-exp pow-exp
78×cbrt-unprod
68×sqr-pow
47×associate-*l/
37×cbrt-undiv
35×frac-times
34×pow1
20×pow-prod-down
16×tan-quot
15×associate-*r/
12×associate-*r* div-inv
8×flip3-+ flip-+
5×unswap-sqr
4×*-commutative add-log-exp
3×distribute-lft-out
1×distribute-rgt-in distribute-lft-in associate-/r/
Counts
4 → 710
Calls
4 calls:
263.0ms
(* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k)))
411.0ms
(* (* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
45.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
1.9s
(* (* (* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (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:
475.0ms
(* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k)))
570.0ms
(* (* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
378.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
1.2s
(* (* (* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

simplify1.5s

Counts
722 → 722
Iterations

Useful iterations: done (1.4s)

IterNodesCost
080620672
1273519460
done500017929

prune5.5s

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 9.5b

localize55.0ms

Local error

Found 4 expressions with local error:

1.1b
(* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (sin k))
3.5b
(* (/ (pow (cbrt t) 3.0) l) (sin k))
4.6b
(/ (* (* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (sin k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0)) (* (/ l (pow (cbrt t) 3.0)) (cos k)))
10.9b
(* (* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (sin k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

rewrite2.3s

Algorithm
rewrite-expression-head
Rules
745×add-exp-log
479×prod-exp
210×div-exp
142×add-cbrt-cube
79×cbrt-unprod
75×pow-to-exp pow-exp
40×add-sqr-sqrt
36×associate-*l*
35×times-frac
32×*-un-lft-identity
30×cbrt-undiv
27×add-cube-cbrt
20×unpow-prod-down
18×associate-*l/
13×pow1
11×associate-*r/ associate-*r*
10×cbrt-prod
5×pow-prod-down associate-/l/ unswap-sqr
4×frac-times flip3-+ flip-+ add-log-exp sqr-pow
3×*-commutative distribute-lft-out
2×div-inv
1×distribute-rgt-in frac-2neg distribute-lft-in clear-num associate-/r* associate-/r/ associate-/l*
Counts
4 → 264
Calls
4 calls:
169.0ms
(* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (sin k))
46.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
955.0ms
(/ (* (* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (sin k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0)) (* (/ l (pow (cbrt t) 3.0)) (cos k)))
1.1s
(* (* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (sin k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

series2.6s

Counts
4 → 12
Calls
4 calls:
365.0ms
(* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (sin k))
304.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
1.1s
(/ (* (* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (sin k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0)) (* (/ l (pow (cbrt t) 3.0)) (cos k)))
894.0ms
(* (* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (sin k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

simplify1.3s

Counts
276 → 276
Iterations

Useful iterations: done (1.3s)

IterNodesCost
040110294
113909243
done50007662

prune1.4s

Pruning

24 alts after pruning (24 fresh and 0 done)

Merged error: 6.7b

regimes1.1s

Accuracy

53% (3.6b remaining)

Error of 10.6b against oracle of 7.0b and baseline of 14.7b

bsearch655.0ms

Steps
ItersRangePoint
9
9.702937987169133e+38
2.620973740523026e+48
9.911411609790157e+38
9
-1.1558673520674327e-24
-6.074523296947391e-32
-1.5086969913089599e-31

simplify19.0ms

Iterations

Useful iterations: 0 (4.0ms)

IterNodesCost
068174
189174
done89174

end0.0ms

sample10.6s

Algorithm
intervals
Results
4.3s2062×body1280valid
2.4s1712×body640valid
2.0s5940×body80valid
664.0ms851×body320valid
651.0ms472×body160valid