Details

Time bar (total: 40.0s)

sample286.0ms

Algorithm
intervals
Results
148.0ms70×body1280valid
48.0ms51×body640valid
38.0ms184×body80valid
13.0ms20×body320valid
8.0ms17×body160valid

simplify897.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01925
14825
215725
388125
done500125

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.7b

localize43.0ms

Local error

Found 4 expressions with local error:

2.9b
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
3.2b
(* (/ (pow t 3.0) (* l l)) (sin k))
12.6b
(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
17.5b
(/ (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:
136.0ms
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
41.0ms
(* (/ (pow t 3.0) (* l l)) (sin k))
840.0ms
(* (* (* (/ (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))

series2.1s

Counts
4 → 12
Calls
4 calls:
526.0ms
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
339.0ms
(* (/ (pow t 3.0) (* l l)) (sin k))
987.0ms
(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
258.0ms
(/ (pow t 3.0) (* l l))

simplify562.0ms

Counts
156 → 156
Iterations

Useful iterations: done (555.0ms)

IterNodesCost
02553209
18253073
done50002625

prune947.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 16.3b

localize72.0ms

Local error

Found 4 expressions with local error:

2.9b
(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
3.8b
(* (/ (pow (cbrt t) 3.0) l) (sin k))
9.1b
(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
12.6b
(* (* (* (/ (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:
183.0ms
(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
51.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
10.0ms
(/ (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))

series2.3s

Counts
4 → 12
Calls
4 calls:
511.0ms
(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
429.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
289.0ms
(/ (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))

simplify865.0ms

Counts
241 → 241
Iterations

Useful iterations: done (853.0ms)

IterNodesCost
04296958
113626586
done50005737

prune1.6s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 9.4b

localize65.0ms

Local error

Found 4 expressions with local error:

0.7b
(pow (cbrt t) 3.0)
2.9b
(* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (/ l (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
3.8b
(* (/ (pow (cbrt t) 3.0) l) (sin k))
12.6b
(* (* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (/ l (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

rewrite1.7s

Algorithm
rewrite-expression-head
Rules
1369×add-exp-log
791×prod-exp
489×div-exp
224×pow-exp
134×pow-to-exp
115×add-cbrt-cube
63×cbrt-unprod
44×associate-*l/
43×add-sqr-sqrt
36×associate-*l*
35×*-un-lft-identity
34×frac-times times-frac
30×pow1 add-cube-cbrt
26×unpow-prod-down
25×cbrt-undiv
17×pow-prod-down
16×tan-quot
14×associate-*r/
13×cbrt-prod
11×associate-*r*
8×flip3-+ flip-+
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 → 378
Calls
4 calls:
4.0ms
(pow (cbrt t) 3.0)
246.0ms
(* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (/ l (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
42.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
1.4s
(* (* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (/ l (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)))) (* (/ (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:
453.0ms
(pow (cbrt t) 3.0)
550.0ms
(* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (/ l (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
383.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
1.0s
(* (* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (/ l (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

simplify993.0ms

Counts
390 → 390
Iterations

Useful iterations: done (970.0ms)

IterNodesCost
054516589
1194715463
done500113950

prune1.8s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 7.5b

localize96.0ms

Local error

Found 4 expressions with local error:

3.0b
(* (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (sin k))
3.8b
(* (/ (pow (cbrt t) 3.0) l) (sin k))
5.9b
(/ (* (* (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (sin k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0)) (* (/ l (pow (* (cbrt t) (cbrt t)) (/ 3.0 2))) (cos k)))
9.5b
(* (* (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (sin k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

rewrite2.4s

Algorithm
rewrite-expression-head
Rules
1214×add-exp-log
792×prod-exp
329×div-exp
159×pow-exp
142×add-cbrt-cube
96×pow-to-exp
79×cbrt-unprod
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 → 322
Calls
4 calls:
214.0ms
(* (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (sin k))
65.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
932.0ms
(/ (* (* (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (sin k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0)) (* (/ l (pow (* (cbrt t) (cbrt t)) (/ 3.0 2))) (cos k)))
1.1s
(* (* (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (sin k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

series3.2s

Counts
4 → 12
Calls
4 calls:
411.0ms
(* (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (sin k))
374.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
1.6s
(/ (* (* (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (sin k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0)) (* (/ l (pow (* (cbrt t) (cbrt t)) (/ 3.0 2))) (cos k)))
861.0ms
(* (* (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (sin k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

simplify799.0ms

Counts
334 → 334
Iterations

Useful iterations: done (763.0ms)

IterNodesCost
045515435
1163214304
done500011835

prune1.6s

Pruning

25 alts after pruning (25 fresh and 0 done)

Merged error: 6.7b

regimes1.2s

Accuracy

32.6% (4.6b remaining)

Error of 12.1b against oracle of 7.6b and baseline of 14.3b

bsearch711.0ms

Steps
ItersRangePoint
8
5.190504828498133e-56
7.148736973730714e-52
2.1105703252304796e-55
10
-1.346179280470772e-79
-1.3503155801709781e-93
-1.3721260571434645e-93

simplify10.0ms

Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
063202
184202
done84202

end0.0ms

sample10.9s

Algorithm
intervals
Results
5.3s2133×body1280valid
2.1s5953×body80valid
2.0s1690×body640valid
656.0ms796×body320valid
258.0ms405×body160valid