Details

Time bar (total: 50.6s)

sample320.0ms

Algorithm
intervals
Results
110.0ms69×body1280valid
91.0ms193×body80valid
63.0ms61×body640valid
19.0ms27×body320valid
7.0ms13×body160valid

simplify4.3s

Counts
1 → 1
Iterations

Useful iterations: 4 (2.3s)

IterNodesCost
01925
14825
216025
388225
4495024
done500024

prune24.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 32.1b

localize28.0ms

Local error

Found 4 expressions with local error:

2.7b
(* (/ (pow t 3.0) (* l l)) (sin k))
3.2b
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
12.8b
(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
16.2b
(/ (pow t 3.0) (* l l))

rewrite995.0ms

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×expm1-log1p-u flip3-+ flip-+ log1p-expm1-u 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 → 152
Calls
4 calls:
44.0ms
(* (/ (pow t 3.0) (* l l)) (sin k))
123.0ms
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
788.0ms
(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
28.0ms
(/ (pow t 3.0) (* l l))

series2.1s

Counts
4 → 12
Calls
4 calls:
378.0ms
(* (/ (pow t 3.0) (* l l)) (sin k))
486.0ms
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
934.0ms
(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
304.0ms
(/ (pow t 3.0) (* l l))

simplify2.3s

Counts
164 → 164
Iterations

Useful iterations: done (2.3s)

IterNodesCost
02633323
17733179
235652673
done50012672

prune881.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 18.3b

localize42.0ms

Local error

Found 4 expressions with local error:

3.2b
(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
3.4b
(* (/ (pow (cbrt t) 3.0) l) (sin k))
11.3b
(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
12.8b
(* (* (* (/ (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))

rewrite1.6s

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×expm1-log1p-u log1p-expm1-u 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 → 237
Calls
4 calls:
258.0ms
(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
64.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
20.0ms
(/ (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:
575.0ms
(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
370.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
291.0ms
(/ (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))

simplify1.1s

Counts
249 → 249
Iterations

Useful iterations: done (1.1s)

IterNodesCost
04377110
112676725
done50005760

prune1.7s

Pruning

24 alts after pruning (24 fresh and 0 done)

Merged error: 11.6b

localize49.0ms

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)))
3.2b
(* (* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
3.4b
(* (/ (pow (cbrt t) 3.0) l) (sin k))
12.8b
(* (* (* (/ (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×expm1-log1p-u *-commutative log1p-expm1-u add-log-exp
3×distribute-lft-out
1×distribute-rgt-in distribute-lft-in associate-/r/
Counts
4 → 718
Calls
4 calls:
272.0ms
(* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k)))
351.0ms
(* (* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
42.0ms
(* (/ (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))

series2.3s

Counts
4 → 12
Calls
4 calls:
377.0ms
(* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k)))
553.0ms
(* (* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
355.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
1.0s
(* (* (* (/ (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))

simplify1.4s

Counts
730 → 730
Iterations

Useful iterations: done (1.4s)

IterNodesCost
081420856
1258419631
done500017266

prune5.6s

Pruning

29 alts after pruning (29 fresh and 0 done)

Merged error: 8.8b

localize62.0ms

Local error

Found 4 expressions with local error:

1.6b
(* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (sin k))
3.4b
(* (/ (pow (cbrt t) 3.0) l) (sin k))
4.4b
(/ (* (* (* (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)))
10.4b
(* (* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (sin k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

rewrite2.2s

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×expm1-log1p-u frac-times flip3-+ flip-+ log1p-expm1-u 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 → 272
Calls
4 calls:
244.0ms
(* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (sin k))
64.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
863.0ms
(/ (* (* (* (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)))
985.0ms
(* (* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (sin k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

series3.0s

Counts
4 → 12
Calls
4 calls:
383.0ms
(* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (sin k))
347.0ms
(* (/ (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)))
1.2s
(* (* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (sin k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

simplify936.0ms

Counts
284 → 284
Iterations

Useful iterations: done (911.0ms)

IterNodesCost
040910482
112209392
done50016989

prune1.3s

Pruning

32 alts after pruning (32 fresh and 0 done)

Merged error: 7.0b

regimes1.4s

Accuracy

57.8% (3.2b remaining)

Error of 10.0b against oracle of 6.8b and baseline of 14.4b

bsearch573.0ms

Steps
ItersRangePoint
7
1.2167838917470026e-32
5.292293405387877e-31
5.383759381485266e-32
7
-2.717358686591691e-72
-7.720368694033712e-74
-4.487942507103073e-73

simplify11.0ms

Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
064167
183167
done83167

end0.0ms

sample11.3s

Algorithm
intervals
Results
4.0s2070×body1280valid
2.9s1657×body640valid
2.3s6037×body80valid
1.4s922×body320valid
206.0ms432×body160valid