Details

Time bar (total: 1.1m)

sample366.0ms

Algorithm
intervals
Results
145.0ms62×body1280valid
86.0ms65×body640valid
50.0ms180×body80valid
28.0ms31×body320valid
7.0ms11×body160valid

simplify1.7s

Counts
1 → 1
Iterations

Useful iterations: done (1.7s)

IterNodesCost
01925
14825
216025
391925
done500024

prune32.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 30.5b

localize65.0ms

Local error

Found 4 expressions with local error:

2.9b
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
4.1b
(* (/ (pow t 3.0) (* l l)) (sin k))
13.0b
(/ (pow t 3.0) (* l l))
14.1b
(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

rewrite1.3s

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:
150.0ms
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
65.0ms
(* (/ (pow t 3.0) (* l l)) (sin k))
22.0ms
(/ (pow t 3.0) (* l l))
1.0s
(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

series2.7s

Counts
4 → 12
Calls
4 calls:
650.0ms
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
464.0ms
(* (/ (pow t 3.0) (* l l)) (sin k))
340.0ms
(/ (pow t 3.0) (* l l))
1.2s
(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

simplify783.0ms

Counts
164 → 164
Iterations

Useful iterations: done (773.0ms)

IterNodesCost
02633323
18383182
done50002733

prune1.7s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 15.4b

localize95.0ms

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))
4.0b
(* (/ (pow (cbrt t) 3.0) l) (sin k))
7.3b
(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
14.1b
(* (* (* (/ (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))

rewrite2.0s

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:
296.0ms
(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
67.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
19.0ms
(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
1.6s
(* (* (* (/ (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))

series3.1s

Counts
4 → 12
Calls
4 calls:
726.0ms
(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
472.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
399.0ms
(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
1.5s
(* (* (* (/ (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
113896803
done50015888

prune3.1s

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 10.3b

localize104.0ms

Local error

Found 4 expressions with local error:

0.8b
(* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k)))
2.9b
(* (* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
4.0b
(* (/ (pow (cbrt t) 3.0) l) (sin k))
14.1b
(* (* (* (/ (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))

rewrite3.3s

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:
318.0ms
(* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k)))
487.0ms
(* (* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
61.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
2.3s
(* (* (* (/ (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))

series3.8s

Counts
4 → 12
Calls
4 calls:
560.0ms
(* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k)))
1.3s
(* (* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
478.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
1.5s
(* (* (* (/ (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))

simplify2.1s

Counts
730 → 730
Iterations

Useful iterations: done (2.0s)

IterNodesCost
081420856
1275019634
done500118138

prune9.0s

Pruning

24 alts after pruning (24 fresh and 0 done)

Merged error: 8.1b

localize101.0ms

Local error

Found 4 expressions with local error:

2.3b
(* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (sin k))
4.0b
(* (/ (pow (cbrt t) 3.0) l) (sin k))
6.2b
(/ (* (* (* (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)))
11.7b
(* (* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (sin k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

rewrite2.9s

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:
268.0ms
(* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (sin k))
62.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin 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)) (* (/ l (pow (cbrt t) 3.0)) (cos k)))
1.4s
(* (* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (sin k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

series3.6s

Counts
4 → 12
Calls
4 calls:
527.0ms
(* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (sin k))
493.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
1.4s
(/ (* (* (* (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))

simplify1.3s

Counts
284 → 284
Iterations

Useful iterations: done (1.3s)

IterNodesCost
040910482
114059419
done50007835

prune2.5s

Pruning

27 alts after pruning (26 fresh and 1 done)

Merged error: 6.4b

regimes2.2s

Accuracy

51.2% (3.7b remaining)

Error of 10.8b against oracle of 7.1b and baseline of 14.7b

bsearch678.0ms

Steps
ItersRangePoint
7
4.735830173312099e-12
1.8004673508164536e-10
5.406629856909875e-12
7
-1.5312203001569835e+19
-1.3073170848719158e+17
-1.3265865393925435e+17

simplify18.0ms

Iterations

Useful iterations: 1 (11.0ms)

IterNodesCost
068162
187160
done87160

end0.0ms

sample14.0s

Algorithm
intervals
Results
5.7s2088×body1280valid
3.3s1709×body640valid
2.6s5985×body80valid
1.2s864×body320valid
369.0ms400×body160valid