Details

Time bar (total: 21.6s)

sample130.0ms

Algorithm
intervals
Results
44.0ms58×body1280valid
29.0ms58×body640valid
25.0ms205×body80valid
7.0ms21×body320valid
4.0ms15×body160valid

simplify29.0ms

Counts
1 → 1
Iterations

Useful iterations: 3 (27.0ms)

IterNodesCost
04813
116113
294413
3500212
done500212

prune11.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 29.4b

localize20.0ms

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))
12.5b
(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
17.0b
(/ (pow t 3.0) (* l l))

rewrite612.0ms

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:
73.0ms
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
31.0ms
(* (/ (pow t 3.0) (* l l)) (sin k))
488.0ms
(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
11.0ms
(/ (pow t 3.0) (* l l))

series1.4s

Counts
4 → 12
Calls
4 calls:
334.0ms
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
256.0ms
(* (/ (pow t 3.0) (* l l)) (sin k))
652.0ms
(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
181.0ms
(/ (pow t 3.0) (* l l))

simplify116.0ms

Counts
164 → 164
Iterations

Useful iterations: 1 (22.0ms)

IterNodesCost
08171679
147261405
250011405
done50011405

prune543.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 17.4b

localize26.0ms

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))
3.8b
(* (/ (pow (cbrt t) 3.0) l) (sin k))
8.9b
(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
12.5b
(* (* (* (/ (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))

rewrite896.0ms

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:
137.0ms
(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
30.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
9.0ms
(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
703.0ms
(* (* (* (/ (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))

series1.6s

Counts
4 → 12
Calls
4 calls:
377.0ms
(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
249.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
199.0ms
(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
741.0ms
(* (* (* (/ (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))

simplify57.0ms

Counts
249 → 249
Iterations

Useful iterations: 1 (29.0ms)

IterNodesCost
013643882
150013394
done50013394

prune1.1s

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 10.9b

localize38.0ms

Local error

Found 4 expressions with local error:

1.1b
(* (/ (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)))
2.3b
(* (* (/ (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))
12.5b
(* (* (* (/ (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))

rewrite1.2s

Algorithm
rewrite-expression-head
Rules
1884×add-exp-log
1025×prod-exp
732×div-exp
334×pow-exp
204×times-frac
199×pow-to-exp
151×add-cbrt-cube
136×associate-*l*
105×add-sqr-sqrt
97×*-un-lft-identity
92×add-cube-cbrt
78×cbrt-unprod
54×unpow-prod-down
47×associate-*l/
38×sqr-pow
37×cbrt-undiv
35×frac-times
34×pow1
20×pow-prod-down
16×tan-quot
15×associate-*r/
12×associate-*r*
10×cbrt-prod
8×flip3-+ flip-+
7×div-inv
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 → 593
Calls
4 calls:
88.0ms
(* (/ (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)))
180.0ms
(* (* (/ (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))
30.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
858.0ms
(* (* (* (/ (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)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

series1.9s

Counts
4 → 12
Calls
4 calls:
291.0ms
(* (/ (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)))
367.0ms
(* (* (/ (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))
245.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
976.0ms
(* (* (* (/ (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)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

simplify141.0ms

Counts
605 → 605
Iterations

Useful iterations: 1 (42.0ms)

IterNodesCost
0252213450
1500112333
done500112333

prune1.8s

Pruning

27 alts after pruning (27 fresh and 0 done)

Merged error: 8.9b

localize34.0ms

Local error

Found 4 expressions with local error:

3.8b
(* (/ (pow (cbrt t) 3.0) l) (sin k))
4.1b
(* (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
5.7b
(/ (* (* (* (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)) (/ l (pow (* (cbrt t) (cbrt t)) (/ 3.0 2))))
10.0b
(* (* (* (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))

rewrite1.4s

Algorithm
rewrite-expression-head
Rules
966×add-exp-log
593×prod-exp
294×div-exp
145×pow-exp
103×add-cbrt-cube
87×pow-to-exp
83×times-frac
58×add-sqr-sqrt
53×cbrt-unprod
50×*-un-lft-identity
45×add-cube-cbrt
36×associate-*l*
28×associate-*l/
26×unpow-prod-down
25×associate-*r/
23×cbrt-undiv
19×frac-times associate-/r*
14×tan-quot
13×pow1
11×associate-*r* associate-/l/
10×cbrt-prod sqr-pow
8×flip3-+ flip-+
5×pow-prod-down unswap-sqr
4×expm1-log1p-u log1p-expm1-u div-inv add-log-exp
3×*-commutative distribute-lft-out
1×distribute-rgt-in frac-2neg distribute-lft-in clear-num associate-/r/ associate-/l*
Counts
4 → 351
Calls
4 calls:
29.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
131.0ms
(* (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
564.0ms
(/ (* (* (* (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)) (/ l (pow (* (cbrt t) (cbrt t)) (/ 3.0 2))))
667.0ms
(* (* (* (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))

series2.2s

Counts
4 → 12
Calls
4 calls:
242.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
369.0ms
(* (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
763.0ms
(/ (* (* (* (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)) (/ l (pow (* (cbrt t) (cbrt t)) (/ 3.0 2))))
829.0ms
(* (* (* (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))

simplify99.0ms

Counts
363 → 363
Iterations

Useful iterations: 1 (33.0ms)

IterNodesCost
017688198
150027556
done50027556

prune1.2s

Pruning

27 alts after pruning (27 fresh and 0 done)

Merged error: 8.1b

regimes776.0ms

Accuracy

36.5% (4.4b remaining)

Error of 12.0b against oracle of 7.5b and baseline of 14.5b

bsearch361.0ms

Steps
ItersRangePoint
9
2.2564848300118077e-105
9.727137357237736e-98
1.1844105148099733e-99
7
-4.729715222041092e-118
-5.136254632782565e-120
-5.2153380316403514e-120

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
093105
193105
done93105

end0.0ms

sample3.9s

Algorithm
intervals
Results
1.7s2097×body1280valid
846.0ms1681×body640valid
618.0ms5841×body80valid
296.0ms851×body320valid
100.0ms429×body160valid