Details

Time bar (total: 44.0s)

sample239.0ms

Algorithm
intervals
Results
77.0ms64×body1280valid
62.0ms174×body80valid
50.0ms55×body640valid
17.0ms30×body320valid
4.0ms12×body160valid

simplify1.2s

Counts
1 → 1
Iterations

Useful iterations: done (1.2s)

IterNodesCost
01925
14825
216025
391925
done500024

prune16.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 31.4b

localize60.0ms

Local error

Found 4 expressions with local error:

2.0b
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
4.1b
(* (/ (pow t 3.0) (* l l)) (sin k))
12.9b
(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
16.1b
(/ (pow t 3.0) (* l l))

rewrite950.0ms

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:
103.0ms
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
59.0ms
(* (/ (pow t 3.0) (* l l)) (sin k))
765.0ms
(* (* (* (/ (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))

series2.0s

Counts
4 → 12
Calls
4 calls:
478.0ms
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
348.0ms
(* (/ (pow t 3.0) (* l l)) (sin k))
953.0ms
(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
235.0ms
(/ (pow t 3.0) (* l l))

simplify529.0ms

Counts
164 → 164
Iterations

Useful iterations: done (524.0ms)

IterNodesCost
02633323
18433182
done50012717

prune1.2s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 14.6b

localize67.0ms

Local error

Found 4 expressions with local error:

2.0b
(* (* (/ (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))
6.5b
(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
12.9b
(* (* (* (/ (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×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:
157.0ms
(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
32.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
10.0ms
(/ (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))

series2.5s

Counts
4 → 12
Calls
4 calls:
606.0ms
(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
337.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
306.0ms
(/ (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))

simplify714.0ms

Counts
249 → 249
Iterations

Useful iterations: done (705.0ms)

IterNodesCost
04377110
113896803
done50015888

prune2.3s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 10.6b

localize87.0ms

Local error

Found 4 expressions with local error:

1.5b
(* (/ (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)))
2.0b
(* (* (/ (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))
4.0b
(* (/ (pow (cbrt t) 3.0) l) (sin k))
12.9b
(* (* (* (/ (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)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

rewrite2.1s

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:
150.0ms
(* (/ (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)))
320.0ms
(* (* (/ (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))
61.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
1.5s
(* (* (* (/ (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:
421.0ms
(* (/ (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)))
508.0ms
(* (* (/ (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))
369.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
1.1s
(* (* (* (/ (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))

simplify1.2s

Counts
605 → 605
Iterations

Useful iterations: done (1.2s)

IterNodesCost
074425066
1255922927
done500120917

prune4.2s

Pruning

25 alts after pruning (25 fresh and 0 done)

Merged error: 8.7b

localize89.0ms

Local error

Found 4 expressions with local error:

3.3b
(* (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (sin k))
4.0b
(* (/ (pow (cbrt t) 3.0) l) (sin k))
6.3b
(/ (* (* (* (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)))
9.1b
(* (* (* (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))

rewrite2.3s

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×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 → 330
Calls
4 calls:
194.0ms
(* (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (sin k))
50.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
875.0ms
(/ (* (* (* (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))

series2.7s

Counts
4 → 12
Calls
4 calls:
378.0ms
(* (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (sin k))
326.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
1.2s
(/ (* (* (* (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)))
804.0ms
(* (* (* (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))

simplify1.0s

Counts
342 → 342
Iterations

Useful iterations: done (1.0s)

IterNodesCost
046315663
1165613992
done500012036

prune1.8s

Pruning

24 alts after pruning (24 fresh and 0 done)

Merged error: 7.6b

regimes1.2s

Accuracy

37% (4.4b remaining)

Error of 11.5b against oracle of 7.1b and baseline of 14.0b

bsearch521.0ms

Steps
ItersRangePoint
7
7.820237258369646e-132
8.244460005075117e-130
8.054118567065828e-130
7
-2.707655284371466e-204
-1.3903104710686896e-205
-3.903301028289217e-205

simplify41.0ms

Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
064175
182175
done82175

end0.0ms

sample11.0s

Algorithm
intervals
Results
3.6s2061×body1280valid
3.0s1717×body640valid
2.5s5913×body80valid
1.1s884×body320valid
253.0ms388×body160valid