Details

Time bar (total: 23.5s)

sample131.0ms

Algorithm
intervals
Results
43.0ms54×body1280valid
37.0ms65×body640valid
22.0ms207×body80valid
8.0ms22×body320valid
3.0ms12×body160valid

simplify1.7s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01925
14725
215325
375925
4383425
done500025

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.0b

localize20.0ms

Local error

Found 4 expressions with local error:

2.9b
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
3.4b
(* (/ (pow t 3.0) (* l l)) (sin k))
13.3b
(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
18.5b
(/ (pow t 3.0) (* l l))

rewrite364.0ms

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×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:
35.0ms
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
16.0ms
(* (/ (pow t 3.0) (* l l)) (sin k))
301.0ms
(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
5.0ms
(/ (pow t 3.0) (* l l))

series1.4s

Counts
4 → 12
Calls
4 calls:
323.0ms
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
248.0ms
(* (/ (pow t 3.0) (* l l)) (sin k))
625.0ms
(* (* (* (/ (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))

simplify1.4s

Counts
156 → 156
Iterations

Useful iterations: 2 (506.0ms)

IterNodesCost
02553209
17943070
237572565
done50012565

prune502.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 19.5b

localize26.0ms

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))
10.0b
(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
13.3b
(* (* (* (/ (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))

rewrite576.0ms

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×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:
79.0ms
(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
18.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
4.0ms
(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
460.0ms
(* (* (* (/ (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))

series1.5s

Counts
4 → 12
Calls
4 calls:
364.0ms
(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
243.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
202.0ms
(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
740.0ms
(* (* (* (/ (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))

simplify546.0ms

Counts
241 → 241
Iterations

Useful iterations: done (533.0ms)

IterNodesCost
04296958
113456583
done50006450

prune955.0ms

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 10.5b

localize34.0ms

Local error

Found 4 expressions with local error:

0.8b
(* (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) l)) (* (/ (pow (cbrt t) 3.0) l) (sin k)))
2.9b
(* (* (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) l)) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
3.8b
(* (/ (pow (cbrt t) 3.0) l) (sin k))
13.3b
(* (* (* (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) l)) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

rewrite853.0ms

Algorithm
rewrite-expression-head
Rules
1884×add-exp-log
1325×prod-exp
432×div-exp
334×pow-exp
199×pow-to-exp
151×add-cbrt-cube
96×cbrt-unprod
47×associate-*l/
40×add-sqr-sqrt
37×associate-*l*
35×frac-times
34×pow1 times-frac
33×associate-*r/
32×*-un-lft-identity
27×add-cube-cbrt
20×unpow-prod-down pow-prod-down
19×cbrt-undiv
16×tan-quot
12×associate-*r*
10×cbrt-prod
8×flip3-+ flip-+
5×unswap-sqr
4×*-commutative add-log-exp sqr-pow
3×distribute-lft-out
1×distribute-rgt-in distribute-lft-in div-inv
Counts
4 → 486
Calls
4 calls:
35.0ms
(* (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) l)) (* (/ (pow (cbrt t) 3.0) l) (sin k)))
124.0ms
(* (* (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) l)) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
19.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
619.0ms
(* (* (* (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) l)) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

series1.7s

Counts
4 → 12
Calls
4 calls:
305.0ms
(* (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) l)) (* (/ (pow (cbrt t) 3.0) l) (sin k)))
381.0ms
(* (* (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) l)) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
241.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
750.0ms
(* (* (* (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) l)) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

simplify607.0ms

Counts
498 → 498
Iterations

Useful iterations: done (586.0ms)

IterNodesCost
052621737
1180416089
done500015851

prune947.0ms

Pruning

25 alts after pruning (25 fresh and 0 done)

Merged error: 9.5b

localize35.0ms

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)) (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) l) (* (/ (pow (cbrt t) 3.0) l) (sin k)))) (tan k))
3.8b
(* (/ (pow (cbrt t) 3.0) l) (sin k))
13.3b
(* (* (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) l) (* (/ (pow (cbrt t) 3.0) l) (sin k)))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

rewrite1.3s

Algorithm
rewrite-expression-head
Rules
1350×add-exp-log
980×prod-exp
283×div-exp
226×pow-exp
134×pow-to-exp
95×add-cbrt-cube
61×cbrt-unprod
44×associate-*l/
43×add-sqr-sqrt
38×associate-*r/
36×associate-*l*
35×*-un-lft-identity
34×frac-times times-frac
30×add-cube-cbrt
26×unpow-prod-down
16×tan-quot
14×pow1
13×cbrt-prod
11×cbrt-undiv associate-*r*
8×flip3-+ flip-+
5×pow-prod-down 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 → 368
Calls
4 calls:
2.0ms
(pow (cbrt t) 3.0)
227.0ms
(* (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) l) (* (/ (pow (cbrt t) 3.0) l) (sin k)))) (tan k))
20.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
1.0s
(* (* (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) l) (* (/ (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:
311.0ms
(pow (cbrt t) 3.0)
372.0ms
(* (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) l) (* (/ (pow (cbrt t) 3.0) l) (sin k)))) (tan k))
235.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
931.0ms
(* (* (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) l) (* (/ (pow (cbrt t) 3.0) l) (sin k)))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

simplify619.0ms

Counts
380 → 380
Iterations

Useful iterations: done (604.0ms)

IterNodesCost
054115932
1179014266
done500111927

prune835.0ms

Pruning

27 alts after pruning (27 fresh and 0 done)

Merged error: 7.8b

regimes819.0ms

Accuracy

16.8% (7.8b remaining)

Error of 15.8b against oracle of 8.0b and baseline of 17.4b

bsearch644.0ms

Steps
ItersRangePoint
6
7.923196814715099e-78
3.341779155283458e-77
1.0752185866752936e-77
8
1.7066497594651376e-125
3.884581370880027e-122
1.3849555057061644e-123
10
-2.229417312865321e-227
-2.6593463927486826e-237
-6.948985049682785e-236
5
-1.2522339484682067e-113
-5.350787604302055e-114
-5.5457382772615714e-114

simplify10.0ms

Iterations

Useful iterations: 0 (3.0ms)

IterNodesCost
095261
1131261
done131261

end0.0ms

sample4.1s

Algorithm
intervals
Results
1.7s2109×body1280valid
903.0ms1664×body640valid
694.0ms6001×body80valid
315.0ms857×body320valid
111.0ms407×body160valid