Details

Time bar (total: 28.1s)

sample126.0ms

Algorithm
intervals
Results
51.0ms67×body1280valid
22.0ms44×body640valid
21.0ms198×body80valid
9.0ms26×body320valid
3.0ms15×body160valid

simplify2.3s

Counts
1 → 1
Iterations

Useful iterations: 4 (1.3s)

IterNodesCost
01925
14825
216025
388225
4495024
done500024

prune11.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 31.8b

localize26.0ms

Local error

Found 4 expressions with local error:

2.7b
(* (/ (pow t 3.0) (* l l)) (sin k))
4.1b
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
11.2b
(/ (/ 2.0 (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))) (fma 2 1.0 (pow (/ k t) 2.0)))
18.5b
(/ (pow t 3.0) (* l l))

rewrite227.0ms

Algorithm
rewrite-expression-head
Rules
119×add-exp-log
59×times-frac add-cbrt-cube
49×prod-exp
43×div-exp
39×add-sqr-sqrt
32×add-cube-cbrt *-un-lft-identity
21×cbrt-unprod
19×cbrt-undiv
17×associate-/l*
16×associate-*l/
12×associate-*l* associate-/r/
11×pow1
10×tan-quot unpow-prod-down
8×pow-to-exp pow-exp
7×div-inv
6×associate-*r*
5×frac-times associate-*r/
4×expm1-log1p-u pow-prod-down associate-/r* log1p-expm1-u add-log-exp unswap-sqr sqr-pow
2×frac-2neg clear-num *-commutative
1×associate-/l/
Counts
4 → 178
Calls
4 calls:
32.0ms
(* (/ (pow t 3.0) (* l l)) (sin k))
78.0ms
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
97.0ms
(/ (/ 2.0 (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))) (fma 2 1.0 (pow (/ k t) 2.0)))
11.0ms
(/ (pow t 3.0) (* l l))

series1.6s

Counts
4 → 12
Calls
4 calls:
254.0ms
(* (/ (pow t 3.0) (* l l)) (sin k))
331.0ms
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
813.0ms
(/ (/ 2.0 (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))) (fma 2 1.0 (pow (/ k t) 2.0)))
184.0ms
(/ (pow t 3.0) (* l l))

simplify1.3s

Counts
190 → 190
Iterations

Useful iterations: done (1.3s)

IterNodesCost
03714464
19304301
233093731
done50013730

prune694.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 19.3b

localize27.0ms

Local error

Found 4 expressions with local error:

4.1b
(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
4.9b
(* (/ (pow (cbrt t) 3.0) l) (sin k))
6.5b
(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
11.2b
(/ (/ 2.0 (* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))) (fma 2 1.0 (pow (/ k t) 2.0)))

rewrite383.0ms

Algorithm
rewrite-expression-head
Rules
333×add-exp-log
157×prod-exp
132×div-exp
103×times-frac
88×add-cbrt-cube
72×add-sqr-sqrt
59×add-cube-cbrt *-un-lft-identity
46×associate-*l/
36×cbrt-unprod
35×associate-*l*
33×pow-exp
29×cbrt-undiv
28×associate-/r/
25×frac-times
24×unpow-prod-down
22×pow-to-exp
20×tan-quot
19×associate-/l*
15×pow1 associate-*r/
10×cbrt-prod
8×sqr-pow
7×pow-prod-down div-inv
6×associate-*r* associate-/r*
5×unswap-sqr
4×expm1-log1p-u log1p-expm1-u add-log-exp
2×frac-2neg clear-num *-commutative
1×associate-/l/
Counts
4 → 266
Calls
4 calls:
143.0ms
(* (* (/ (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)
185.0ms
(/ (/ 2.0 (* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))) (fma 2 1.0 (pow (/ k t) 2.0)))

series1.5s

Counts
4 → 12
Calls
4 calls:
362.0ms
(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
240.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
195.0ms
(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
706.0ms
(/ (/ 2.0 (* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))) (fma 2 1.0 (pow (/ k t) 2.0)))

simplify2.0s

Counts
278 → 278
Iterations

Useful iterations: done (1.9s)

IterNodesCost
05638511
114168094
248247039
done50007038

prune1.2s

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 14.6b

localize30.0ms

Local error

Found 4 expressions with local error:

1.1b
(* (* (/ (pow (cbrt t) 3.0) (* (cbrt l) (cbrt l))) (/ (pow (cbrt t) 3.0) (cbrt l))) (* (/ (pow (cbrt t) 3.0) l) (sin k)))
4.1b
(* (* (* (/ (pow (cbrt t) 3.0) (* (cbrt l) (cbrt l))) (/ (pow (cbrt t) 3.0) (cbrt l))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
4.9b
(* (/ (pow (cbrt t) 3.0) l) (sin k))
11.2b
(/ (/ 2.0 (* (* (* (/ (pow (cbrt t) 3.0) (* (cbrt l) (cbrt l))) (/ (pow (cbrt t) 3.0) (cbrt l))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))) (fma 2 1.0 (pow (/ k t) 2.0)))

rewrite1.5s

Algorithm
rewrite-expression-head
Rules
3047×add-exp-log
1679×prod-exp
1234×div-exp
365×add-cbrt-cube
313×pow-to-exp pow-exp
223×cbrt-unprod
135×associate-*l/
132×cbrt-undiv
112×times-frac
90×frac-times
70×add-sqr-sqrt
60×associate-/r/
57×add-cube-cbrt *-un-lft-identity
40×tan-quot
38×associate-*r/
36×pow1 associate-*l*
22×pow-prod-down associate-/l*
20×unpow-prod-down
10×cbrt-prod
7×associate-*r*
6×div-inv
5×unswap-sqr
4×expm1-log1p-u log1p-expm1-u add-log-exp sqr-pow
3×associate-/r* *-commutative
1×frac-2neg clear-num associate-/l/
Counts
4 → 727
Calls
4 calls:
159.0ms
(* (* (/ (pow (cbrt t) 3.0) (* (cbrt l) (cbrt l))) (/ (pow (cbrt t) 3.0) (cbrt l))) (* (/ (pow (cbrt t) 3.0) l) (sin k)))
595.0ms
(* (* (* (/ (pow (cbrt t) 3.0) (* (cbrt l) (cbrt l))) (/ (pow (cbrt t) 3.0) (cbrt l))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
30.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
662.0ms
(/ (/ 2.0 (* (* (* (/ (pow (cbrt t) 3.0) (* (cbrt l) (cbrt l))) (/ (pow (cbrt t) 3.0) (cbrt l))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))) (fma 2 1.0 (pow (/ k t) 2.0)))

series1.6s

Counts
4 → 12
Calls
4 calls:
300.0ms
(* (* (/ (pow (cbrt t) 3.0) (* (cbrt l) (cbrt l))) (/ (pow (cbrt t) 3.0) (cbrt l))) (* (/ (pow (cbrt t) 3.0) l) (sin k)))
382.0ms
(* (* (* (/ (pow (cbrt t) 3.0) (* (cbrt l) (cbrt l))) (/ (pow (cbrt t) 3.0) (cbrt l))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
235.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
716.0ms
(/ (/ 2.0 (* (* (* (/ (pow (cbrt t) 3.0) (* (cbrt l) (cbrt l))) (/ (pow (cbrt t) 3.0) (cbrt l))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))) (fma 2 1.0 (pow (/ k t) 2.0)))

simplify906.0ms

Counts
739 → 739
Iterations

Useful iterations: done (873.0ms)

IterNodesCost
090632662
1232327328
done500023803

prune1.8s

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 13.3b

localize35.0ms

Local error

Found 4 expressions with local error:

0.8b
(pow (cbrt t) 3.0)
4.1b
(* (* (/ (pow (cbrt t) 3.0) (* (cbrt l) (cbrt l))) (* (/ (pow (cbrt t) 3.0) (cbrt l)) (* (/ (pow (cbrt t) 3.0) l) (sin k)))) (tan k))
4.9b
(* (/ (pow (cbrt t) 3.0) l) (sin k))
11.2b
(/ (/ 2.0 (* (* (/ (pow (cbrt t) 3.0) (* (cbrt l) (cbrt l))) (* (/ (pow (cbrt t) 3.0) (cbrt l)) (* (/ (pow (cbrt t) 3.0) l) (sin k)))) (tan k))) (fma 2 1.0 (pow (/ k t) 2.0)))

rewrite1.3s

Algorithm
rewrite-expression-head
Rules
2252×add-exp-log
1224×prod-exp
932×div-exp
274×add-cbrt-cube
212×pow-to-exp pow-exp
162×cbrt-unprod
112×times-frac
106×cbrt-undiv associate-*l/
85×frac-times
73×add-sqr-sqrt
60×add-cube-cbrt *-un-lft-identity associate-/r/
55×associate-*r/
40×tan-quot
35×associate-*l*
26×unpow-prod-down
22×associate-/l*
21×pow1
13×cbrt-prod
11×pow-prod-down
6×associate-*r* div-inv
5×unswap-sqr sqr-pow
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×pow-unpow associate-/r*
2×pow-pow *-commutative
1×frac-2neg pow1/3 clear-num associate-/l/
Counts
4 → 564
Calls
4 calls:
3.0ms
(pow (cbrt t) 3.0)
543.0ms
(* (* (/ (pow (cbrt t) 3.0) (* (cbrt l) (cbrt l))) (* (/ (pow (cbrt t) 3.0) (cbrt l)) (* (/ (pow (cbrt t) 3.0) l) (sin k)))) (tan k))
30.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
638.0ms
(/ (/ 2.0 (* (* (/ (pow (cbrt t) 3.0) (* (cbrt l) (cbrt l))) (* (/ (pow (cbrt t) 3.0) (cbrt l)) (* (/ (pow (cbrt t) 3.0) l) (sin k)))) (tan k))) (fma 2 1.0 (pow (/ k t) 2.0)))

series1.8s

Counts
4 → 12
Calls
4 calls:
294.0ms
(pow (cbrt t) 3.0)
378.0ms
(* (* (/ (pow (cbrt t) 3.0) (* (cbrt l) (cbrt l))) (* (/ (pow (cbrt t) 3.0) (cbrt l)) (* (/ (pow (cbrt t) 3.0) l) (sin k)))) (tan k))
242.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
918.0ms
(/ (/ 2.0 (* (* (/ (pow (cbrt t) 3.0) (* (cbrt l) (cbrt l))) (* (/ (pow (cbrt t) 3.0) (cbrt l)) (* (/ (pow (cbrt t) 3.0) l) (sin k)))) (tan k))) (fma 2 1.0 (pow (/ k t) 2.0)))

simplify913.0ms

Counts
576 → 576
Iterations

Useful iterations: done (887.0ms)

IterNodesCost
092025596
1234822998
done500120142

prune1.6s

Pruning

27 alts after pruning (27 fresh and 0 done)

Merged error: 8.9b

regimes714.0ms

Accuracy

28.9% (3.1b remaining)

Error of 14.4b against oracle of 11.3b and baseline of 15.6b

bsearch330.0ms

Steps
ItersRangePoint
6
1.6457497334062564e-143
1.3231587995388702e-142
1.0340901995183787e-142
10
-5.723225917453812e-115
-8.689195205265119e-134
-1.2569790059980338e-132

simplify6.0ms

Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
047146
160102
done60102

end0.0ms

sample4.0s

Algorithm
intervals
Results
1.6s2014×body1280valid
862.0ms1653×body640valid
680.0ms6072×body80valid
333.0ms881×body320valid
112.0ms466×body160valid