Details

Time bar (total: 43.7s)

sample178.0ms

Algorithm
intervals
Results
71.0ms70×body1280valid
36.0ms52×body640valid
25.0ms182×body80valid
12.0ms27×body320valid
5.0ms16×body160valid

simplify3.5s

Counts
1 → 1
Iterations

Useful iterations: 4 (1.8s)

IterNodesCost
01925
14825
216025
388225
4495024
done500024

prune12.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 34.1b

localize39.0ms

Local error

Found 4 expressions with local error:

1.8b
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
2.9b
(* (/ (pow t 3.0) (* l l)) (sin k))
13.6b
(/ (/ 2.0 (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))) (fma 2 1.0 (pow (/ k t) 2.0)))
17.7b
(/ (pow t 3.0) (* l l))

rewrite424.0ms

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:
101.0ms
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
70.0ms
(* (/ (pow t 3.0) (* l l)) (sin k))
220.0ms
(/ (/ 2.0 (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))) (fma 2 1.0 (pow (/ k t) 2.0)))
25.0ms
(/ (pow t 3.0) (* l l))

series2.1s

Counts
4 → 12
Calls
4 calls:
466.0ms
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
393.0ms
(* (/ (pow t 3.0) (* l l)) (sin k))
934.0ms
(/ (/ 2.0 (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))) (fma 2 1.0 (pow (/ k t) 2.0)))
262.0ms
(/ (pow t 3.0) (* l l))

simplify2.2s

Counts
190 → 190
Iterations

Useful iterations: done (2.2s)

IterNodesCost
03714464
19304301
233093731
done50013730

prune987.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 20.5b

localize36.0ms

Local error

Found 4 expressions with local error:

1.8b
(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
4.5b
(* (/ (pow (cbrt t) 3.0) l) (sin k))
8.9b
(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
13.6b
(/ (/ 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)))

rewrite594.0ms

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:
179.0ms
(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
35.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
11.0ms
(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
332.0ms
(/ (/ 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)))

series2.3s

Counts
4 → 12
Calls
4 calls:
530.0ms
(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
339.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
294.0ms
(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
1.1s
(/ (/ 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)))

simplify3.2s

Counts
278 → 278
Iterations

Useful iterations: done (3.2s)

IterNodesCost
05638511
114168094
248247039
done50007038

prune1.9s

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 15.5b

localize62.0ms

Local error

Found 4 expressions with local error:

0.8b
(* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (cbrt l) (cbrt l))) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l))) (* (/ (pow (cbrt t) 3.0) l) (sin k)))
1.8b
(* (* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (cbrt l) (cbrt l))) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
4.5b
(* (/ (pow (cbrt t) 3.0) l) (sin k))
13.6b
(/ (/ 2.0 (* (* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (cbrt l) (cbrt l))) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))) (fma 2 1.0 (pow (/ k t) 2.0)))

rewrite2.3s

Algorithm
rewrite-expression-head
Rules
5268×add-exp-log
2968×prod-exp
2022×div-exp
709×pow-exp
424×pow-to-exp
365×add-cbrt-cube
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 → 982
Calls
4 calls:
213.0ms
(* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (cbrt l) (cbrt l))) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l))) (* (/ (pow (cbrt t) 3.0) l) (sin k)))
810.0ms
(* (* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (cbrt l) (cbrt l))) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
64.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
1.0s
(/ (/ 2.0 (* (* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (cbrt l) (cbrt l))) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))) (fma 2 1.0 (pow (/ k t) 2.0)))

series2.4s

Counts
4 → 12
Calls
4 calls:
439.0ms
(* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (cbrt l) (cbrt l))) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l))) (* (/ (pow (cbrt t) 3.0) l) (sin k)))
599.0ms
(* (* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (cbrt l) (cbrt l))) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
343.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
999.0ms
(/ (/ 2.0 (* (* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (cbrt l) (cbrt l))) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))) (fma 2 1.0 (pow (/ k t) 2.0)))

simplify1.7s

Counts
994 → 994
Iterations

Useful iterations: done (1.6s)

IterNodesCost
0114054094
1257240933
done500036773

prune3.5s

Pruning

28 alts after pruning (28 fresh and 0 done)

Merged error: 13.6b

localize48.0ms

Local error

Found 4 expressions with local error:

0.8b
(pow (cbrt t) 3.0)
1.8b
(* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (cbrt l) (cbrt l))) (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l)) (* (/ (pow (cbrt t) 3.0) l) (sin k)))) (tan k))
4.5b
(* (/ (pow (cbrt t) 3.0) l) (sin k))
13.6b
(/ (/ 2.0 (* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (cbrt l) (cbrt l))) (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l)) (* (/ (pow (cbrt t) 3.0) l) (sin k)))) (tan k))) (fma 2 1.0 (pow (/ k t) 2.0)))

rewrite2.1s

Algorithm
rewrite-expression-head
Rules
3872×add-exp-log
2154×prod-exp
1522×div-exp
480×pow-exp
286×pow-to-exp
274×add-cbrt-cube
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 → 738
Calls
4 calls:
7.0ms
(pow (cbrt t) 3.0)
848.0ms
(* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (cbrt l) (cbrt l))) (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l)) (* (/ (pow (cbrt t) 3.0) l) (sin k)))) (tan k))
39.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
1.0s
(/ (/ 2.0 (* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (cbrt l) (cbrt l))) (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l)) (* (/ (pow (cbrt t) 3.0) l) (sin k)))) (tan k))) (fma 2 1.0 (pow (/ k t) 2.0)))

series2.2s

Counts
4 → 12
Calls
4 calls:
424.0ms
(pow (cbrt t) 3.0)
560.0ms
(* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (cbrt l) (cbrt l))) (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l)) (* (/ (pow (cbrt t) 3.0) l) (sin k)))) (tan k))
306.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
918.0ms
(/ (/ 2.0 (* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (cbrt l) (cbrt l))) (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l)) (* (/ (pow (cbrt t) 3.0) l) (sin k)))) (tan k))) (fma 2 1.0 (pow (/ k t) 2.0)))

simplify1.4s

Counts
750 → 750
Iterations

Useful iterations: done (1.3s)

IterNodesCost
0115241056
1259736596
done500033090

prune2.5s

Pruning

28 alts after pruning (28 fresh and 0 done)

Merged error: 11.4b

regimes1.1s

Accuracy

12.9% (4.0b remaining)

Error of 15.9b against oracle of 11.9b and baseline of 16.5b

bsearch642.0ms

Steps
ItersRangePoint
9
3.8192959329364606e-283
4.2985835605462347e-277
4.254224555756203e-277
8
-1.1083326154331794e-145
-2.557633363288514e-148
-4.687929201103465e-146

simplify9.0ms

Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
057179
172179
done72179

end0.0ms

sample6.4s

Algorithm
intervals
Results
2.7s2098×body1280valid
1.5s1752×body640valid
1.0s5895×body80valid
463.0ms820×body320valid
166.0ms424×body160valid