Details

Time bar (total: 22.3s)

sample141.0ms

Algorithm
intervals
Results
57.0ms70×body1280valid
29.0ms55×body640valid
23.0ms195×body80valid
11.0ms29×body320valid
4.0ms15×body160valid

simplify1.4s

Counts
1 → 1
Iterations

Useful iterations: 4 (377.0ms)

IterNodesCost
01925
14725
215625
379125
4393424
done500124

prune11.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 36.9b

localize21.0ms

Local error

Found 4 expressions with local error:

2.7b
(* (/ (pow t 3.0) (* l l)) (sin k))
3.4b
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
16.5b
(/ (/ 2.0 (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))) (fma 2 1.0 (pow (/ k t) 2.0)))
17.2b
(/ (pow t 3.0) (* l l))

rewrite106.0ms

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:
15.0ms
(* (/ (pow t 3.0) (* l l)) (sin k))
33.0ms
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
43.0ms
(/ (/ 2.0 (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))) (fma 2 1.0 (pow (/ k t) 2.0)))
5.0ms
(/ (pow t 3.0) (* l l))

series1.4s

Counts
4 → 12
Calls
4 calls:
249.0ms
(* (/ (pow t 3.0) (* l l)) (sin k))
321.0ms
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
637.0ms
(/ (/ 2.0 (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))) (fma 2 1.0 (pow (/ k t) 2.0)))
180.0ms
(/ (pow t 3.0) (* l l))

simplify1.3s

Counts
190 → 190
Iterations

Useful iterations: 2 (483.0ms)

IterNodesCost
03714464
19894301
242223731
done50013731

prune692.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 24.6b

localize27.0ms

Local error

Found 4 expressions with local error:

2.6b
(* (/ (pow (cbrt t) 3.0) l) (sin k))
3.4b
(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
7.7b
(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
16.5b
(/ (/ 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)))

rewrite207.0ms

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:
19.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
76.0ms
(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
3.0ms
(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
92.0ms
(/ (/ 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:
238.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
362.0ms
(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
196.0ms
(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
696.0ms
(/ (/ 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)))

simplify556.0ms

Counts
278 → 278
Iterations

Useful iterations: done (545.0ms)

IterNodesCost
05638511
115818094
done50007950

prune1.2s

Pruning

23 alts after pruning (23 fresh and 0 done)

Merged error: 18.6b

localize34.0ms

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)))
2.6b
(* (/ (pow (cbrt t) 3.0) l) (sin k))
3.4b
(* (* (/ (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))
16.5b
(/ (/ 2.0 (* (* (/ (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))) (fma 2 1.0 (pow (/ k t) 2.0)))

rewrite376.0ms

Algorithm
rewrite-expression-head
Rules
1993×add-exp-log
947×div-exp
918×prod-exp
334×pow-exp
258×times-frac
199×pow-to-exp
164×add-cbrt-cube
135×associate-*l*
127×add-sqr-sqrt
114×add-cube-cbrt *-un-lft-identity
67×cbrt-unprod
60×cbrt-undiv
54×unpow-prod-down
49×associate-*l/
38×sqr-pow
29×associate-/r/
26×frac-times
20×tan-quot pow1
16×associate-*r/
14×associate-/l*
12×div-inv
10×cbrt-prod pow-prod-down
7×associate-*r*
5×unswap-sqr
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×associate-/r* *-commutative
1×frac-2neg clear-num associate-/l/
Counts
4 → 622
Calls
4 calls:
56.0ms
(* (/ (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)))
18.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
106.0ms
(* (* (/ (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))
129.0ms
(/ (/ 2.0 (* (* (/ (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))) (fma 2 1.0 (pow (/ k t) 2.0)))

series1.6s

Counts
4 → 12
Calls
4 calls:
287.0ms
(* (/ (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)))
236.0ms
(* (/ (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))
712.0ms
(/ (/ 2.0 (* (* (/ (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))) (fma 2 1.0 (pow (/ k t) 2.0)))

simplify928.0ms

Counts
634 → 634
Iterations

Useful iterations: done (899.0ms)

IterNodesCost
091427064
1296524810
done500124546

prune2.1s

Pruning

26 alts after pruning (26 fresh and 0 done)

Merged error: 15.9b

localize37.0ms

Local error

Found 4 expressions with local error:

9.3b
(/ (/ l (pow (* (cbrt t) (cbrt t)) (/ 3.0 2))) (sqrt (fma 2 1.0 (pow (/ k t) 2.0))))
10.0b
(sqrt (fma 2 1.0 (pow (/ k t) 2.0)))
10.0b
(sqrt (fma 2 1.0 (pow (/ k t) 2.0)))
13.8b
(/ (/ 2.0 (* (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))) (sqrt (fma 2 1.0 (pow (/ k t) 2.0))))

rewrite117.0ms

Algorithm
rewrite-expression-head
Rules
300×times-frac
151×add-exp-log
147×add-sqr-sqrt
145×add-cube-cbrt *-un-lft-identity
99×sqrt-prod
66×div-exp
63×prod-exp
36×add-cbrt-cube
29×associate-/l*
21×unpow-prod-down associate-*r/ associate-*l/ associate-/r/ sqr-pow
16×pow-exp div-inv
15×cbrt-undiv
14×tan-quot
12×associate-/r*
10×pow-to-exp
9×cbrt-unprod
7×frac-times
6×pow1
4×expm1-log1p-u log1p-expm1-u add-log-exp
2×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 clear-num associate-/l/
Counts
4 → 307
Calls
4 calls:
13.0ms
(/ (/ l (pow (* (cbrt t) (cbrt t)) (/ 3.0 2))) (sqrt (fma 2 1.0 (pow (/ k t) 2.0))))
1.0ms
(sqrt (fma 2 1.0 (pow (/ k t) 2.0)))
1.0ms
(sqrt (fma 2 1.0 (pow (/ k t) 2.0)))
86.0ms
(/ (/ 2.0 (* (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))) (sqrt (fma 2 1.0 (pow (/ k t) 2.0))))

series1.2s

Counts
4 → 12
Calls
4 calls:
334.0ms
(/ (/ l (pow (* (cbrt t) (cbrt t)) (/ 3.0 2))) (sqrt (fma 2 1.0 (pow (/ k t) 2.0))))
101.0ms
(sqrt (fma 2 1.0 (pow (/ k t) 2.0)))
103.0ms
(sqrt (fma 2 1.0 (pow (/ k t) 2.0)))
658.0ms
(/ (/ 2.0 (* (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))) (sqrt (fma 2 1.0 (pow (/ k t) 2.0))))

simplify570.0ms

Counts
319 → 319
Iterations

Useful iterations: done (550.0ms)

IterNodesCost
061612942
1156412036
done500011950

prune1.5s

Pruning

26 alts after pruning (26 fresh and 0 done)

Merged error: 13.5b

regimes740.0ms

Accuracy

16.8% (2.7b remaining)

Error of 13.9b against oracle of 11.2b and baseline of 14.4b

bsearch391.0ms

Steps
ItersRangePoint
10
1.1722386373035286e-21
5.968040026638966e-05
2.1673491063617143e-21
10
-1.0928018917701282e+131
-5.399713014669202e+118
-5.480277056394561e+118

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
063268
177268
done77268

end0.0ms

sample4.1s

Algorithm
intervals
Results
1.7s2072×body1280valid
985.0ms1801×body640valid
662.0ms5906×body80valid
319.0ms845×body320valid
102.0ms391×body160valid