Details

Time bar (total: 19.8s)

sample127.0ms

Algorithm
intervals
Results
37.0ms41×body1280valid
31.0ms17×body2560valid
19.0ms33×body640valid
17.0ms142×body80valid
8.0ms19×body320valid
1.0msbody160valid

simplify6.0ms

Counts
1 → 1
Iterations
IterNodes
done11
111
08

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.1b

localize55.0ms

Local error

Found 3 expressions with local error:

6.7b
(/ (tan (/ x (* y 2.0))) (sin (/ x (* y 2.0))))
26.3b
(tan (/ x (* y 2.0)))
26.4b
(sin (/ x (* y 2.0)))

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
times-frac
add-cbrt-cube add-exp-log
expm1-log1p-u pow1 associate-/r* log1p-expm1-u associate-/l* add-log-exp
tan-quot
cbrt-undiv clear-num frac-2neg div-exp div-inv associate-/l/
Counts
3 → 49
Calls
3 calls:
14.0ms
(/ (tan (/ x (* y 2.0))) (sin (/ x (* y 2.0))))
4.0ms
(tan (/ x (* y 2.0)))
6.0ms
(sin (/ x (* y 2.0)))

series168.0ms

Counts
3 → 9
Calls
3 calls:
79.0ms
(/ (tan (/ x (* y 2.0))) (sin (/ x (* y 2.0))))
71.0ms
(tan (/ x (* y 2.0)))
18.0ms
(sin (/ x (* y 2.0)))

simplify1.4s

Counts
58 → 58
Iterations
IterNodes
done5001
31547
2422
1152
083

prune459.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 24.1b

localize0.0ms

rewrite0.0ms

Algorithm
rewrite-expression-head
Rules
Counts
0 → 0

series0.0ms

Counts
0 → 0

simplify0.0ms

Counts
0 → 0
Iterations
IterNodes
done0
00

prune121.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 24.1b

localize36.0ms

Local error

Found 4 expressions with local error:

6.7b
(/ (/ (sin (/ x (* y 2.0))) (cos (/ x (* y 2.0)))) (sin (/ x (* y 2.0))))
26.0b
(cos (/ x (* y 2.0)))
26.4b
(sin (/ x (* y 2.0)))
26.4b
(sin (/ x (* y 2.0)))

rewrite85.0ms

Algorithm
rewrite-expression-head
Rules
75×times-frac
46×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
13×associate-/l*
add-cbrt-cube add-exp-log
div-inv
expm1-log1p-u pow1 log1p-expm1-u add-log-exp
cbrt-undiv associate-/r* div-exp
clear-num frac-2neg associate-/l/
Counts
4 → 99
Calls
4 calls:
56.0ms
(/ (/ (sin (/ x (* y 2.0))) (cos (/ x (* y 2.0)))) (sin (/ x (* y 2.0))))
8.0ms
(cos (/ x (* y 2.0)))
7.0ms
(sin (/ x (* y 2.0)))
7.0ms
(sin (/ x (* y 2.0)))

series116.0ms

Counts
4 → 12
Calls
4 calls:
48.0ms
(/ (/ (sin (/ x (* y 2.0))) (cos (/ x (* y 2.0)))) (sin (/ x (* y 2.0))))
27.0ms
(cos (/ x (* y 2.0)))
21.0ms
(sin (/ x (* y 2.0)))
20.0ms
(sin (/ x (* y 2.0)))

simplify4.0s

Counts
111 → 111
Iterations
IterNodes
done5011
34484
21199
1390
0167

prune752.0ms

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 24.1b

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ 1 (cos (/ (/ x y) 2.0)))
0.7b
(log1p (expm1 (/ 1 (cos (/ (/ x y) 2.0)))))
0.8b
(expm1 (/ 1 (cos (/ (/ x y) 2.0))))
26.0b
(cos (/ (/ x y) 2.0))

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
times-frac
add-exp-log
add-cbrt-cube
pow1 log1p-expm1-u
expm1-log1p-u add-log-exp
associate-/r* associate-/l*
div-exp
cbrt-undiv rec-exp log1p-udef expm1-log1p clear-num frac-2neg 1-exp log1p-expm1 div-inv pow-flip inv-pow expm1-udef
Counts
4 → 64
Calls
4 calls:
6.0ms
(/ 1 (cos (/ (/ x y) 2.0)))
0.0ms
(log1p (expm1 (/ 1 (cos (/ (/ x y) 2.0)))))
0.0ms
(expm1 (/ 1 (cos (/ (/ x y) 2.0))))
7.0ms
(cos (/ (/ x y) 2.0))

series283.0ms

Counts
4 → 12
Calls
4 calls:
45.0ms
(/ 1 (cos (/ (/ x y) 2.0)))
144.0ms
(log1p (expm1 (/ 1 (cos (/ (/ x y) 2.0)))))
68.0ms
(expm1 (/ 1 (cos (/ (/ x y) 2.0))))
24.0ms
(cos (/ (/ x y) 2.0))

simplify4.3s

Counts
76 → 76
Iterations
IterNodes
done5000
54354
41590
3671
2290
1158
091

prune386.0ms

Pruning

19 alts after pruning (18 fresh and 1 done)

Merged error: 24.0b

regimes821.0ms

Accuracy

0% (2.5b remaining)

Error of 28.2b against oracle of 25.8b and baseline of 28.2b

bsearch0.0ms

simplify5.0ms

Iterations
IterNodes
done16
116
013

end0.0ms

sample6.6s

Algorithm
intervals
Results
1.7s1349×body1280valid
1.6s652×body2560valid
962.0ms1014×body640valid
739.0ms552×body320valid
712.0ms4149×body80valid
538.0ms284×body160valid