Details

Time bar (total: 8.6s)

sample94.0ms

Algorithm
intervals
Results
31.0ms24×body2560valid
24.0ms42×body1280valid
12.0ms34×body640valid
9.0ms127×body80valid
4.0ms16×body320valid
2.0ms13×body160valid

simplify5.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0813
11113
21313
done1313

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.0b

localize10.0ms

Local error

Found 3 expressions with local error:

7.2b
(/ (tan (/ x (* y 2.0))) (sin (/ x (* y 2.0))))
28.6b
(sin (/ x (* y 2.0)))
29.9b
(tan (/ x (* y 2.0)))

rewrite8.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
times-frac
add-exp-log add-cbrt-cube
pow1 associate-/r* associate-/l* add-log-exp
tan-quot
cbrt-undiv frac-2neg div-exp clear-num div-inv associate-/l/
Counts
3 → 43
Calls
3 calls:
4.0ms
(/ (tan (/ x (* y 2.0))) (sin (/ x (* y 2.0))))
2.0ms
(sin (/ x (* y 2.0)))
1.0ms
(tan (/ x (* y 2.0)))

series90.0ms

Counts
3 → 9
Calls
3 calls:
37.0ms
(/ (tan (/ x (* y 2.0))) (sin (/ x (* y 2.0))))
8.0ms
(sin (/ x (* y 2.0)))
44.0ms
(tan (/ x (* y 2.0)))

simplify544.0ms

Counts
52 → 52
Iterations

Useful iterations: 3 (137.0ms)

IterNodesCost
077822
1139813
2339737
31188733
done5001733

prune174.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 27.3b

localize0.0ms

rewrite0.0ms

Algorithm
rewrite-expression-head
Rules
Counts
0 → 0

series0.0ms

Counts
0 → 0

simplify1.0ms

Counts
0 → 0
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
000
done00

prune24.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 27.3b

localize15.0ms

Local error

Found 4 expressions with local error:

7.2b
(/ (/ (sin (/ x (* y 2.0))) (cos (/ x (* y 2.0)))) (sin (/ x (* y 2.0))))
28.6b
(sin (/ x (* y 2.0)))
28.6b
(sin (/ x (* y 2.0)))
29.6b
(cos (/ x (* y 2.0)))

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
75×times-frac
46×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
13×associate-/l*
add-exp-log add-cbrt-cube
div-inv
pow1 add-log-exp
cbrt-undiv div-exp associate-/r*
frac-2neg clear-num associate-/l/
Counts
4 → 91
Calls
4 calls:
12.0ms
(/ (/ (sin (/ x (* y 2.0))) (cos (/ x (* y 2.0)))) (sin (/ x (* y 2.0))))
2.0ms
(sin (/ x (* y 2.0)))
2.0ms
(sin (/ x (* y 2.0)))
2.0ms
(cos (/ x (* y 2.0)))

series47.0ms

Counts
4 → 12
Calls
4 calls:
20.0ms
(/ (/ (sin (/ x (* y 2.0))) (cos (/ x (* y 2.0)))) (sin (/ x (* y 2.0))))
8.0ms
(sin (/ x (* y 2.0)))
8.0ms
(sin (/ x (* y 2.0)))
11.0ms
(cos (/ x (* y 2.0)))

simplify2.8s

Counts
103 → 103
Iterations

Useful iterations: 3 (1.8s)

IterNodesCost
01612815
13512764
210612348
340522211
done50002211

prune315.0ms

Pruning

19 alts after pruning (18 fresh and 1 done)

Merged error: 27.3b

localize9.0ms

Local error

Found 2 expressions with local error:

0.1b
(/ (/ 1 1) (cos (/ x (* y 2.0))))
29.6b
(cos (/ x (* y 2.0)))

rewrite12.0ms

Algorithm
rewrite-expression-head
Rules
75×times-frac
44×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
15×add-exp-log
13×associate-/l*
11×div-exp
add-cbrt-cube
1-exp div-inv
cbrt-undiv associate-/r*
pow1 rec-exp add-log-exp
frac-2neg clear-num associate-/l/
Counts
2 → 82
Calls
2 calls:
6.0ms
(/ (/ 1 1) (cos (/ x (* y 2.0))))
2.0ms
(cos (/ x (* y 2.0)))

series36.0ms

Counts
2 → 6
Calls
2 calls:
25.0ms
(/ (/ 1 1) (cos (/ x (* y 2.0))))
11.0ms
(cos (/ x (* y 2.0)))

simplify1.2s

Counts
88 → 88
Iterations

Useful iterations: 2 (102.0ms)

IterNodesCost
01501599
13271163
24421075
37491075
419581075
done50001075

prune99.0ms

Pruning

20 alts after pruning (18 fresh and 2 done)

Merged error: 27.2b

regimes363.0ms

Accuracy

31.6% (1.7b remaining)

Error of 27.9b against oracle of 26.2b and baseline of 28.6b

bsearch2.0ms

simplify1.0ms

Iterations

Useful iterations: 1 (1.0ms)

IterNodesCost
01627
11925
done1925

end0.0ms

sample2.8s

Algorithm
intervals
Results
861.0ms1403×body1280valid
851.0ms657×body2560valid
354.0ms990×body640valid
306.0ms4077×body80valid
138.0ms521×body320valid
67.0ms352×body160valid