Details

Time bar (total: 10.7s)

sample112.0ms

Algorithm
intervals
Results
36.0ms51×body1280valid
31.0ms22×body2560valid
16.0ms140×body80valid
10.0ms22×body640valid
5.0ms17×body320valid
1.0ms4×body160valid

simplify20.0ms

Counts
1 → 1

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.5b

localize15.0ms

Local error

Found 3 expressions with local error:

6.5b
(/ (tan (/ x (* y 2.0))) (sin (/ x (* y 2.0))))
26.6b
(sin (/ x (* y 2.0)))
26.8b
(tan (/ x (* y 2.0)))

rewrite60.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
9×times-frac
5×add-exp-log add-cbrt-cube
3×pow1 associate-/r* associate-/l* add-log-exp
2×tan-quot
1×cbrt-undiv frac-2neg div-exp clear-num div-inv associate-/l/
Counts
3 → 43
Calls
3 calls:
46.0ms
(/ (tan (/ x (* y 2.0))) (sin (/ x (* y 2.0))))
7.0ms
(sin (/ x (* y 2.0)))
5.0ms
(tan (/ x (* y 2.0)))

series144.0ms

Counts
3 → 9
Calls
3 calls:
72.0ms
(/ (tan (/ x (* y 2.0))) (sin (/ x (* y 2.0))))
14.0ms
(sin (/ x (* y 2.0)))
57.0ms
(tan (/ x (* y 2.0)))

simplify657.0ms

Counts
52 → 52

prune249.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 24.7b

localize0.0ms

rewrite0.0ms

Algorithm
rewrite-expression-head
Rules
Counts
0 → 0

series0.0ms

Counts
0 → 0

simplify16.0ms

Counts
0 → 0

prune49.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 24.7b

localize22.0ms

Local error

Found 4 expressions with local error:

0.4b
(pow (/ (tan (/ x (* y 2.0))) (sin (/ x (* y 2.0)))) 3)
6.5b
(/ (tan (/ x (* y 2.0))) (sin (/ x (* y 2.0))))
26.6b
(sin (/ x (* y 2.0)))
26.8b
(tan (/ x (* y 2.0)))

rewrite53.0ms

Algorithm
rewrite-expression-head
Rules
27×add-sqr-sqrt add-cube-cbrt *-un-lft-identity times-frac
13×unpow-prod-down cube-prod
9×add-exp-log add-cbrt-cube
5×pow1
4×add-log-exp
3×pow-unpow associate-/r* div-inv associate-/l*
2×tan-quot cbrt-undiv div-exp pow-exp rem-cube-cbrt
1×cube-div cube-mult pow-to-exp pow-pow frac-2neg unpow3 clear-num associate-/l/ sqr-pow
Counts
4 → 89
Calls
4 calls:
20.0ms
(pow (/ (tan (/ x (* y 2.0))) (sin (/ x (* y 2.0)))) 3)
17.0ms
(/ (tan (/ x (* y 2.0))) (sin (/ x (* y 2.0))))
7.0ms
(sin (/ x (* y 2.0)))
5.0ms
(tan (/ x (* y 2.0)))

series193.0ms

Counts
4 → 12
Calls
4 calls:
64.0ms
(pow (/ (tan (/ x (* y 2.0))) (sin (/ x (* y 2.0)))) 3)
61.0ms
(/ (tan (/ x (* y 2.0))) (sin (/ x (* y 2.0))))
13.0ms
(sin (/ x (* y 2.0)))
55.0ms
(tan (/ x (* y 2.0)))

simplify713.0ms

Counts
101 → 101

prune398.0ms

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 24.7b

localize25.0ms

Local error

Found 4 expressions with local error:

6.5b
(/ (/ (sin (/ x (* y 2.0))) (cos (/ x (* y 2.0)))) (sin (/ x (* y 2.0))))
26.5b
(cos (/ x (* y 2.0)))
26.6b
(sin (/ x (* y 2.0)))
26.6b
(sin (/ x (* y 2.0)))

rewrite83.0ms

Algorithm
rewrite-expression-head
Rules
75×times-frac
46×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
13×associate-/l*
9×add-exp-log add-cbrt-cube
5×div-inv
4×pow1 add-log-exp
3×cbrt-undiv div-exp associate-/r*
1×frac-2neg clear-num associate-/l/
Counts
4 → 91
Calls
4 calls:
55.0ms
(/ (/ (sin (/ x (* y 2.0))) (cos (/ x (* y 2.0)))) (sin (/ x (* y 2.0))))
7.0ms
(cos (/ x (* y 2.0)))
7.0ms
(sin (/ x (* y 2.0)))
7.0ms
(sin (/ x (* y 2.0)))

series76.0ms

Counts
4 → 12
Calls
4 calls:
31.0ms
(/ (/ (sin (/ x (* y 2.0))) (cos (/ x (* y 2.0)))) (sin (/ x (* y 2.0))))
18.0ms
(cos (/ x (* y 2.0)))
14.0ms
(sin (/ x (* y 2.0)))
14.0ms
(sin (/ x (* y 2.0)))

simplify554.0ms

Counts
103 → 103

prune461.0ms

Pruning

20 alts after pruning (19 fresh and 1 done)

Merged error: 24.7b

regimes416.0ms

Accuracy

0.1% (2.3b remaining)

Error of 28.8b against oracle of 26.5b and baseline of 28.8b

bsearch0.0ms

simplify648.0ms

end0.0ms

sample5.7s

Algorithm
intervals
Results
2.0s650×body2560valid
1.6s1441×body1280valid
734.0ms1028×body640valid
708.0ms4055×body80valid
277.0ms552×body320valid
89.0ms274×body160valid