Details

Time bar (total: 13.1s)

sample156.0ms

Algorithm
intervals
Results
50.0ms36×body1280valid
48.0ms24×body2560valid
17.0ms139×body80valid
14.0ms26×body640valid
9.0ms20×body320valid
4.0ms11×body160valid

simplify10.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0813
11113
21313
done1313

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.2b

localize24.0ms

Local error

Found 3 expressions with local error:

7.7b
(/ (tan (/ x (* y 2.0))) (sin (/ x (* y 2.0))))
26.3b
(sin (/ x (* y 2.0)))
27.0b
(tan (/ x (* y 2.0)))

rewrite43.0ms

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 expm1-log1p-u associate-/r* log1p-expm1-u associate-/l* add-log-exp
2×tan-quot
1×cbrt-undiv frac-2neg div-exp clear-num div-inv associate-/l/
Counts
3 → 49
Calls
3 calls:
24.0ms
(/ (tan (/ x (* y 2.0))) (sin (/ x (* y 2.0))))
10.0ms
(sin (/ x (* y 2.0)))
7.0ms
(tan (/ x (* y 2.0)))

series191.0ms

Counts
3 → 9
Calls
3 calls:
63.0ms
(/ (tan (/ x (* y 2.0))) (sin (/ x (* y 2.0))))
18.0ms
(sin (/ x (* y 2.0)))
109.0ms
(tan (/ x (* y 2.0)))

simplify2.2s

Counts
58 → 58
Iterations

Useful iterations: 3 (258.0ms)

IterNodesCost
083878
1147865
2330789
3814785
42543785
done5001785

prune304.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 24.3b

localize1.0ms

rewrite0.0ms

Algorithm
rewrite-expression-head
Rules
Counts
0 → 0

series0.0ms

Counts
0 → 0

simplify1.0ms

Counts
0 → 0
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
000
done00

prune54.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 24.3b

localize16.0ms

Local error

Found 4 expressions with local error:

7.7b
(/ (sin (/ x (* y 2.0))) (* (sin (/ x (* y 2.0))) (cos (/ x (* y 2.0)))))
26.3b
(sin (/ x (* y 2.0)))
26.3b
(sin (/ x (* y 2.0)))
26.6b
(cos (/ x (* y 2.0)))

rewrite72.0ms

Algorithm
rewrite-expression-head
Rules
9×add-exp-log add-cbrt-cube
6×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
4×pow1 expm1-log1p-u log1p-expm1-u add-log-exp
3×times-frac associate-/l*
2×cbrt-undiv div-exp
1×frac-2neg prod-exp clear-num associate-/r* associate-/r/ sin-cos-mult cbrt-unprod div-inv
Counts
4 → 51
Calls
4 calls:
38.0ms
(/ (sin (/ x (* y 2.0))) (* (sin (/ x (* y 2.0))) (cos (/ x (* y 2.0)))))
6.0ms
(sin (/ x (* y 2.0)))
16.0ms
(sin (/ x (* y 2.0)))
10.0ms
(cos (/ x (* y 2.0)))

series89.0ms

Counts
4 → 12
Calls
4 calls:
40.0ms
(/ (sin (/ x (* y 2.0))) (* (sin (/ x (* y 2.0))) (cos (/ x (* y 2.0)))))
15.0ms
(sin (/ x (* y 2.0)))
18.0ms
(sin (/ x (* y 2.0)))
16.0ms
(cos (/ x (* y 2.0)))

simplify5.8s

Counts
63 → 63
Iterations

Useful iterations: 3 (450.0ms)

IterNodesCost
077989
1152777
2416604
31226600
done5000600

prune247.0ms

Pruning

19 alts after pruning (18 fresh and 1 done)

Merged error: 24.3b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ 1 (cos (/ x (* y 2.0))))
0.1b
(* (sqrt (/ 1 (cos (/ x (* y 2.0))))) (sqrt (/ 1 (cos (/ x (* y 2.0))))))
26.6b
(cos (/ x (* y 2.0)))
26.6b
(cos (/ x (* y 2.0)))

rewrite63.0ms

Algorithm
rewrite-expression-head
Rules
88×add-sqr-sqrt
82×sqrt-prod
61×times-frac
54×*-un-lft-identity
44×add-cube-cbrt
28×pow1
24×sqrt-pow1
20×swap-sqr
16×associate-*r* associate-*l* unswap-sqr
10×add-exp-log
9×pow-flip pow-prod-up inv-pow
8×pow1/2 add-cbrt-cube
7×div-inv
5×pow-prod-down pow-sqr
4×expm1-log1p-u sqrt-div log1p-expm1-u add-log-exp
3×associate-/r* associate-/l*
2×div-exp
1×cbrt-undiv pow2 frac-times rec-exp frac-2neg pow-plus sqrt-unprod 1-exp associate-*r/ associate-*l/ prod-exp clear-num rem-square-sqrt *-commutative cbrt-unprod
Counts
4 → 157
Calls
4 calls:
6.0ms
(/ 1 (cos (/ x (* y 2.0))))
41.0ms
(* (sqrt (/ 1 (cos (/ x (* y 2.0))))) (sqrt (/ 1 (cos (/ x (* y 2.0))))))
5.0ms
(cos (/ x (* y 2.0)))
5.0ms
(cos (/ x (* y 2.0)))

series80.0ms

Counts
4 → 12
Calls
4 calls:
28.0ms
(/ 1 (cos (/ x (* y 2.0))))
25.0ms
(* (sqrt (/ 1 (cos (/ x (* y 2.0))))) (sqrt (/ 1 (cos (/ x (* y 2.0))))))
13.0ms
(cos (/ x (* y 2.0)))
13.0ms
(cos (/ x (* y 2.0)))

simplify3.3s

Counts
169 → 169
Iterations

Useful iterations: done (3.3s)

IterNodesCost
01713412
12612287
24832121
310572094
430952007
done50001998

prune442.0ms

Pruning

22 alts after pruning (21 fresh and 1 done)

Merged error: 24.3b

regimes12.0ms