Details

Time bar (total: 38.8s)

sample176.0ms

Algorithm
intervals
Results
54.0ms73×body1280valid
40.0ms49×body640valid
31.0ms254×body80valid
13.0ms34×body320valid
5.0ms20×body160valid

simplify180.0ms

Counts
1 → 1
Iterations
IterNodes
done134
7134
6122
5110
498
380
255
126
012

prune29.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.3b

localize51.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
0.3b
(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
0.7b
(/ (cos th) (sqrt 2.0))
0.7b
(/ (cos th) (sqrt 2.0))

rewrite112.0ms

Algorithm
rewrite-expression-head
Rules
76×times-frac
70×add-sqr-sqrt
60×*-un-lft-identity add-cube-cbrt
44×associate-*l* sqrt-prod
32×add-cbrt-cube add-exp-log
14×pow1
12×associate-/r* prod-exp cbrt-unprod
6×cbrt-undiv div-exp pow-prod-down associate-/l* unswap-sqr
4×expm1-log1p-u log1p-expm1-u div-inv add-log-exp
2×clear-num frac-2neg associate-*r* associate-*l/ *-commutative
Counts
4 → 176
Calls
4 calls:
50.0ms
(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
26.0ms
(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
8.0ms
(/ (cos th) (sqrt 2.0))
17.0ms
(/ (cos th) (sqrt 2.0))

series481.0ms

Counts
4 → 12
Calls
4 calls:
166.0ms
(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
152.0ms
(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
68.0ms
(/ (cos th) (sqrt 2.0))
94.0ms
(/ (cos th) (sqrt 2.0))

simplify1.8s

Counts
188 → 188
Iterations
IterNodes
done5001
21723
1533
0187

prune1.2s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize46.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (* a1 a1))
0.6b
(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
0.6b
(/ (cos th) (sqrt (sqrt 2.0)))
0.7b
(/ (cos th) (sqrt 2.0))

rewrite246.0ms

Algorithm
rewrite-expression-head
Rules
1149×sqrt-prod
1137×times-frac
626×add-sqr-sqrt
592×*-un-lft-identity add-cube-cbrt
283×associate-*l*
37×associate-/l*
34×add-cbrt-cube add-exp-log
24×associate-/r*
23×div-inv
13×unswap-sqr
11×cbrt-undiv div-exp
9×pow1 prod-exp cbrt-unprod
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×clear-num frac-2neg pow-prod-down
1×associate-*r* associate-*l/ *-commutative associate-/l/
Counts
4 → 752
Calls
4 calls:
139.0ms
(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (* a1 a1))
24.0ms
(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
9.0ms
(/ (cos th) (sqrt (sqrt 2.0)))
8.0ms
(/ (cos th) (sqrt 2.0))

series488.0ms

Counts
4 → 12
Calls
4 calls:
157.0ms
(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (* a1 a1))
73.0ms
(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
161.0ms
(/ (cos th) (sqrt (sqrt 2.0)))
97.0ms
(/ (cos th) (sqrt 2.0))

simplify2.3s

Counts
764 → 764
Iterations
IterNodes
done5000
11634
0568

prune4.2s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize62.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (cbrt (sqrt 2.0)))) (* a1 a1))
0.6b
(/ (cos th) (sqrt (sqrt 2.0)))
0.6b
(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (cbrt (sqrt 2.0))))
0.7b
(/ (cos th) (sqrt 2.0))

rewrite396.0ms

Algorithm
rewrite-expression-head
Rules
1507×sqrt-prod
1492×times-frac
814×add-sqr-sqrt
769×*-un-lft-identity add-cube-cbrt
386×cbrt-prod
376×associate-*l*
37×associate-/l*
34×add-cbrt-cube add-exp-log
29×div-inv
27×associate-/r*
17×unswap-sqr
11×cbrt-undiv div-exp
9×pow1 prod-exp cbrt-unprod
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×clear-num frac-2neg pow-prod-down
1×associate-*r* associate-*l/ *-commutative associate-/l/
Counts
4 → 945
Calls
4 calls:
215.0ms
(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (cbrt (sqrt 2.0)))) (* a1 a1))
17.0ms
(/ (cos th) (sqrt (sqrt 2.0)))
45.0ms
(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (cbrt (sqrt 2.0))))
8.0ms
(/ (cos th) (sqrt 2.0))

series1.3s

Counts
4 → 12
Calls
4 calls:
545.0ms
(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (cbrt (sqrt 2.0)))) (* a1 a1))
180.0ms
(/ (cos th) (sqrt (sqrt 2.0)))
458.0ms
(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (cbrt (sqrt 2.0))))
93.0ms
(/ (cos th) (sqrt 2.0))

simplify2.4s

Counts
957 → 957
Iterations
IterNodes
done5000
12019
0726

prune7.3s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize91.0ms

Local error

Found 4 expressions with local error:

0.6b
(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
0.6b
(/ (cos th) (sqrt (sqrt 2.0)))
0.6b
(/ (cos th) (sqrt (sqrt 2.0)))
0.6b
(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (cbrt (sqrt 2.0))))

rewrite189.0ms

Algorithm
rewrite-expression-head
Rules
1365×sqrt-prod
1326×times-frac
709×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
192×cbrt-prod
68×associate-/l*
39×associate-/r*
27×div-inv
18×add-cbrt-cube add-exp-log
8×cbrt-undiv div-exp
4×expm1-log1p-u pow1 clear-num frac-2neg log1p-expm1-u add-log-exp
2×associate-/l/
Counts
4 → 874
Calls
4 calls:
45.0ms
(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
9.0ms
(/ (cos th) (sqrt (sqrt 2.0)))
9.0ms
(/ (cos th) (sqrt (sqrt 2.0)))
43.0ms
(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (cbrt (sqrt 2.0))))

series837.0ms

Counts
4 → 12
Calls
4 calls:
77.0ms
(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
129.0ms
(/ (cos th) (sqrt (sqrt 2.0)))
128.0ms
(/ (cos th) (sqrt (sqrt 2.0)))
503.0ms
(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (cbrt (sqrt 2.0))))

simplify3.5s

Counts
886 → 886
Iterations
IterNodes
done5003
23733
11686
0755

prune5.2s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

regimes533.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 0.5b

bsearch0.0ms

simplify6.0ms

Iterations
IterNodes
done29
129
023

end0.0ms

sample5.9s

Algorithm
intervals
Results
1.6s2566×body1280valid
1.6s8116×body80valid
1.5s2044×body640valid
499.0ms1079×body320valid
108.0ms510×body160valid