Details

Time bar (total: 25.3s)

sample101.0ms

Algorithm
intervals
Results
35.0ms80×body1280valid
23.0ms70×body640valid
17.0ms225×body80valid
7.0ms31×body320valid
3.0ms22×body160valid

simplify171.0ms

Counts
1 → 1
Iterations
IterNodes
done113
7113
6101
591
479
370
248
125
012

prune25.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.4b

localize26.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (/ (cos th) (sqrt 2)) (* a1 a1))
0.3b
(* (/ (cos th) (sqrt 2)) (* a2 a2))
0.7b
(/ (cos th) (sqrt 2))
0.7b
(/ (cos th) (sqrt 2))

rewrite95.0ms

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×insert-posit16 div-inv add-log-exp
2×clear-num frac-2neg associate-*r* associate-*l/ *-commutative
Counts
4 → 172
Calls
4 calls:
32.0ms
(* (/ (cos th) (sqrt 2)) (* a1 a1))
36.0ms
(* (/ (cos th) (sqrt 2)) (* a2 a2))
10.0ms
(/ (cos th) (sqrt 2))
11.0ms
(/ (cos th) (sqrt 2))

series434.0ms

Counts
4 → 12
Calls
4 calls:
136.0ms
(* (/ (cos th) (sqrt 2)) (* a1 a1))
144.0ms
(* (/ (cos th) (sqrt 2)) (* a2 a2))
69.0ms
(/ (cos th) (sqrt 2))
85.0ms
(/ (cos th) (sqrt 2))

simplify1.6s

Counts
184 → 184
Iterations
IterNodes
done5007
21563
1533
0183

prune1.1s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (/ a1 (sqrt 2)) a1)
0.3b
(* (/ (cos th) (sqrt 2)) (* a2 a2))
0.4b
(/ a1 (sqrt 2))
0.7b
(/ (cos th) (sqrt 2))

rewrite137.0ms

Algorithm
rewrite-expression-head
Rules
76×times-frac
74×add-sqr-sqrt
61×*-un-lft-identity add-cube-cbrt
44×associate-*l* sqrt-prod
25×add-cbrt-cube add-exp-log
12×associate-/r*
11×pow1
8×prod-exp cbrt-unprod
6×associate-/l* unswap-sqr
5×cbrt-undiv div-exp
4×associate-*r* pow-prod-down insert-posit16 div-inv add-log-exp
2×clear-num frac-2neg associate-*l/ *-commutative
Counts
4 → 169
Calls
4 calls:
41.0ms
(* (/ a1 (sqrt 2)) a1)
69.0ms
(* (/ (cos th) (sqrt 2)) (* a2 a2))
6.0ms
(/ a1 (sqrt 2))
10.0ms
(/ (cos th) (sqrt 2))

series430.0ms

Counts
4 → 12
Calls
4 calls:
100.0ms
(* (/ a1 (sqrt 2)) a1)
141.0ms
(* (/ (cos th) (sqrt 2)) (* a2 a2))
99.0ms
(/ a1 (sqrt 2))
90.0ms
(/ (cos th) (sqrt 2))

simplify2.0s

Counts
181 → 181
Iterations
IterNodes
done5000
21722
1554
0211

prune900.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0b

localize37.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2))) (* a2 a2))
0.4b
(/ a1 (sqrt 2))
0.6b
(/ (cos th) (sqrt (sqrt 2)))
0.6b
(/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2)))

rewrite295.0ms

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×insert-posit16 add-log-exp
3×clear-num frac-2neg pow-prod-down
1×associate-*r* associate-*l/ *-commutative associate-/l/
Counts
4 → 748
Calls
4 calls:
163.0ms
(* (/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2))) (* a2 a2))
11.0ms
(/ a1 (sqrt 2))
12.0ms
(/ (cos th) (sqrt (sqrt 2)))
49.0ms
(/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2)))

series490.0ms

Counts
4 → 12
Calls
4 calls:
145.0ms
(* (/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2))) (* a2 a2))
75.0ms
(/ a1 (sqrt 2))
170.0ms
(/ (cos th) (sqrt (sqrt 2)))
100.0ms
(/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2)))

simplify2.9s

Counts
760 → 760
Iterations
IterNodes
done5004
24473
11665
0581

prune3.7s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

localize44.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (* a2 a2) (* (sqrt (sqrt (sqrt 2))) (sqrt (sqrt 2))))
0.2b
(* (/ a1 (sqrt 2)) a1)
0.2b
(* (/ (cos th) (sqrt (sqrt (sqrt 2)))) (/ (* a2 a2) (* (sqrt (sqrt (sqrt 2))) (sqrt (sqrt 2)))))
0.4b
(/ a1 (sqrt 2))

rewrite193.0ms

Algorithm
rewrite-expression-head
Rules
82×sqrt-prod
81×add-sqr-sqrt
80×times-frac
64×add-cbrt-cube add-exp-log
62×associate-*l*
59×*-un-lft-identity add-cube-cbrt
24×prod-exp cbrt-unprod
19×cbrt-undiv div-exp
8×pow1 associate-*r* unswap-sqr
7×associate-/r*
5×div-inv
4×insert-posit16 associate-/l* add-log-exp
2×clear-num frac-2neg pow-prod-down associate-*l/ *-commutative
1×frac-times associate-*r/
Counts
4 → 188
Calls
4 calls:
39.0ms
(/ (* a2 a2) (* (sqrt (sqrt (sqrt 2))) (sqrt (sqrt 2))))
39.0ms
(* (/ a1 (sqrt 2)) a1)
102.0ms
(* (/ (cos th) (sqrt (sqrt (sqrt 2)))) (/ (* a2 a2) (* (sqrt (sqrt (sqrt 2))) (sqrt (sqrt 2)))))
6.0ms
(/ a1 (sqrt 2))

series1.0s

Counts
4 → 12
Calls
4 calls:
594.0ms
(/ (* a2 a2) (* (sqrt (sqrt (sqrt 2))) (sqrt (sqrt 2))))
131.0ms
(* (/ a1 (sqrt 2)) a1)
206.0ms
(* (/ (cos th) (sqrt (sqrt (sqrt 2)))) (/ (* a2 a2) (* (sqrt (sqrt (sqrt 2))) (sqrt (sqrt 2)))))
82.0ms
(/ a1 (sqrt 2))

simplify1.8s

Counts
200 → 200
Iterations
IterNodes
done5005
23004
1731
0264

prune1.2s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

regimes649.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify4.0ms

Iterations
IterNodes
done23
123
018

end0.0ms

sample6.0s

Algorithm
intervals
Results
2.4s2500×body1280valid
1.5s7991×body80valid
1.2s2086×body640valid
355.0ms997×body320valid
166.0ms559×body160valid