Details

Time bar (total: 29.8s)

sample193.0ms

Algorithm
intervals
Results
88.0ms94×body1280valid
36.0ms75×body640valid
28.0ms246×body80valid
10.0ms29×body320valid
4.0ms15×body160valid

simplify163.0ms

Counts
1 → 1
Iterations

Useful iterations: 1 (4.0ms)

IterNodesCost
012344
125304
248304
370304
479304
591304
6101304
7113304
done113304

prune19.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.5b

localize26.0ms

Local error

Found 2 expressions with local error:

0.4b
(* (/ (cos th) (sqrt 2.0)) (+ (* a1 a1) (* a2 a2)))
0.7b
(/ (cos th) (sqrt 2.0))

rewrite69.0ms

Algorithm
rewrite-expression-head
Rules
39×add-sqr-sqrt
38×times-frac
31×*-un-lft-identity add-cube-cbrt
22×associate-*l* sqrt-prod
9×add-cbrt-cube add-exp-log
6×associate-/r*
4×pow1
3×associate-*r* associate-/l* unswap-sqr
2×frac-times cbrt-undiv flip3-+ div-exp prod-exp associate-*r/ cbrt-unprod flip-+ div-inv add-log-exp
1×distribute-rgt-in clear-num frac-2neg distribute-lft-in pow-prod-down associate-*l/ *-commutative
Counts
2 → 87
Calls
2 calls:
54.0ms
(* (/ (cos th) (sqrt 2.0)) (+ (* a1 a1) (* a2 a2)))
9.0ms
(/ (cos th) (sqrt 2.0))

series447.0ms

Counts
2 → 6
Calls
2 calls:
340.0ms
(* (/ (cos th) (sqrt 2.0)) (+ (* a1 a1) (* a2 a2)))
107.0ms
(/ (cos th) (sqrt 2.0))

simplify2.6s

Counts
93 → 93
Iterations

Useful iterations: done (2.6s)

IterNodesCost
015335455
150332481
2200432160
done500131960

prune542.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize32.0ms

Local error

Found 2 expressions with local error:

0.1b
(* (cos th) (+ (* a1 a1) (* a2 a2)))
0.4b
(/ (* (cos th) (+ (* a1 a1) (* a2 a2))) (sqrt 2.0))

rewrite37.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
9×add-cbrt-cube add-exp-log
8×*-un-lft-identity add-cube-cbrt
6×associate-/r* times-frac sqrt-prod
4×pow1 associate-*r/
3×associate-*r* associate-*l*
2×cbrt-undiv flip3-+ div-exp prod-exp cbrt-unprod flip-+ add-log-exp associate-/l/
1×distribute-rgt-in clear-num frac-2neg distribute-lft-in pow-prod-down *-commutative div-inv associate-/l* unswap-sqr
Counts
2 → 51
Calls
2 calls:
19.0ms
(* (cos th) (+ (* a1 a1) (* a2 a2)))
16.0ms
(/ (* (cos th) (+ (* a1 a1) (* a2 a2))) (sqrt 2.0))

series921.0ms

Counts
2 → 6
Calls
2 calls:
182.0ms
(* (cos th) (+ (* a1 a1) (* a2 a2)))
739.0ms
(/ (* (cos th) (+ (* a1 a1) (* a2 a2))) (sqrt 2.0))

simplify2.0s

Counts
57 → 57
Iterations

Useful iterations: 2 (399.0ms)

IterNodesCost
011121140
131118108
2127117748
done500017748

prune373.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize47.0ms

Local error

Found 3 expressions with local error:

0.4b
(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (+ (* a1 a1) (* a2 a2)))
0.6b
(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
0.6b
(/ (cos th) (sqrt (sqrt 2.0)))

rewrite308.0ms

Algorithm
rewrite-expression-head
Rules
1137×sqrt-prod
1119×times-frac
624×add-sqr-sqrt
577×*-un-lft-identity add-cube-cbrt
283×associate-*l*
34×associate-/l*
22×div-inv
19×add-cbrt-cube add-exp-log
18×associate-/r*
13×unswap-sqr
7×cbrt-undiv div-exp
5×pow1
3×associate-*r* prod-exp cbrt-unprod add-log-exp
2×frac-times clear-num frac-2neg flip3-+ associate-*r/ flip-+
1×distribute-rgt-in distribute-lft-in pow-prod-down associate-*l/ *-commutative associate-/l/
Counts
3 → 706
Calls
3 calls:
151.0ms
(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (+ (* a1 a1) (* a2 a2)))
45.0ms
(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
19.0ms
(/ (cos th) (sqrt (sqrt 2.0)))

series529.0ms

Counts
3 → 9
Calls
3 calls:
249.0ms
(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (+ (* a1 a1) (* a2 a2)))
96.0ms
(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
183.0ms
(/ (cos th) (sqrt (sqrt 2.0)))

simplify2.4s

Counts
715 → 715
Iterations

Useful iterations: done (2.3s)

IterNodesCost
0548410969
11973379828
done5001370100

prune3.8s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize53.0ms

Local error

Found 3 expressions with local error:

0.3b
(* (/ (cos th) (sqrt (sqrt 2.0))) (+ (* a1 a1) (* a2 a2)))
0.3b
(* (/ (/ 1 (sqrt (sqrt (sqrt 2.0)))) (sqrt (sqrt (sqrt 2.0)))) (* (/ (cos th) (sqrt (sqrt 2.0))) (+ (* a1 a1) (* a2 a2))))
0.6b
(/ (cos th) (sqrt (sqrt 2.0)))

rewrite387.0ms

Algorithm
rewrite-expression-head
Rules
1434×sqrt-prod
969×times-frac
517×add-sqr-sqrt
515×associate-*l*
506×*-un-lft-identity add-cube-cbrt
70×add-exp-log
46×add-cbrt-cube
27×prod-exp
25×div-exp
17×cbrt-unprod
15×div-inv
14×cbrt-undiv
11×frac-times associate-*r/
10×pow1
9×associate-/r*
6×flip3-+ flip-+
5×distribute-rgt-in distribute-lft-in
4×associate-*r* pow-prod-down associate-*l/ unswap-sqr
3×rec-exp 1-exp associate-/l* add-log-exp
2×*-commutative
1×clear-num frac-2neg
Counts
3 → 643
Calls
3 calls:
37.0ms
(* (/ (cos th) (sqrt (sqrt 2.0))) (+ (* a1 a1) (* a2 a2)))
279.0ms
(* (/ (/ 1 (sqrt (sqrt (sqrt 2.0)))) (sqrt (sqrt (sqrt 2.0)))) (* (/ (cos th) (sqrt (sqrt 2.0))) (+ (* a1 a1) (* a2 a2))))
12.0ms
(/ (cos th) (sqrt (sqrt 2.0)))

series841.0ms

Counts
3 → 9
Calls
3 calls:
421.0ms
(* (/ (cos th) (sqrt (sqrt 2.0))) (+ (* a1 a1) (* a2 a2)))
282.0ms
(* (/ (/ 1 (sqrt (sqrt (sqrt 2.0)))) (sqrt (sqrt (sqrt 2.0)))) (* (/ (cos th) (sqrt (sqrt 2.0))) (+ (* a1 a1) (* a2 a2))))
138.0ms
(/ (cos th) (sqrt (sqrt 2.0)))

simplify3.0s

Counts
652 → 652
Iterations

Useful iterations: done (2.9s)

IterNodesCost
0532401298
11780367097
done5000355529

prune4.4s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

regimes605.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify6.0ms

Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
015464
118464
done18464

end0.0ms

sample5.9s

Algorithm
intervals
Results
2.3s2426×body1280valid
1.5s7980×body80valid
1.0s2127×body640valid
408.0ms1048×body320valid
110.0ms555×body160valid