Details

Time bar (total: 15.5s)

sample85.0ms

Algorithm
intervals
Results
26.0ms84×body1280valid
17.0ms80×body640valid
17.0ms294×body80valid
5.0ms31×body320valid
2.0ms15×body160valid

simplify68.0ms

Counts
1 → 1
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
01219
12513
24513
36513
48413
510213
611513
done11513

prune7.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.5b

localize14.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (/ (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))

rewrite44.0ms

Algorithm
rewrite-expression-head
Rules
76×times-frac
70×add-sqr-sqrt
60×add-cube-cbrt *-un-lft-identity
44×associate-*l* sqrt-prod
32×add-exp-log add-cbrt-cube
14×pow1
12×prod-exp associate-/r* cbrt-unprod
6×cbrt-undiv div-exp pow-prod-down associate-/l* unswap-sqr
4×div-inv add-log-exp
2×frac-2neg associate-*r* associate-*l/ clear-num *-commutative
Counts
4 → 168
Calls
4 calls:
15.0ms
(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
15.0ms
(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
4.0ms
(/ (cos th) (sqrt 2.0))
4.0ms
(/ (cos th) (sqrt 2.0))

series359.0ms

Counts
4 → 12
Calls
4 calls:
114.0ms
(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
114.0ms
(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
63.0ms
(/ (cos th) (sqrt 2.0))
66.0ms
(/ (cos th) (sqrt 2.0))

simplify853.0ms

Counts
180 → 180
Iterations

Useful iterations: done (848.0ms)

IterNodesCost
01812118
14932028
215871836
done50011816

prune487.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (cos th) (/ (* a1 a1) (sqrt 2.0)))
0.3b
(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
0.3b
(/ (* a1 a1) (sqrt 2.0))
0.7b
(/ (cos th) (sqrt 2.0))

rewrite42.0ms

Algorithm
rewrite-expression-head
Rules
52×times-frac
51×add-sqr-sqrt
40×add-cube-cbrt *-un-lft-identity
32×add-exp-log sqrt-prod add-cbrt-cube
25×associate-*l*
12×associate-/r*
11×pow1 associate-*r* prod-exp cbrt-unprod
7×cbrt-undiv div-exp
6×unswap-sqr
4×pow-prod-down div-inv associate-/l* add-log-exp
2×frac-2neg clear-num *-commutative
1×associate-*r/ associate-*l/
Counts
4 → 143
Calls
4 calls:
11.0ms
(* (cos th) (/ (* a1 a1) (sqrt 2.0)))
17.0ms
(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
4.0ms
(/ (* a1 a1) (sqrt 2.0))
4.0ms
(/ (cos th) (sqrt 2.0))

series365.0ms

Counts
4 → 12
Calls
4 calls:
116.0ms
(* (cos th) (/ (* a1 a1) (sqrt 2.0)))
120.0ms
(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
63.0ms
(/ (* a1 a1) (sqrt 2.0))
66.0ms
(/ (cos th) (sqrt 2.0))

simplify858.0ms

Counts
155 → 155
Iterations

Useful iterations: done (854.0ms)

IterNodesCost
02021785
15111695
217841515
done50001493

prune408.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (* a2 a2))
0.3b
(/ (* a1 a1) (sqrt 2.0))
0.6b
(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
0.7b
(/ (cos th) (sqrt (sqrt 2.0)))

rewrite187.0ms

Algorithm
rewrite-expression-head
Rules
1143×sqrt-prod
1125×times-frac
615×add-sqr-sqrt
581×add-cube-cbrt *-un-lft-identity
283×associate-*l*
37×add-exp-log add-cbrt-cube
35×associate-/l*
24×associate-/r*
23×div-inv
13×unswap-sqr
12×cbrt-undiv div-exp
10×prod-exp cbrt-unprod
9×pow1
4×add-log-exp
3×frac-2neg pow-prod-down clear-num
1×associate-*r* associate-*l/ *-commutative associate-/l/
Counts
4 → 732
Calls
4 calls:
98.0ms
(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (* a2 a2))
4.0ms
(/ (* a1 a1) (sqrt 2.0))
17.0ms
(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
5.0ms
(/ (cos th) (sqrt (sqrt 2.0)))

series356.0ms

Counts
4 → 12
Calls
4 calls:
124.0ms
(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (* a2 a2))
66.0ms
(/ (* a1 a1) (sqrt 2.0))
61.0ms
(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
104.0ms
(/ (cos th) (sqrt (sqrt 2.0)))

simplify2.0s

Counts
744 → 744
Iterations

Useful iterations: done (2.0s)

IterNodesCost
057014537
1157813192
2420111982
done500011880

prune1.7s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (/ (cos th) (sqrt (sqrt 2.0))) (* a2 a2))
0.2b
(* (/ (/ 1 (sqrt (sqrt (sqrt 2.0)))) (sqrt (sqrt (sqrt 2.0)))) (* (/ (cos th) (sqrt (sqrt 2.0))) (* a2 a2)))
0.3b
(/ (* a1 a1) (sqrt 2.0))
0.7b
(/ (cos th) (sqrt (sqrt 2.0)))

rewrite286.0ms

Algorithm
rewrite-expression-head
Rules
1440×sqrt-prod
975×times-frac
517×add-sqr-sqrt
515×associate-*l*
510×add-cube-cbrt *-un-lft-identity
138×add-exp-log
92×add-cbrt-cube
62×prod-exp
45×div-exp
40×cbrt-unprod
26×cbrt-undiv
18×pow1
16×div-inv
15×associate-/r*
9×pow-prod-down
5×rec-exp 1-exp
4×associate-*l/ associate-/l* add-log-exp unswap-sqr
2×frac-2neg associate-*r* clear-num *-commutative
1×frac-times associate-*r/
Counts
4 → 672
Calls
4 calls:
22.0ms
(* (/ (cos th) (sqrt (sqrt 2.0))) (* a2 a2))
189.0ms
(* (/ (/ 1 (sqrt (sqrt (sqrt 2.0)))) (sqrt (sqrt (sqrt 2.0)))) (* (/ (cos th) (sqrt (sqrt 2.0))) (* a2 a2)))
4.0ms
(/ (* a1 a1) (sqrt 2.0))
5.0ms
(/ (cos th) (sqrt (sqrt 2.0)))

series481.0ms

Counts
4 → 12
Calls
4 calls:
180.0ms
(* (/ (cos th) (sqrt (sqrt 2.0))) (* a2 a2))
126.0ms
(* (/ (/ 1 (sqrt (sqrt (sqrt 2.0)))) (sqrt (sqrt (sqrt 2.0)))) (* (/ (cos th) (sqrt (sqrt 2.0))) (* a2 a2)))
67.0ms
(/ (* a1 a1) (sqrt 2.0))
107.0ms
(/ (cos th) (sqrt (sqrt 2.0)))

simplify2.0s

Counts
684 → 684
Iterations

Useful iterations: 2 (1.2s)

IterNodesCost
054715424
1167114106
2473611464
done500011464

prune2.4s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

regimes200.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01730
12130
done2130

end0.0ms

sample2.3s

Algorithm
intervals
Results
826.0ms2580×body1280valid
460.0ms2039×body640valid
409.0ms8132×body80valid
163.0ms1049×body320valid
53.0ms508×body160valid