Details

Time bar (total: 15.3s)

sample81.0ms

Algorithm
intervals
Results
26.0ms77×body1280valid
15.0ms66×body640valid
13.0ms250×body80valid
7.0ms39×body320valid
3.0ms26×body160valid

simplify68.0ms

Counts
1 → 1
Iterations

Useful iterations: 1 (2.0ms)

IterNodesCost
01219
12513
24513
36513
48413
510213
611513
done11513

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.5b

localize12.0ms

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))

rewrite45.0ms

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))

series344.0ms

Counts
4 → 12
Calls
4 calls:
109.0ms
(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
110.0ms
(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
62.0ms
(/ (cos th) (sqrt 2.0))
63.0ms
(/ (cos th) (sqrt 2.0))

simplify1.0s

Counts
180 → 180
Iterations

Useful iterations: done (1.0s)

IterNodesCost
01812118
14932012
215991832
done50001812

prune441.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (cos th) (/ (pow a1 2) (sqrt 2.0)))
0.3b
(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
0.3b
(/ (pow a1 2) (sqrt 2.0))
0.7b
(/ (cos th) (sqrt 2.0))

rewrite57.0ms

Algorithm
rewrite-expression-head
Rules
142×times-frac
121×add-sqr-sqrt
94×add-cube-cbrt *-un-lft-identity
77×sqrt-prod
53×associate-*r*
41×unpow-prod-down
33×add-exp-log
25×associate-*l* add-cbrt-cube
15×unpow2 sqr-pow
12×associate-/r* unswap-sqr
11×pow1 associate-/l*
10×prod-exp
9×div-exp
8×cbrt-unprod
5×cbrt-undiv
4×pow-prod-down div-inv add-log-exp
2×pow-to-exp frac-2neg pow-exp clear-num *-commutative
1×associate-*r/ associate-*l/
Counts
4 → 240
Calls
4 calls:
21.0ms
(* (cos th) (/ (pow a1 2) (sqrt 2.0)))
15.0ms
(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
5.0ms
(/ (pow a1 2) (sqrt 2.0))
4.0ms
(/ (cos th) (sqrt 2.0))

series333.0ms

Counts
4 → 12
Calls
4 calls:
106.0ms
(* (cos th) (/ (pow a1 2) (sqrt 2.0)))
107.0ms
(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
59.0ms
(/ (pow a1 2) (sqrt 2.0))
61.0ms
(/ (cos th) (sqrt 2.0))

simplify1.0s

Counts
252 → 252
Iterations

Useful iterations: done (1.0s)

IterNodesCost
03003180
16882857
223512526
done50002510

prune590.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (* a2 a2))
0.3b
(/ (pow a1 2) (sqrt 2.0))
0.7b
(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
0.7b
(/ (cos th) (sqrt (sqrt 2.0)))

rewrite194.0ms

Algorithm
rewrite-expression-head
Rules
1167×times-frac
1164×sqrt-prod
643×add-sqr-sqrt
609×add-cube-cbrt *-un-lft-identity
283×associate-*l*
42×associate-/l*
37×add-exp-log
34×add-cbrt-cube
24×associate-/r*
23×div-inv
21×unpow-prod-down
13×div-exp unswap-sqr
11×cbrt-undiv
9×pow1 prod-exp cbrt-unprod
7×unpow2 sqr-pow
4×add-log-exp
3×frac-2neg pow-prod-down clear-num
1×pow-to-exp associate-*r* associate-*l/ pow-exp *-commutative associate-/l/
Counts
4 → 781
Calls
4 calls:
98.0ms
(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (* a2 a2))
5.0ms
(/ (pow a1 2) (sqrt 2.0))
18.0ms
(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
5.0ms
(/ (cos th) (sqrt (sqrt 2.0)))

series339.0ms

Counts
4 → 12
Calls
4 calls:
111.0ms
(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (* a2 a2))
62.0ms
(/ (pow a1 2) (sqrt 2.0))
63.0ms
(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
101.0ms
(/ (cos th) (sqrt (sqrt 2.0)))

simplify1.9s

Counts
793 → 793
Iterations

Useful iterations: done (1.9s)

IterNodesCost
063315282
1164113518
2411312420
done500112418

prune1.8s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (sqrt (sqrt 2.0)) (cos th))
0.2b
(/ (* a2 a2) (/ (sqrt (sqrt 2.0)) (cos th)))
0.3b
(/ (pow a1 2) (sqrt 2.0))
0.3b
(* (/ (/ 1 (sqrt (sqrt (sqrt 2.0)))) (sqrt (sqrt (sqrt 2.0)))) (/ (* a2 a2) (/ (sqrt (sqrt 2.0)) (cos th))))

rewrite478.0ms

Algorithm
rewrite-expression-head
Rules
2136×sqrt-prod
1736×times-frac
1326×add-sqr-sqrt
657×*-un-lft-identity
577×add-cube-cbrt
484×associate-*l*
190×unswap-sqr
138×add-exp-log
89×add-cbrt-cube
70×div-exp
41×cbrt-undiv
40×associate-/r*
37×prod-exp
36×associate-*r*
25×div-inv
23×cbrt-unprod
21×unpow-prod-down
18×associate-/l*
7×unpow2 sqr-pow
6×pow1
5×rec-exp 1-exp
4×add-log-exp
3×frac-2neg clear-num
2×associate-/r/
1×frac-times pow-to-exp associate-*r/ pow-prod-down associate-*l/ pow-exp *-commutative
Counts
4 → 971
Calls
4 calls:
4.0ms
(/ (sqrt (sqrt 2.0)) (cos th))
10.0ms
(/ (* a2 a2) (/ (sqrt (sqrt 2.0)) (cos th)))
5.0ms
(/ (pow a1 2) (sqrt 2.0))
347.0ms
(* (/ (/ 1 (sqrt (sqrt (sqrt 2.0)))) (sqrt (sqrt (sqrt 2.0)))) (/ (* a2 a2) (/ (sqrt (sqrt 2.0)) (cos th))))

series393.0ms

Counts
4 → 12
Calls
4 calls:
68.0ms
(/ (sqrt (sqrt 2.0)) (cos th))
152.0ms
(/ (* a2 a2) (/ (sqrt (sqrt 2.0)) (cos th)))
63.0ms
(/ (pow a1 2) (sqrt 2.0))
109.0ms
(* (/ (/ 1 (sqrt (sqrt (sqrt 2.0)))) (sqrt (sqrt (sqrt 2.0)))) (/ (* a2 a2) (/ (sqrt (sqrt 2.0)) (cos th))))

simplify905.0ms

Counts
983 → 983
Iterations

Useful iterations: done (861.0ms)

IterNodesCost
070426719
1206124605
done500022352

prune2.5s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

regimes249.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01830
12130
done2130

end0.0ms

sample2.4s

Algorithm
intervals
Results
870.0ms2536×body1280valid
483.0ms2108×body640valid
435.0ms8024×body80valid
175.0ms1051×body320valid
68.0ms543×body160valid