Details

Time bar (total: 14.9s)

sample82.0ms

Algorithm
intervals
Results
25.0ms77×body1280valid
16.0ms250×body80valid
15.0ms66×body640valid
7.0ms39×body320valid
3.0ms26×body160valid

simplify125.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (6.0ms)

IterNodesCost
01219
12613
25212
37512
410212
512212
613912
714312
814512
done14512

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.5b

localize16.0ms

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×expm1-log1p-u log1p-expm1-u div-inv add-log-exp
2×frac-2neg associate-*r* associate-*l/ clear-num *-commutative
Counts
4 → 176
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))

series496.0ms

Counts
4 → 12
Calls
4 calls:
108.0ms
(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
110.0ms
(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
62.0ms
(/ (cos th) (sqrt 2.0))
215.0ms
(/ (cos th) (sqrt 2.0))

simplify905.0ms

Counts
188 → 188
Iterations

Useful iterations: done (900.0ms)

IterNodesCost
01872182
14982076
216091894
done50001874

prune481.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize14.0ms

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))

rewrite58.0ms

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×expm1-log1p-u pow-prod-down log1p-expm1-u div-inv add-log-exp
2×pow-to-exp frac-2neg pow-exp clear-num *-commutative
1×associate-*r/ associate-*l/
Counts
4 → 248
Calls
4 calls:
21.0ms
(* (cos th) (/ (pow a1 2) (sqrt 2.0)))
17.0ms
(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
5.0ms
(/ (pow a1 2) (sqrt 2.0))
4.0ms
(/ (cos th) (sqrt 2.0))

series339.0ms

Counts
4 → 12
Calls
4 calls:
107.0ms
(* (cos th) (/ (pow a1 2) (sqrt 2.0)))
110.0ms
(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
61.0ms
(/ (pow a1 2) (sqrt 2.0))
62.0ms
(/ (cos th) (sqrt 2.0))

simplify1.0s

Counts
260 → 260
Iterations

Useful iterations: done (1.0s)

IterNodesCost
03083246
16942923
223682637
done50002621

prune629.0ms

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)))

rewrite188.0ms

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×expm1-log1p-u log1p-expm1-u 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 → 789
Calls
4 calls:
95.0ms
(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (* a2 a2))
5.0ms
(/ (pow a1 2) (sqrt 2.0))
17.0ms
(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
5.0ms
(/ (cos th) (sqrt (sqrt 2.0)))

series336.0ms

Counts
4 → 12
Calls
4 calls:
116.0ms
(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (* a2 a2))
59.0ms
(/ (pow a1 2) (sqrt 2.0))
62.0ms
(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
99.0ms
(/ (cos th) (sqrt (sqrt 2.0)))

simplify2.0s

Counts
801 → 801
Iterations

Useful iterations: done (2.0s)

IterNodesCost
064115362
1165013578
2413712479
done500112475

prune1.8s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (* a2 a2))
0.4b
(/ a1 (sqrt 2.0))
0.7b
(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
0.7b
(/ (cos th) (sqrt (sqrt 2.0)))

rewrite185.0ms

Algorithm
rewrite-expression-head
Rules
1149×sqrt-prod
1137×times-frac
626×add-sqr-sqrt
592×add-cube-cbrt *-un-lft-identity
283×associate-*l*
37×associate-/l*
34×add-exp-log add-cbrt-cube
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×frac-2neg pow-prod-down clear-num
1×associate-*r* associate-*l/ *-commutative associate-/l/
Counts
4 → 752
Calls
4 calls:
96.0ms
(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (* a2 a2))
3.0ms
(/ a1 (sqrt 2.0))
17.0ms
(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
5.0ms
(/ (cos th) (sqrt (sqrt 2.0)))

series336.0ms

Counts
4 → 12
Calls
4 calls:
118.0ms
(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (* a2 a2))
52.0ms
(/ a1 (sqrt 2.0))
65.0ms
(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
100.0ms
(/ (cos th) (sqrt (sqrt 2.0)))

simplify1.5s

Counts
764 → 764
Iterations

Useful iterations: done (1.5s)

IterNodesCost
058614710
1157113016
2377112024
done500012020

prune1.6s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

regimes252.0ms

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
01935
12335
done2335

end0.0ms

sample2.3s

Algorithm
intervals
Results
839.0ms2536×body1280valid
461.0ms2108×body640valid
404.0ms8024×body80valid
167.0ms1051×body320valid
63.0ms543×body160valid